메뉴 건너뛰기




Volumn 73, Issue 2, 2011, Pages 123-214

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

Author keywords

Bayesian inference; Geometry in statistics; Hamiltonian Monte Carlo methods; Langevin diffusion; Markov chain Monte Carlo methods; Riemann manifolds

Indexed keywords


EID: 79952295497     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2010.00765.x     Document Type: Article
Times cited : (1497)

References (229)
  • 1
    • 0003530945 scopus 로고    scopus 로고
    • Methods of Information Geometry
    • Oxford: Oxford University Press.
    • Amari, S. and Nagaoka, H. (2000) Methods of Information Geometry. Oxford: Oxford University Press.
    • (2000)
    • Amari, S.1    Nagaoka, H.2
  • 2
    • 77953523599 scopus 로고    scopus 로고
    • Particle Markov chain Monte Carlo methods (with discussion)
    • Andrieu, C., Doucet, A. and Holenstein, R. (2010) Particle Markov chain Monte Carlo methods (with discussion). J. R. Statist. Soc. B, 72, 269-342.
    • (2010) J. R. Statist. Soc. B , vol.72 , pp. 269-342
    • Andrieu, C.1    Doucet, A.2    Holenstein, R.3
  • 3
    • 57849088168 scopus 로고    scopus 로고
    • A tutorial on adaptive MCMC
    • Andrieu, C. and Thoms, J. (2008) A tutorial on adaptive MCMC. Statist. Comput., 18, 343-373.
    • (2008) Statist. Comput. , vol.18 , pp. 343-373
    • Andrieu, C.1    Thoms, J.2
  • 4
    • 0002303010 scopus 로고
    • The role of differential geometry in statistical theory
    • Barndorff-Nielsen, O. E., Cox, D. R. and Reid, N. (1986) The role of differential geometry in statistical theory. Int. Statist. Rev., 54, 83-96.
    • (1986) Int. Statist. Rev. , vol.54 , pp. 83-96
    • Barndorff-Nielsen, O.E.1    Cox, D.R.2    Reid, N.3
  • 7
    • 69449098014 scopus 로고    scopus 로고
    • Estimating Bayes factors via thermodynamic integration and population MCMC
    • Calderhead, B. and Girolami, M. (2009) Estimating Bayes factors via thermodynamic integration and population MCMC. Computnl Statist. Data Anal., 53, 4028-4045.
    • (2009) Computnl Statist. Data Anal. , vol.53 , pp. 4028-4045
    • Calderhead, B.1    Girolami, M.2
  • 8
    • 78049443039 scopus 로고    scopus 로고
    • Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes
    • Calderhead, B., Girolami, M. and Lawrence, N. D. (2009) Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes. Adv. Neur. Inform. Process., 21, 217-224.
    • (2009) Adv. Neur. Inform. Process. , vol.21 , pp. 217-224
    • Calderhead, B.1    Girolami, M.2    Lawrence, N.D.3
  • 9
    • 34447319494 scopus 로고    scopus 로고
    • Geometric Mechanics on Riemannian Manifolds
    • Basel: Birkhäuser.
    • Calin, O. and Chang, D. C. (2004) Geometric Mechanics on Riemannian Manifolds. Basel: Birkhäuser.
    • (2004)
    • Calin, O.1    Chang, D.C.2
  • 10
    • 16244387937 scopus 로고    scopus 로고
    • Scaling limits for the transient phase of local Metropolis-Hastings algorithms
    • Christensen, O. F., Roberts, G. O. and Rosenthal, J. S. (2005) Scaling limits for the transient phase of local Metropolis-Hastings algorithms. J. R. Statist. Soc. B, 67, 253-268.
    • (2005) J. R. Statist. Soc. B , vol.67 , pp. 253-268
    • Christensen, O.F.1    Roberts, G.O.2    Rosenthal, J.S.3
  • 11
    • 0003585463 scopus 로고
    • Lectures from Markov Processes to Brownian Motion
    • New York: Springer.
    • Chung, K. L. (1982) Lectures from Markov Processes to Brownian Motion. New York: Springer.
    • (1982)
    • Chung, K.L.1
  • 12
    • 21344483516 scopus 로고
    • Preferred point geometry and statistical manifolds
    • Critchley, F., Marriott, P. K. and Salmon, M. (1993) Preferred point geometry and statistical manifolds. Ann. Statist., 21, 1197-1224.
    • (1993) Ann. Statist. , vol.21 , pp. 1197-1224
    • Critchley, F.1    Marriott, P.K.2    Salmon, M.3
  • 13
    • 0000399239 scopus 로고
    • Discussion on 'Defining the curvature of a statistical problem (with applications to second-order efficiency' (by B. Efron)
    • Dawid, A. P. (1975) Discussion on 'Defining the curvature of a statistical problem (with applications to second-order efficiency' (by B. Efron). Ann. Statist., 3, 1231-1234.
    • (1975) Ann. Statist. , vol.3 , pp. 1231-1234
    • Dawid, A.P.1
  • 15
    • 0000551847 scopus 로고
    • Defining the curvature of a statistical problem (with applications to second-order efficiency)
    • Efron, B. (1975) Defining the curvature of a statistical problem (with applications to second-order efficiency). Ann. Statist., 3, 1189-1242.
    • (1975) Ann. Statist. , vol.3 , pp. 1189-1242
    • Efron, B.1
  • 16
    • 0018115641 scopus 로고
    • Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information
    • Efron, B. and Hinkley, D. V. (1978) Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika, 65, 457-487.
    • (1978) Biometrika , vol.65 , pp. 457-487
    • Efron, B.1    Hinkley, D.V.2
  • 17
    • 77953081438 scopus 로고
    • Extending Fisher's measure of information
    • Ferreira, P. E. (1981) Extending Fisher's measure of information. Biometrika, 68, 695-698.
    • (1981) Biometrika , vol.68 , pp. 695-698
    • Ferreira, P.E.1
  • 18
    • 0042042167 scopus 로고    scopus 로고
    • Sampling from the posterior distribution in generalized linear mixed models
    • Gamerman, D. (1997) Sampling from the posterior distribution in generalized linear mixed models. Statist. Comput., 7, 57-68.
    • (1997) Statist. Comput. , vol.7 , pp. 57-68
    • Gamerman, D.1
  • 19
    • 0004012196 scopus 로고    scopus 로고
    • Bayesian Data Analysis
    • New York: Chapman and Hall.
    • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004) Bayesian Data Analysis. New York: Chapman and Hall.
    • (2004)
    • Gelman, A.1    Carlin, J.B.2    Stern, H.S.3    Rubin, D.B.4
  • 20
    • 84972511893 scopus 로고
    • Practical Markov Chain Monte Carlo
    • Geyer, C. J. (1992) Practical Markov Chain Monte Carlo. Statist. Sci., 7, 473-483.
    • (1992) Statist. Sci. , vol.7 , pp. 473-483
    • Geyer, C.J.1
  • 21
    • 0030980644 scopus 로고    scopus 로고
    • Large hierarchical Bayesian analysis of multivariate survival data
    • Gustafson, P. (1997) Large hierarchical Bayesian analysis of multivariate survival data. Biometrics, 53, 230-242.
    • (1997) Biometrics , vol.53 , pp. 230-242
    • Gustafson, P.1
  • 22
    • 0003835647 scopus 로고    scopus 로고
    • Geometric Numerical Integration, Structure Preserving Algorithms for Ordinary Differential Equations
    • 2nd edn. Berlin: Springer.
    • Hairer, E., Lubich, C. and Wanner, G. (2006) Geometric Numerical Integration, Structure Preserving Algorithms for Ordinary Differential Equations, 2nd edn. Berlin: Springer.
    • (2006)
    • Hairer, E.1    Lubich, C.2    Wanner, G.3
  • 23
    • 34247598888 scopus 로고    scopus 로고
    • Efficient cosmological parameter estimation with Hamiltonian Monte Carlo technique
    • 083525-1-11.
    • Hajian, A. (2007) Efficient cosmological parameter estimation with Hamiltonian Monte Carlo technique. Phys. Rev. D, 75, 083525-1-11.
    • (2007) Phys. Rev. D , vol.75
    • Hajian, A.1
  • 24
    • 0034847223 scopus 로고    scopus 로고
    • Markov Chain Monte Carlo posterior sampling with the Hamiltonian method
    • Hanson, K. M. (2001) Markov Chain Monte Carlo posterior sampling with the Hamiltonian method. Proc. SPIE, 4322, 456-467.
    • (2001) Proc. SPIE , vol.4322 , pp. 456-467
    • Hanson, K.M.1
  • 26
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
    • (1970) Biometrika , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 27
    • 84867151416 scopus 로고    scopus 로고
    • Bayesian auxiliary variable models for binary and multinomial regression
    • Holmes, C. C. and Held, L. (2005) Bayesian auxiliary variable models for binary and multinomial regression. Baysn Anal., 1, 145-168.
    • (2005) Baysn Anal. , vol.1 , pp. 145-168
    • Holmes, C.C.1    Held, L.2
  • 28
    • 79551487646 scopus 로고    scopus 로고
    • Approximate Riemannian conjugate gradient learning for fixed-form variational Bayes
    • Honkela, A., Raiko, T., Kuusela, M., Tornio, M. and Karhunen, J. (2010) Approximate Riemannian conjugate gradient learning for fixed-form variational Bayes. J. Mach. Learn. Res., 11, 3235-3268.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 3235-3268
    • Honkela, A.1    Raiko, T.2    Kuusela, M.3    Tornio, M.4    Karhunen, J.5
  • 29
    • 0032787276 scopus 로고    scopus 로고
    • An empirical evaluation of Bayesian sampling with hybrid Monte Carlo for training neural network classifiers
    • Husmeier, D., Penny, W. and Roberts, S. J. (1999) An empirical evaluation of Bayesian sampling with hybrid Monte Carlo for training neural network classifiers. Neur. Netwrks, 12, 677-705.
    • (1999) Neur. Netwrks , vol.12 , pp. 677-705
    • Husmeier, D.1    Penny, W.2    Roberts, S.J.3
  • 30
    • 8644257632 scopus 로고    scopus 로고
    • Applications of hybrid Monte Carlo to Bayesian generalised linear models: quasicomplete separation and neural networks
    • Ishwaran, H. (1999) Applications of hybrid Monte Carlo to Bayesian generalised linear models: quasicomplete separation and neural networks. J. Computnl Graph. Statist., 8, 779-799.
    • (1999) J. Computnl Graph. Statist. , vol.8 , pp. 779-799
    • Ishwaran, H.1
  • 31
    • 0003784110 scopus 로고    scopus 로고
    • Ordinal Data Modeling
    • New York: Springer.
    • Johnson, V. E., Krantz, S. G. and Albert, J. H. (1999) Ordinal Data Modeling. New York: Springer.
    • (1999)
    • Johnson, V.E.1    Krantz, S.G.2    Albert, J.H.3
  • 32
    • 84972503977 scopus 로고
    • The geometry of asymptotic inference
    • Kass, R. E. (1989) The geometry of asymptotic inference. Statist. Sci., 4, 188-234.
    • (1989) Statist. Sci. , vol.4 , pp. 188-234
    • Kass, R.E.1
  • 33
    • 0001306694 scopus 로고
    • Time reversible diffusions
    • Kent, J. (1978) Time reversible diffusions. Adv. Appl. Probab., 10, 819-835.
    • (1978) Adv. Appl. Probab. , vol.10 , pp. 819-835
    • Kent, J.1
  • 34
    • 0001251517 scopus 로고    scopus 로고
    • Stochastic volatility: likelihood inference and comparison with ARCH models
    • Kim, S., Shephard, N. and Chib, S. (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Rev. Econ. Stud., 65, 361-393.
    • (1998) Rev. Econ. Stud. , vol.65 , pp. 361-393
    • Kim, S.1    Shephard, N.2    Chib, S.3
  • 35
    • 58649107876 scopus 로고    scopus 로고
    • Bayesian density estimation from grouped continuous data
    • Lambert, P. and Eilers, P. H. C. (2009) Bayesian density estimation from grouped continuous data. Computnl Statist. Data Anal., 53, 1388-1399.
    • (2009) Computnl Statist. Data Anal. , vol.53 , pp. 1388-1399
    • Lambert, P.1    Eilers, P.H.C.2
  • 36
    • 0000772138 scopus 로고
    • Differential Geometry in Statistical Inference
    • In - Hayward: Institute of Mathematical Statistics.
    • Lauritzen, S. L. (1987) Statistical manifolds. In Differential Geometry in Statistical Inference, pp. 165-216. Hayward: Institute of Mathematical Statistics.
    • (1987) Statistical manifolds , pp. 165-216
    • Lauritzen, S.L.1
  • 37
    • 28844494719 scopus 로고    scopus 로고
    • Simulating Hamiltonian Dynamics
    • Cambridge: Cambridge University Press.
    • Leimkuhler, B. and Reich, S. (2004) Simulating Hamiltonian Dynamics. Cambridge: Cambridge University Press.
    • (2004)
    • Leimkuhler, B.1    Reich, S.2
  • 38
    • 0004182828 scopus 로고    scopus 로고
    • Monte Carlo Strategies in Scientific Computing
    • New York: Springer.
    • Liu, J. S. (2001) Monte Carlo Strategies in Scientific Computing. New York: Springer.
    • (2001)
    • Liu, J.S.1
  • 39
    • 0037340625 scopus 로고    scopus 로고
    • Are Hamiltonian flows geodesic flows?
    • McCord, C., Meyer, K. R. and Offin, D. (2002) Are Hamiltonian flows geodesic flows? Trans. Am. Math. Soc., 355, 1237-1250.
    • (2002) Trans. Am. Math. Soc. , vol.355 , pp. 1237-1250
    • Mccord, C.1    Meyer, K.R.2    Offin, D.3
  • 41
    • 0003612091 scopus 로고
    • Machine Learning, Neural and Statistical Classification
    • Englewood Cliffs: Prentice Hall.
    • Michie, D., Spiegelhalter, D. J. and Taylor, C. C. (1994) Machine Learning, Neural and Statistical Classification. Englewood Cliffs: Prentice Hall.
    • (1994)
    • Michie, D.1    Spiegelhalter, D.J.2    Taylor, C.C.3
  • 42
    • 0004277797 scopus 로고
    • Differential Geometry and Statistics
    • New York: Chapman and Hall.
    • Murray, M. K. and Rice, J. W. (1993) Differential Geometry and Statistics. New York: Chapman and Hall.
    • (1993)
    • Murray, M.K.1    Rice, J.W.2
  • 44
    • 0037591475 scopus 로고
    • Bayesian learning via stochastic dynamics
    • Neal, R. M. (1993b) Bayesian learning via stochastic dynamics. Adv. Neur. Inform. Process. Syst., 5, 475-482.
    • (1993) Adv. Neur. Inform. Process. Syst. , vol.5 , pp. 475-482
    • Neal, R.M.1
  • 46
    • 79251576558 scopus 로고    scopus 로고
    • Handbook of Markov Chain Monte Carlo
    • (eds S. Brooks, A. Gelman, G. Jones and X.-L. Meng). Boca Raton: Chapman and Hall-CRC Press.
    • Neal, R. M. (2010) MCMC using Hamiltonian dynamics. In Handbook of Markov Chain Monte Carlo (eds S. Brooks, A. Gelman, G. Jones and X.-L. Meng). Boca Raton: Chapman and Hall-CRC Press.
    • (2010) MCMC using Hamiltonian dynamics
    • Neal, R.M.1
  • 48
    • 35648981518 scopus 로고    scopus 로고
    • Parameter estimation for differential equations: a generalized smoothing approach
    • (with discussion).
    • Ramsay, J. O., Hooker, G., Campbell, D. and Cao, J. (2007) Parameter estimation for differential equations: a generalized smoothing approach (with discussion). J. R. Statist. Soc. B, 69, 741-796.
    • (2007) J. R. Statist. Soc. B , vol.69 , pp. 741-796
    • Ramsay, J.O.1    Hooker, G.2    Campbell, D.3    Cao, J.4
  • 49
    • 0001915002 scopus 로고
    • Information and accuracy attainable in the estimation of statistical parameters
    • Rao, C. R. (1945) Information and accuracy attainable in the estimation of statistical parameters. Bull. Calc. Math. Soc., 37, 81-91.
    • (1945) Bull. Calc. Math. Soc. , vol.37 , pp. 81-91
    • Rao, C.R.1
  • 50
    • 84953405534 scopus 로고    scopus 로고
    • Pattern Recognition and Neural Networks
    • Cambridge: Cambridge University Press.
    • Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.
    • (1996)
    • Ripley, B.D.1
  • 51
    • 0003919677 scopus 로고    scopus 로고
    • Monte Carlo Statistical Methods
    • New York: Springer.
    • Robert, C. and Casella, G. (2004) Monte Carlo Statistical Methods. New York: Springer.
    • (2004)
    • Robert, C.1    Casella, G.2
  • 52
    • 0000936678 scopus 로고    scopus 로고
    • Optimal scaling of discrete approximations to Langevin diffusions
    • Roberts, G. O. and Rosenthal, J. S. (1998) Optimal scaling of discrete approximations to Langevin diffusions. J. R. Statist. Soc. B, 60, 255-268.
    • (1998) J. R. Statist. Soc. B , vol.60 , pp. 255-268
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 53
    • 15244341043 scopus 로고    scopus 로고
    • Langevin diffusions and Metropolis-Hastings algorithms
    • Roberts, G. and Stramer, O. (2003) Langevin diffusions and Metropolis-Hastings algorithms. Methodol. Comput. Appl. Probab., 4, 337-358.
    • (2003) Methodol. Comput. Appl. Probab. , vol.4 , pp. 337-358
    • Roberts, G.1    Stramer, O.2
  • 54
    • 62849120031 scopus 로고    scopus 로고
    • Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion)
    • Rue, H., Martino, S. and Chopin, N. (2009) Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion). J. R. Statist. Soc. B, 71, 319-392.
    • (2009) J. R. Statist. Soc. B , vol.71 , pp. 319-392
    • Rue, H.1    Martino, S.2    Chopin, N.3
  • 55
    • 79952302215 scopus 로고    scopus 로고
    • European Space Agency-European Union Satellite Conf. Image Information Mining for Security and Intelligence
    • In (Available from)
    • Skilling, J. (2006) Probability and geometry. In European Space Agency-European Union Satellite Conf. Image Information Mining for Security and Intelligence. (Available from)
    • (2006) Probability and geometry
    • Skilling, J.1
  • 56
    • 29544451379 scopus 로고    scopus 로고
    • Monte Carlo computation of the Fisher information matrix in nonstandard settings
    • Spall, J. C. (2005) Monte Carlo computation of the Fisher information matrix in nonstandard settings. J. Computnl Graph. Statist., 14, 889-909.
    • (2005) J. Computnl Graph. Statist. , vol.14 , pp. 889-909
    • Spall, J.C.1
  • 57
    • 0000370393 scopus 로고
    • Design of experiment for bioassay
    • Tsutakawa, R. K. (1972) Design of experiment for bioassay. J. Am. Statist. Ass., 67, 584-590.
    • (1972) J. Am. Statist. Ass. , vol.67 , pp. 584-590
    • Tsutakawa, R.K.1
  • 59
    • 40749094910 scopus 로고    scopus 로고
    • Bayesian ranking of biochemical system models
    • Vyshemirsky, V. and Girolami, M. (2008) Bayesian ranking of biochemical system models. Bioinformatics, 24, 833-839.
    • (2008) Bioinformatics , vol.24 , pp. 833-839
    • Vyshemirsky, V.1    Girolami, M.2
  • 60
    • 0040333774 scopus 로고    scopus 로고
    • Manifold stochastic dynamics for Bayesian learning
    • Zlochin, M. and Baram, Y. (2001) Manifold stochastic dynamics for Bayesian learning. Neur. Computn, 13, 2549-2572.
    • (2001) Neur. Computn , vol.13 , pp. 2549-2572
    • Zlochin, M.1    Baram, Y.2
  • 61
    • 84884085211 scopus 로고    scopus 로고
    • Optimization Algorithms on Matrix Manifolds
    • Princeton: Princeton University Press.
    • Absil, P. A., Mahony, R. and Sepulchre, R. (2008) Optimization Algorithms on Matrix Manifolds. Princeton: Princeton University Press.
    • (2008)
    • Absil, P.A.1    Mahony, R.2    Sepulchre, R.3
  • 62
    • 0032381318 scopus 로고    scopus 로고
    • Fisher information and maximum-likelihood estimation of covariance parameters in Gaussian stochastic processess
    • Abt, M. and Welch, W. (1998) Fisher information and maximum-likelihood estimation of covariance parameters in Gaussian stochastic processess. Can. J. Statist., 26, 127-137.
    • (1998) Can. J. Statist. , vol.26 , pp. 127-137
    • Abt, M.1    Welch, W.2
  • 63
    • 0000344740 scopus 로고
    • Differential geometry of curved exponential families-curvatures and information loss
    • Amari, S. (1982) Differential geometry of curved exponential families-curvatures and information loss. Ann. Statist., 10, 357-385.
    • (1982) Ann. Statist. , vol.10 , pp. 357-385
    • Amari, S.1
  • 64
    • 0003355631 scopus 로고
    • Differential-geometrical methods in statistics
    • Amari, S.-I. (1985) Differential-geometrical methods in statistics. Lect. Notes Statist., 28.
    • (1985) Lect. Notes Statist. , vol.28
    • Amari, S.-I.1
  • 65
    • 0034202724 scopus 로고    scopus 로고
    • Nonholonomic orthogonal learning algorithms for blind source separation
    • Amari, S., Chen, T. P. and Chichocki, A. (2000) Nonholonomic orthogonal learning algorithms for blind source separation. Neur. Computn, 12, 1463-1484.
    • (2000) Neur. Computn , vol.12 , pp. 1463-1484
    • Amari, S.1    Chen, T.P.2    Chichocki, A.3
  • 66
    • 0003530945 scopus 로고    scopus 로고
    • Methods of Information Geometry
    • (2000) Oxford: Oxford University Press.
    • Amari, S. and Nagaoka, H. (2000) Methods of Information Geometry. Oxford: Oxford University Press.
    • Amari, S.1    Nagaoka, H.2
  • 68
    • 47249119570 scopus 로고    scopus 로고
    • Local mixture models of exponential families
    • Anaya-Izquierdo, K. A. and Marriott, P. (2007) Local mixture models of exponential families. Bernoulli, 13, 623-640.
    • (2007) Bernoulli , vol.13 , pp. 623-640
    • Anaya-Izquierdo, K.A.1    Marriott, P.2
  • 69
    • 77953523599 scopus 로고    scopus 로고
    • Particle Markov chain Monte Carlo methods (with discussion)
    • Andrieu, C., Doucet, A. and Holenstein, R. (2010) Particle Markov chain Monte Carlo methods (with discussion). J. R. Statist. Soc. B, 72, 269-342.
    • (2010) J. R. Statist. Soc. B , vol.72 , pp. 269-342
    • Andrieu, C.1    Doucet, A.2    Holenstein, R.3
  • 70
    • 33750512542 scopus 로고    scopus 로고
    • On the ergodicity properties of some adaptive MCMC algorithms
    • Andrieu, C. and Moulines, E. (2006) On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab., 16, 1462-1505.
    • (2006) Ann. Appl. Probab. , vol.16 , pp. 1462-1505
    • Andrieu, C.1    Moulines, E.2
  • 71
    • 57849088168 scopus 로고    scopus 로고
    • A tutorial on adaptive MCMC
    • Andrieu, C. and Thoms, J. (2008) A tutorial on adaptive MCMC. Statist. Comput., 18, 343-373.
    • (2008) Statist. Comput. , vol.18 , pp. 343-373
    • Andrieu, C.1    Thoms, J.2
  • 72
    • 0348207641 scopus 로고    scopus 로고
    • Zero-variance zero-bias principle for observables in quantum monte carlo: application to forces
    • Assaraf, R. and Caffarel, M. (2003) Zero-variance zero-bias principle for observables in quantum monte carlo: application to forces. J. Chem. Phys., 119, 10536-10552.
    • (2003) J. Chem. Phys. , vol.119 , pp. 10536-10552
    • Assaraf, R.1    Caffarel, M.2
  • 73
    • 33747075845 scopus 로고    scopus 로고
    • An adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift
    • Atchadé, Y. F. (2006) An adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift. Methodol. Comput. Appl. Probab., 8, 235-254.
    • (2006) Methodol. Comput. Appl. Probab. , vol.8 , pp. 235-254
    • Atchadé, Y.F.1
  • 75
    • 84898964031 scopus 로고    scopus 로고
    • Advances in Neural Information Processing Systems
    • (eds S. A. Solla, T. K. Leen and K.-R. Müller) - Cambridge: MIT Press.
    • Attias, H. (1999) A variational Bayesian framework for graphical models. In Advances in Neural Information Processing Systems (eds S. A. Solla, T. K. Leen and K.-R. Müller), pp. 209-215. Cambridge: MIT Press.
    • (1999) A variational Bayesian framework for graphical models , pp. 209-215
    • Attias, H.1
  • 76
    • 48449087175 scopus 로고    scopus 로고
    • Discussion on 'Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes' (by A. Beskos, O. Papaspiliopoulos, G. O. Roberts and P. Fearnhead)
    • Ball, F., Dryden, I. and Golalizadeh, M. (2006) Discussion on 'Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes' (by A. Beskos, O. Papaspiliopoulos, G. O. Roberts and P. Fearnhead). J. R. Statist. Soc. B, 68, 367-368.
    • (2006) J. R. Statist. Soc. B , vol.68 , pp. 367-368
    • Ball, F.1    Dryden, I.2    Golalizadeh, M.3
  • 77
    • 48449105350 scopus 로고    scopus 로고
    • Brownian motion and Ornstein-Uhlenbeck processes in planar shape space
    • Ball, F. G., Dryden, I. L. and Golalizadeh, M. (2008) Brownian motion and Ornstein-Uhlenbeck processes in planar shape space. Methodol. Comput. Appl. Probab., 10, 1-22.
    • (2008) Methodol. Comput. Appl. Probab. , vol.10 , pp. 1-22
    • Ball, F.G.1    Dryden, I.L.2    Golalizadeh, M.3
  • 78
    • 0002303010 scopus 로고
    • The role of differential geometry in statistical theory
    • Barndorff-Nielsen, O. E., Cox, D. R. and Reid, N. (1986) The role of differential geometry in statistical theory. Int. Statist. Rev., 54, 83-96.
    • (1986) Int. Statist. Rev. , vol.54 , pp. 83-96
    • Barndorff-Nielsen, O.E.1    Cox, D.R.2    Reid, N.3
  • 81
    • 0003111416 scopus 로고
    • Calculation of intrinsic and parameter-effects curvatures for nonlinear regression models
    • Bates, D., Hamilton, D. and Watts, D. (1983) Calculation of intrinsic and parameter-effects curvatures for nonlinear regression models. Communs Statist. Simuln Computn, 12, 469-477.
    • (1983) Communs Statist. Simuln Computn , vol.12 , pp. 469-477
    • Bates, D.1    Hamilton, D.2    Watts, D.3
  • 82
    • 0002256849 scopus 로고
    • Relative curvature measures of nonlinearity
    • Bates, D. and Watts, D. (1980) Relative curvature measures of nonlinearity. J. R. Statist. Soc. B, 42, 1-25.
    • (1980) J. R. Statist. Soc. B , vol.42 , pp. 1-25
    • Bates, D.1    Watts, D.2
  • 83
    • 0003456815 scopus 로고
    • Nonlinear Regression Analysis and Its Applications
    • New York: Wiley.
    • Bates, D. and Watts, D. (1988) Nonlinear Regression Analysis and Its Applications. New York: Wiley.
    • (1988)
    • Bates, D.1    Watts, D.2
  • 85
    • 0003713964 scopus 로고    scopus 로고
    • Nonlinear Programming
    • 2nd edn. Belmont: Athena Scientific.
    • Bertsekas, D. (1999) Nonlinear Programming, 2nd edn. Belmont: Athena Scientific.
    • (1999)
    • Bertsekas, D.1
  • 87
  • 88
    • 33646690994 scopus 로고    scopus 로고
    • Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)
    • Beskos, A., Papaspiliopoulos, O., Roberts, G. O. and Fearnhead, P. (2006) Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion). J. R. Statist. Soc. B, 68, 333-382.
    • (2006) J. R. Statist. Soc. B , vol.68 , pp. 333-382
    • Beskos, A.1    Papaspiliopoulos, O.2    Roberts, G.O.3    Fearnhead, P.4
  • 92
    • 79952287918 scopus 로고    scopus 로고
    • Discussion on 'Particle Markov chain Monte Carlo methods' (by C. Andrieu, A. Doucet and R. Holenstein)
    • Bhadra, A. (2010) Discussion on 'Particle Markov chain Monte Carlo methods' (by C. Andrieu, A. Doucet and R. Holenstein). J. R. Statist. Soc. B, 72, 314-315.
    • (2010) J. R. Statist. Soc. B , vol.72 , pp. 314-315
    • Bhadra, A.1
  • 94
    • 0033484699 scopus 로고    scopus 로고
    • Thermalization of quantum states
    • Brody, D. C. and Hughston, L. P. (1999) Thermalization of quantum states. J. Math. Phys., 40, 12-18.
    • (1999) J. Math. Phys. , vol.40 , pp. 12-18
    • Brody, D.C.1    Hughston, L.P.2
  • 95
    • 79952293516 scopus 로고    scopus 로고
    • Signal transduction, sloppy models, and statistical mechanics
    • PhD Thesis Cornell University, Ithaca.
    • Brown, K. S. (2003) Signal transduction, sloppy models, and statistical mechanics. PhD Thesis Cornell University, Ithaca.
    • (2003)
    • Brown, K.S.1
  • 96
    • 33748557777 scopus 로고    scopus 로고
    • The statistical mechanics of complex signaling networks: nerve growth factor signaling
    • Brown, K., Hill, C., Calero, G., Myers, C., Lee, K., Sethna, J. and Cerione, R. (2004) The statistical mechanics of complex signaling networks: nerve growth factor signaling. Phys. Biol., 1, 184-195.
    • (2004) Phys. Biol. , vol.1 , pp. 184-195
    • Brown, K.1    Hill, C.2    Calero, G.3    Myers, C.4    Lee, K.5    Sethna, J.6    Cerione, R.7
  • 97
    • 42749109054 scopus 로고    scopus 로고
    • Statistical mechanical approaches to models with many poorly known parameters
    • Brown, K. and Sethna, J. (2003) Statistical mechanical approaches to models with many poorly known parameters. Phys. Rev. E, 68, 21904.
    • (2003) Phys. Rev. E , vol.68 , pp. 21904
    • Brown, K.1    Sethna, J.2
  • 98
    • 0001445688 scopus 로고
    • Entropy differential metric, distance and divergence measures in probability spaces
    • Burbea, J. and Rao, C. R. (1982) Entropy differential metric, distance and divergence measures in probability spaces. J. Multiv. Anal., 12, 575-596.
    • (1982) J. Multiv. Anal. , vol.12 , pp. 575-596
    • Burbea, J.1    Rao, C.R.2
  • 99
    • 0011624568 scopus 로고
    • Differential metrics in probability spaces
    • Burbea, J. and Rao, C. R. (1984) Differential metrics in probability spaces. Probab. Math. Statist., 3, 241-258.
    • (1984) Probab. Math. Statist. , vol.3 , pp. 241-258
    • Burbea, J.1    Rao, C.R.2
  • 100
    • 69449098014 scopus 로고    scopus 로고
    • Estimating Bayes factors via thermodynamic integration and population MCMC
    • Calderhead, B. and Girolami, M. (2009) Estimating Bayes factors via thermodynamic integration and population MCMC. Computnl Statist. Data Anal., 53, 4028-4045.
    • (2009) Computnl Statist. Data Anal. , vol.53 , pp. 4028-4045
    • Calderhead, B.1    Girolami, M.2
  • 101
    • 0030417779 scopus 로고    scopus 로고
    • Equivariant adaptive source separation
    • Cardoso, J. and Laheld, B. H. (1996) Equivariant adaptive source separation. IEEE Trans. Signal Process., 44, 3017-3030.
    • (1996) IEEE Trans. Signal Process. , vol.44 , pp. 3017-3030
    • Cardoso, J.1    Laheld, B.H.2
  • 102
    • 75149191785 scopus 로고    scopus 로고
    • Tailored randomized block MCMC methods with application to DSGE models
    • Chib, S. and Ramamurthy, S. (2010) Tailored randomized block MCMC methods with application to DSGE models. J. Econmetr., 155, 19-38.
    • (2010) J. Econmetr. , vol.155 , pp. 19-38
    • Chib, S.1    Ramamurthy, S.2
  • 103
    • 79952283864 scopus 로고    scopus 로고
    • Learning hyperparameters for neural network models using Hamiltonian dynamics. Masters Thesis Department of Computer Science, University of Toronto, Toronto. (Available from)
    • Choo, K. (2000) Learning hyperparameters for neural network models using Hamiltonian dynamics. Masters Thesis Department of Computer Science, University of Toronto, Toronto. (Available from)
    • (2000)
    • Choo, K.1
  • 104
    • 0012338718 scopus 로고    scopus 로고
    • A sequential particle filter for static models
    • Chopin, N. (2002) A sequential particle filter for static models. Biometrika, 89, 539-552.
    • (2002) Biometrika , vol.89 , pp. 539-552
    • Chopin, N.1
  • 105
    • 79952289742 scopus 로고    scopus 로고
    • Bayesian Statistics 8
    • In (eds S. Bayarri, J. O. Berger, J. M. Bernardo, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West). Oxford: Oxford University Press.
    • Chopin, N. (2007) Discussion of Del Moral et al. In Bayesian Statistics 8(eds S. Bayarri, J. O. Berger, J. M. Bernardo, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West). Oxford: Oxford University Press.
    • (2007) Discussion of Del Moral et al
    • Chopin, N.1
  • 106
    • 16244387937 scopus 로고    scopus 로고
    • Scaling limits for the transient phase of local Metropolis-Hastings algorithms
    • Christensen, O. F., Roberts, G. O. and Rosenthal, J. S. (2005) Scaling limits for the transient phase of local Metropolis-Hastings algorithms. J. R. Statist. Soc. B, 67, 253-268.
    • (2005) J. R. Statist. Soc. B , vol.67 , pp. 253-268
    • Christensen, O.F.1    Roberts, G.O.2    Rosenthal, J.S.3
  • 107
    • 33645558077 scopus 로고    scopus 로고
    • Robust Markov chain Monte Carlo methods for spatial generalized linear mixed models
    • Christensen, O. F., Roberts, G. O. and Sköld, M. (2006) Robust Markov chain Monte Carlo methods for spatial generalized linear mixed models. J. Computnl Graph. Statist., 15, 1-17.
    • (2006) J. Computnl Graph. Statist. , vol.15 , pp. 1-17
    • Christensen, O.F.1    Roberts, G.O.2    Sköld, M.3
  • 108
    • 25144445267 scopus 로고    scopus 로고
    • Local model uncertainty and incomplete data bias (with discussion)
    • Copas, J. and Eguchi, S. (2005) Local model uncertainty and incomplete data bias (with discussion). J. R. Statist. Soc. B, 67, 459-512.
    • (2005) J. R. Statist. Soc. B , vol.67 , pp. 459-512
    • Copas, J.1    Eguchi, S.2
  • 109
    • 77949534898 scopus 로고    scopus 로고
    • Likelihood for statistically equivalent models
    • Copas, J. and Eguchi, S. (2010) Likelihood for statistically equivalent models. J. R. Statist. Soc. B, 72, 193-217.
    • (2010) J. R. Statist. Soc. B , vol.72 , pp. 193-217
    • Copas, J.1    Eguchi, S.2
  • 110
  • 111
    • 21344483516 scopus 로고
    • Preferred point geometry and statistical manifolds
    • Critchley, F., Marriott, P. K. and Salmon, M. (1993) Preferred point geometry and statistical manifolds. Ann. Statist., 21, 1197-1224.
    • (1993) Ann. Statist. , vol.21 , pp. 1197-1224
    • Critchley, F.1    Marriott, P.K.2    Salmon, M.3
  • 113
    • 70350568207 scopus 로고    scopus 로고
    • Efficient Monte Carlo computation of Fisher information matrix using prior information
    • Das, S., Spall, J. and Ghanem, R. (2010) Efficient Monte Carlo computation of Fisher information matrix using prior information. Computnl Statist. Data Anal., 54, 272-289.
    • (2010) Computnl Statist. Data Anal. , vol.54 , pp. 272-289
    • Das, S.1    Spall, J.2    Ghanem, R.3
  • 114
    • 0000399239 scopus 로고
    • Discussion on 'Defining the curvature of a statistical problem (with applications to second-order efficiency)' (by B. Efron)
    • Dawid, A. P. (1975) Discussion on 'Defining the curvature of a statistical problem (with applications to second-order efficiency)' (by B. Efron). Ann. Statist., 3, 1231-1234.
    • (1975) Ann. Statist. , vol.3 , pp. 1231-1234
    • Dawid, A.P.1
  • 117
    • 0034346693 scopus 로고    scopus 로고
    • Analysis of a nonreversible Markov chain sampler
    • Diaconis, P., Holmes, S. and Neal, R. (2000) Analysis of a nonreversible Markov chain sampler. Ann. Appl. Probab., 10, 726-752.
    • (2000) Ann. Appl. Probab. , vol.10 , pp. 726-752
    • Diaconis, P.1    Holmes, S.2    Neal, R.3
  • 118
    • 79952304909 scopus 로고    scopus 로고
    • MCMC acceleration: methods and results. Technical Report. Department of Applied Mathematics and Statistics, University of California, Santa Cruz.
    • Draper, D. and Liu, S. (2006) MCMC acceleration: methods and results. Technical Report. Department of Applied Mathematics and Statistics, University of California, Santa Cruz.
    • (2006)
    • Draper, D.1    Liu, S.2
  • 120
    • 0003828513 scopus 로고    scopus 로고
    • Time Series Analysis by State Space Methods
    • Oxford: Oxford University Press.
    • Durbin, J. and Koopman, S. (2001) Time Series Analysis by State Space Methods. Oxford: Oxford University Press.
    • (2001)
    • Durbin, J.1    Koopman, S.2
  • 121
    • 77955152465 scopus 로고    scopus 로고
    • Cross-fertilizing strategies for better EM mountain climbing and DA field exploration: a graphical guide book
    • to be published.
    • van Dyk, D. A. and Meng, X.-L. (2010) Cross-fertilizing strategies for better EM mountain climbing and DA field exploration: a graphical guide book. Statist. Sci., to be published.
    • (2010) Statist. Sci.
    • van Dyk, D.A.1    Meng, X.-L.2
  • 122
    • 0032216898 scopus 로고    scopus 로고
    • The geometry of algorithms with orthogonality constraints
    • Edelman, A., Arias, T. and Smith, S. (1999) The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Applic., 20, 303-353.
    • (1999) SIAM J. Matrix Anal. Applic. , vol.20 , pp. 303-353
    • Edelman, A.1    Arias, T.2    Smith, S.3
  • 123
    • 0000551847 scopus 로고
    • Defining the curvature of a statistical problem (with applications to second-order efficiency)
    • Efron, B. (1975) Defining the curvature of a statistical problem (with applications to second-order efficiency). Ann. Statist., 3, 1189-1242.
    • (1975) Ann. Statist. , vol.3 , pp. 1189-1242
    • Efron, B.1
  • 124
    • 0000852027 scopus 로고
    • Second order efficiency of minimum contrast estimators in a curved exponential family
    • Eguchi, S. (1983) Second order efficiency of minimum contrast estimators in a curved exponential family. Ann. Statist., 11, 793-803.
    • (1983) Ann. Statist. , vol.11 , pp. 793-803
    • Eguchi, S.1
  • 125
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • Fitzhugh, R. (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys. J., 1, 445-466.
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 126
    • 0003768769 scopus 로고
    • Practical Methods of Optimization
    • 2nd edn. New York: Wiley.
    • Fletcher, R. (1987) Practical Methods of Optimization2nd edn. New York: Wiley.
    • (1987)
    • Fletcher, R.1
  • 127
    • 18644380792 scopus 로고    scopus 로고
    • Fourth-order algorithms for solving the multi-variable Langevin equation and the Kramers equation
    • Forbert, H. A. and Chin, S. A. (2000) Fourth-order algorithms for solving the multi-variable Langevin equation and the Kramers equation. Phys. Rev. E, 63, 016703.
    • (2000) Phys. Rev. E , vol.63 , pp. 016703
    • Forbert, H.A.1    Chin, S.A.2
  • 128
    • 49449108749 scopus 로고    scopus 로고
    • Struggles with survey weighting and regression modeling (with discussion)
    • Gelman, A. (2007) Struggles with survey weighting and regression modeling (with discussion). Statist. Sci., 22, 153-188.
    • (2007) Statist. Sci. , vol.22 , pp. 153-188
    • Gelman, A.1
  • 130
    • 0000736067 scopus 로고    scopus 로고
    • Computing normalizing constants: from importance sampling to bridge sampling to path sampling
    • Gelman, A. E. and Meng, X.-L. (1998) Computing normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci., 13, 163-185.
    • (1998) Statist. Sci. , vol.13 , pp. 163-185
    • Gelman, A.E.1    Meng, X.-L.2
  • 131
    • 84884028391 scopus 로고    scopus 로고
    • Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do
    • 2nd edn. Princeton: Princeton University Press.
    • Gelman, A., Park, D., Shor, B. and Cortina, J. (2009) Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do2nd edn. Princeton: Princeton University Press.
    • (2009)
    • Gelman, A.1    Park, D.2    Shor, B.3    Cortina, J.4
  • 132
    • 0002795650 scopus 로고
    • Computing Science and Statistics: Proc. 23rd Symp. Interface
    • Geyer, C. J. (1991) Markov chain Monte Carlo maximum likelihood. In Computing Science and Statistics: Proc. 23rd Symp. Interface, pp. 156-163.
    • (1991) Markov chain Monte Carlo maximum likelihood , pp. 156-163
    • Geyer, C.J.1
  • 133
    • 0031780720 scopus 로고    scopus 로고
    • Estimating parameters in stochastic compartmental models using Markov Chain methods
    • Gibson, G. and Renshaw, E. (1998) Estimating parameters in stochastic compartmental models using Markov Chain methods. IMA J. Math. Appl. Med. Biol., 15, 19-40.
    • (1998) IMA J. Math. Appl. Med. Biol. , vol.15 , pp. 19-40
    • Gibson, G.1    Renshaw, E.2
  • 134
    • 77956676472 scopus 로고    scopus 로고
    • Adaptive independent Metropolis-Hastings by fast estimation of mixtures of normals
    • Giordani, P. and Kohn, R. (2010) Adaptive independent Metropolis-Hastings by fast estimation of mixtures of normals. J. Computnl Graph. Statist., 19, 243-259.
    • (2010) J. Computnl Graph. Statist. , vol.19 , pp. 243-259
    • Giordani, P.1    Kohn, R.2
  • 135
    • 77956889087 scopus 로고
    • Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
    • Green, P. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
    • (1995) Biometrika , vol.82 , pp. 711-732
    • Green, P.1
  • 137
    • 0000281374 scopus 로고
    • Representations of knowledge in complex systems (with discussion)
    • Grenander, U. and Miller, M. I. (1994) Representations of knowledge in complex systems (with discussion). J. R. Statist. Soc. B, 56, 549-603.
    • (1994) J. R. Statist. Soc. B , vol.56 , pp. 549-603
    • Grenander, U.1    Miller, M.I.2
  • 139
    • 79952293379 scopus 로고    scopus 로고
    • Bayesian calibration of the thermosphere-ionosphere electrodynamics general circulation model (TIE-GCM)
    • Guillas, S., Rougier, J., Maute, A., Richmond, A. D. and Linkletter, C. D. (2009) Bayesian calibration of the thermosphere-ionosphere electrodynamics general circulation model (TIE-GCM). Geosci. Model Dev., 2, 137-144.
    • (2009) Geosci. Model Dev. , vol.2 , pp. 137-144
    • Guillas, S.1    Rougier, J.2    Maute, A.3    Richmond, A.D.4    Linkletter, C.D.5
  • 140
    • 79952299953 scopus 로고    scopus 로고
    • Sloppiness, modeling, and evolution in biochemical networks. PhD Thesis Cornell University, Ithaca.
    • Gutenkunst, R. (2008) Sloppiness, modeling, and evolution in biochemical networks. PhD Thesis Cornell University, Ithaca.
    • (2008)
    • Gutenkunst, R.1
  • 143
    • 0033436531 scopus 로고    scopus 로고
    • Adaptive proposal distribution for random walk Metropolis algorithm
    • Haario, H., Saksman, E. and Tamminen, J. (1999) Adaptive proposal distribution for random walk Metropolis algorithm. Computnl Statist., 14, 375-395.
    • (1999) Computnl Statist. , vol.14 , pp. 375-395
    • Haario, H.1    Saksman, E.2    Tamminen, J.3
  • 144
    • 0038563932 scopus 로고    scopus 로고
    • An adaptive Metropolis algorithm
    • Haario, H., Saksman, E. and Tamminen, J. (2001) An adaptive Metropolis algorithm Bernoulli, 7, 223-242.
    • (2001) Bernoulli , vol.7 , pp. 223-242
    • Haario, H.1    Saksman, E.2    Tamminen, J.3
  • 145
    • 74049096785 scopus 로고    scopus 로고
    • Plug-and-play inference for disease dynamics: measles in large and small towns as a case study
    • He, D., Ionides, E. L. and King, A. A. (2010) Plug-and-play inference for disease dynamics: measles in large and small towns as a case study. J. R. Soc. Interface, 7, 271-283.
    • (2010) J. R. Soc. Interface , vol.7 , pp. 271-283
    • He, D.1    Ionides, E.L.2    King, A.A.3
  • 147
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes, M. R. and Stiefel, E. (1952) Methods of conjugate gradients for solving linear systems. J. Res. Natn Bur. Stand., 49, 409-436.
    • (1952) J. Res. Natn Bur. Stand. , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 148
    • 84867151416 scopus 로고    scopus 로고
    • Bayesian auxiliary variable models for binary and multinomial regression
    • Holmes, C. C. and Held, L. (2005) Bayesian auxiliary variable models for binary and multinomial regression. Baysn Anal., 1, 145-168.
    • (2005) Baysn Anal. , vol.1 , pp. 145-168
    • Holmes, C.C.1    Held, L.2
  • 149
    • 79551487646 scopus 로고    scopus 로고
    • Approximate Riemannian conjugate gradient learning for fixed-form variational Bayes
    • Honkela, A., Raiko, T., Kuusela, M., Tornio, M. and Karhunen, J. (2010) Approximate Riemannian conjugate gradient learning for fixed-form variational Bayes. J. Mach. Learn. Res., 11, 3235-3268.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 3235-3268
    • Honkela, A.1    Raiko, T.2    Kuusela, M.3    Tornio, M.4    Karhunen, J.5
  • 150
    • 0009349032 scopus 로고
    • A generalized guided monte carlo algorithm
    • Horowitz, A. M. (1991) A generalized guided monte carlo algorithm. Phys. Lett. B, 268, 247-252.
    • (1991) Phys. Lett. B , vol.268 , pp. 247-252
    • Horowitz, A.M.1
  • 151
    • 33746741787 scopus 로고    scopus 로고
    • Geometry of stochastic state vector reduction
    • Hughston, L. P. (1996) Geometry of stochastic state vector reduction. Proc. R. Soc. Lond., 452, 953-979.
    • (1996) Proc. R. Soc. Lond. , vol.452 , pp. 953-979
    • Hughston, L.P.1
  • 152
    • 0034320394 scopus 로고    scopus 로고
    • The Bayesian evidence scheme for regularising probability-density estimating neural networks
    • Husmeier, D. (2000) The Bayesian evidence scheme for regularising probability-density estimating neural networks. Neur. Computn, 12, 2685-2717.
    • (2000) Neur. Computn , vol.12 , pp. 2685-2717
    • Husmeier, D.1
  • 153
    • 9644300955 scopus 로고    scopus 로고
    • A bayesian analysis of the multinomial probit model using marginal data augmentation
    • Imai, K. and van Dyk, D. A. (2005) A bayesian analysis of the multinomial probit model using marginal data augmentation. J. Econmetr., 124, 311-334.
    • (2005) J. Econmetr. , vol.124 , pp. 311-334
    • Imai, K.1    van Dyk, D.A.2
  • 155
    • 0003414592 scopus 로고    scopus 로고
    • Theory of Probability
    • New York: Oxford University Press.
    • Jeffreys, H. (1998) Theory of Probability. New York: Oxford University Press.
    • (1998)
    • Jeffreys, H.1
  • 156
    • 77953081318 scopus 로고    scopus 로고
    • A van Trees inequality for estimators on manifolds
    • Jupp, P. E. (2010) A van Trees inequality for estimators on manifolds. J. Multiv. Anal., 101, 1814-1825.
    • (2010) J. Multiv. Anal. , vol.101 , pp. 1814-1825
    • Jupp, P.E.1
  • 157
    • 0003596421 scopus 로고    scopus 로고
    • Geometrical Foundations of Asymptotic Inference
    • New York: Wiley.
    • Kass, R. E. and Vos, P. W. (1997) Geometrical Foundations of Asymptotic Inference. New York: Wiley.
    • (1997)
    • Kass, R.E.1    Vos, P.W.2
  • 158
    • 0035648165 scopus 로고    scopus 로고
    • Bayesian calibration of computer models (with discussion)
    • Kennedy, M. C. and O' Hagan, A. (2001) Bayesian calibration of computer models (with discussion). J. R. Statist. Soc. B, 63, 425-464.
    • (2001) J. R. Statist. Soc. B , vol.63 , pp. 425-464
    • Kennedy, M.C.1    O' Hagan, A.2
  • 159
    • 78751501372 scopus 로고    scopus 로고
    • Proc. 51st A. Symp. Foundations of Computer Science
    • In Silver Spring: Institute of Electrical and Electronics Engineers Computer Society Press.
    • Koutis, I., Miller, G. L. and Peng, R. (2010) Approaching optimality for solving SDD linear systems. In Proc. 51st A. Symp. Foundations of Computer Science. Silver Spring: Institute of Electrical and Electronics Engineers Computer Society Press.
    • (2010) Approaching optimality for solving SDD linear systems
    • Koutis, I.1    Miller, G.L.2    Peng, R.3
  • 160
    • 79952303792 scopus 로고    scopus 로고
    • Efficient Bayesian inference for partially observed stochastic epidemics and a new class of semiparametric time series models. PhD Thesis Department of Mathematics and Statistics, Lancaster University, Lancaster. (Available from)
    • Kypraios, T. (2007) Efficient Bayesian inference for partially observed stochastic epidemics and a new class of semiparametric time series models. PhD Thesis Department of Mathematics and Statistics, Lancaster University, Lancaster. (Available from)
    • (2007)
    • Kypraios, T.1
  • 162
    • 45149117115 scopus 로고    scopus 로고
    • Long-time convergence of an Adaptive Biasing Force method
    • Lelievre, T., Otto, F., Rousset, M. and Stoltz, G. (2008) Long-time convergence of an Adaptive Biasing Force method. Nonlinearity, 21, 1155-1181.
    • (2008) Nonlinearity , vol.21 , pp. 1155-1181
    • Lelievre, T.1    Otto, F.2    Rousset, M.3    Stoltz, G.4
  • 163
    • 66249092400 scopus 로고    scopus 로고
    • Non-finite Fisher information and homogeneity: an EM approach
    • Li, P., Chen, J. and Marriott, P. (2009) Non-finite Fisher information and homogeneity: an EM approach. Biometrika, 411-426.
    • (2009) Biometrika , pp. 411-426
    • Li, P.1    Chen, J.2    Marriott, P.3
  • 165
    • 79952285915 scopus 로고    scopus 로고
    • Masters Project
    • Department of Computer Science, University of California, Santa Cruz.
    • Liu, S. (2003) Mirror-jump sampling: a strategy for MCMC acceleration. Masters Project. Department of Computer Science, University of California, Santa Cruz.
    • (2003) Mirror-jump sampling: a strategy for MCMC acceleration
    • Liu, S.1
  • 166
    • 30344435926 scopus 로고    scopus 로고
    • Fixed-domain asymptotics for a subclass of Matern-type Gaussian random fields
    • Loh, W. (2005) Fixed-domain asymptotics for a subclass of Matern-type Gaussian random fields. Ann. Statist., 33, 2344-2394.
    • (2005) Ann. Statist. , vol.33 , pp. 2344-2394
    • Loh, W.1
  • 167
    • 62049083002 scopus 로고    scopus 로고
    • Ricci curvature for metric-measure spaces via optimal transport
    • Lott, J. and Villani, C. (2009) Ricci curvature for metric-measure spaces via optimal transport. Ann. Math., 169, 903-991.
    • (2009) Ann. Math. , vol.169 , pp. 903-991
    • Lott, J.1    Villani, C.2
  • 168
  • 169
    • 46649101085 scopus 로고    scopus 로고
    • Bayesian Core: a Practical Approach to Computational Bayesian Statistics
    • New York: Springer.
    • Marin, J. M. and Robert, C. P. (2007) Bayesian Core: a Practical Approach to Computational Bayesian Statistics. New York: Springer.
    • (2007)
    • Marin, J.M.1    Robert, C.P.2
  • 170
    • 79952292497 scopus 로고    scopus 로고
    • Frontiers of Statistical Decision Making and Bayesian Analysis
    • (eds M.-H. Chen, D. Dey, P. Müller, D. Sun and K. Ye), ch. 14. New York: Springer.
    • Marin, J. and Robert, C. (2010) Importance sampling methods for Bayesian discrimination between embedded models. In Frontiers of Statistical Decision Making and Bayesian Analysis (eds M.-H. Chen, D. Dey, P. Müller, D. Sun and K. Ye), ch. 14. New York: Springer.
    • (2010) Importance sampling methods for Bayesian discrimination between embedded models
    • Marin, J.1    Robert, C.2
  • 171
    • 0001434493 scopus 로고    scopus 로고
    • A bayesian analysis of the multinomial probit model with fully identified parameters
    • McCulloch, R. E., Polson, N. G. and Rossi, P. E. (2000) A bayesian analysis of the multinomial probit model with fully identified parameters. J. Econmetr., 99, 173-193.
    • (2000) J. Econmetr. , vol.99 , pp. 173-193
    • Mcculloch, R.E.1    Polson, N.G.2    Rossi, P.E.3
  • 173
    • 0030551974 scopus 로고    scopus 로고
    • Rates of convergence of the Hastings and Metropolis algorithms
    • Mengersen, K. L. and Tweedie, R. L. (1996) Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist., 24, 101-121.
    • (1996) Ann. Statist. , vol.24 , pp. 101-121
    • Mengersen, K.L.1    Tweedie, R.L.2
  • 174
    • 0038387331 scopus 로고    scopus 로고
    • A family of algorithms for approximate Bayesian inference
    • Massachusetts Institute of Technology, Cambridge.
    • Minka, T. (2001) A family of algorithms for approximate Bayesian inference. PhD Thesis. Massachusetts Institute of Technology, Cambridge.
    • (2001) PhD Thesis
    • Minka, T.1
  • 176
    • 79952307200 scopus 로고    scopus 로고
    • Zero-variance Markov chain Monte Carlo for Bayesian estimators
    • University of Insubria, Insubria. (Available from)
    • Mira, A., Solgi, R. and Imparato, D. (2010) Zero-variance Markov chain Monte Carlo for Bayesian estimators. Technical Report. University of Insubria, Insubria. (Available from)
    • (2010) Technical Report
    • Mira, A.1    Solgi, R.2    Imparato, D.3
  • 177
    • 33644782020 scopus 로고    scopus 로고
    • Wavelet-based functional mixed models
    • Morris, J. S. and Carroll, R. J. (2006) Wavelet-based functional mixed models. J. R. Statist. Soc. B, 68, 179-199.
    • (2006) J. R. Statist. Soc. B , vol.68 , pp. 179-199
    • Morris, J.S.1    Carroll, R.J.2
  • 178
    • 85162029646 scopus 로고    scopus 로고
    • Advances in Neural Information Processing Systems
    • (eds J. Lafferty, C. K. I. Williams, R. Zemel, J. Shawe-Taylor and A. Culotta) -
    • Murray, I. and Adams, R. P. (2010) Slice sampling covariance hyperparameters of latent Gaussian models. In Advances in Neural Information Processing Systems (eds J. Lafferty, C. K. I. Williams, R. Zemel, J. Shawe-Taylor and A. Culotta), pp. 1723-1731.
    • (2010) Slice sampling covariance hyperparameters of latent Gaussian models , pp. 1723-1731
    • Murray, I.1    Adams, R.P.2
  • 179
    • 0004087397 scopus 로고
    • Probabilistic inference using Markov Chain Monte Carlo Methods
    • University of Toronto, Toronto. (Available from)
    • Neal, R. M. (1993) Probabilistic inference using Markov Chain Monte Carlo Methods. Technical Report. University of Toronto, Toronto. (Available from)
    • (1993) Technical Report
    • Neal, R.M.1
  • 180
    • 0002628667 scopus 로고    scopus 로고
    • Regression and classification using Gaussian process priors (with discussion)
    • Neal, R. M. (1999) Regression and classification using Gaussian process priors (with discussion). Baysn Statist., 6, 475-501.
    • (1999) Baysn Statist. , vol.6 , pp. 475-501
    • Neal, R.M.1
  • 181
    • 0000273048 scopus 로고    scopus 로고
    • Annealed importance sampling
    • Neal, R. M. (2001) Annealed importance sampling. Statist. Comput., 11, 125-139.
    • (2001) Statist. Comput. , vol.11 , pp. 125-139
    • Neal, R.M.1
  • 182
    • 1642370803 scopus 로고    scopus 로고
    • Slice sampling
    • Neal, R. M. (2003) Slice sampling. Ann. Statist., 31, 705-767.
    • (2003) Ann. Statist. , vol.31 , pp. 705-767
    • Neal, R.M.1
  • 183
    • 79251576558 scopus 로고    scopus 로고
    • Handbook of Markov Chain Monte Carlo
    • (eds S. Brooks, A. Gelman, G. Jones and X.-L Meng). Boca Raton: Chapman and Hall-CRC Press.
    • Neal, R. M. (2010) MCMC using Hamiltonian dynamics. In Handbook of Markov Chain Monte Carlo (eds S. Brooks, A. Gelman, G. Jones and X.-L Meng). Boca Raton: Chapman and Hall-CRC Press.
    • (2010) MCMC using Hamiltonian dynamics
    • Neal, R.M.1
  • 184
    • 26644434878 scopus 로고    scopus 로고
    • A case study in non-centering for data augmentation: stochasic epidemics
    • Neal, P. and Roberts, G. (2005) A case study in non-centering for data augmentation: stochasic epidemics. Statist. Comput., 15, 315-327.
    • (2005) Statist. Comput. , vol.15 , pp. 315-327
    • Neal, P.1    Roberts, G.2
  • 186
    • 0042725427 scopus 로고    scopus 로고
    • A hybrid markov chain for the bayesian analysis of the multinomial probit model
    • Nobile, A. (1998) A hybrid markov chain for the bayesian analysis of the multinomial probit model. Statist. Comput., 8, 229-242.
    • (1998) Statist. Comput. , vol.8 , pp. 229-242
    • Nobile, A.1
  • 187
    • 0141600855 scopus 로고    scopus 로고
    • Comment: Bayesian multinomial probit models with a normalization constraint
    • Nobile, A. (2000) Comment: Bayesian multinomial probit models with a normalization constraint. J. Econmetr., 99, 335-345.
    • (2000) J. Econmetr. , vol.99 , pp. 335-345
    • Nobile, A.1
  • 188
    • 79952304044 scopus 로고    scopus 로고
    • Long range search for maximum likelihood in exponential families
    • Okabayashi, S. and Geyer, C. J. (2010) Long range search for maximum likelihood in exponential families. Technical Report.
    • (2010) Technical Report
    • Okabayashi, S.1    Geyer, C.J.2
  • 190
    • 0033473456 scopus 로고    scopus 로고
    • Bayesian inference for partially observed stochastic epidemics
    • O'Neill, P. D. and Roberts, G. O. (1999) Bayesian inference for partially observed stochastic epidemics. J. R. Statist. Soc. A, 162, 121-129.
    • (1999) J. R. Statist. Soc. A , vol.162 , pp. 121-129
    • O'Neill, P.D.1    Roberts, G.O.2
  • 191
    • 0034320350 scopus 로고    scopus 로고
    • Gaussian processes for classification: mean field algorithms
    • Opper, M. and Winther, O. (2000) Gaussian processes for classification: mean field algorithms. Neur. Computn, 12, 2655-2684.
    • (2000) Neur. Computn , vol.12 , pp. 2655-2684
    • Opper, M.1    Winther, O.2
  • 192
    • 34249101736 scopus 로고    scopus 로고
    • A general framework for the parametrization of hierarchical models
    • Papaspiliopoulos, O., Roberts, G. O. and Sköld, M. (2007) A general framework for the parametrization of hierarchical models. Statist. Sci., 22, 59-73.
    • (2007) Statist. Sci. , vol.22 , pp. 59-73
    • Papaspiliopoulos, O.1    Roberts, G.O.2    Sköld, M.3
  • 193
    • 41149127139 scopus 로고    scopus 로고
    • Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator
    • no. 2.
    • Pearlmutter, B. A. and Siskind, J. M. (2008) Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator. ACM Trans. Program. Lang. Syst., 30, no. 2.
    • (2008) ACM Trans. Program. Lang. Syst. , vol.30
    • Pearlmutter, B.A.1    Siskind, J.M.2
  • 194
    • 79951577327 scopus 로고    scopus 로고
    • An empirical study of the efficiency of the EA for diffusion simulation
    • University of Warwick, Coventry.
    • Peluchetti, S. and Roberts, G. O. (2008) An empirical study of the efficiency of the EA for diffusion simulation. Technical Report. University of Warwick, Coventry.
    • (2008) Technical Report.
    • Peluchetti, S.1    Roberts, G.O.2
  • 195
    • 79952288346 scopus 로고    scopus 로고
    • Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)
    • Peters, G. W., Hosack, G. R. and Hayes, K. R. (2010) Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC). Technical Report.
    • (2010) Technical Report
    • Peters, G.W.1    Hosack, G.R.2    Hayes, K.R.3
  • 196
    • 79952286203 scopus 로고    scopus 로고
    • Particle approximations of the score and observed information matrix in state-space models with application to parameter estimation
    • to be published.
    • Poyiadjis, G., Doucet, A. and Singh, S. S. (2010) Particle approximations of the score and observed information matrix in state-space models with application to parameter estimation. Biometrika, to be published.
    • (2010) Biometrika
    • Poyiadjis, G.1    Doucet, A.2    Singh, S.S.3
  • 197
    • 35648981518 scopus 로고    scopus 로고
    • Parameter estimation for differential equations: a generalized smoothing approach
    • (with discussion).
    • Ramsay, J., Hooker, H., Campbell, D. and Cao, J. (2007) Parameter estimation for differential equations: a generalized smoothing approach (with discussion). J. R. Statist. Soc. B, 69, 741-796.
    • (2007) J. R. Statist. Soc. B , vol.69 , pp. 741-796
    • Ramsay, J.1    Hooker, H.2    Campbell, D.3    Cao, J.4
  • 198
    • 25444448065 scopus 로고    scopus 로고
    • Gaussian Processes for Machine Learning
    • Cambridge: MIT Press.
    • Rasmussen, C. E. and Williams, C. (2006) Gaussian Processes for Machine Learning. Cambridge: MIT Press.
    • (2006)
    • Rasmussen, C.E.1    Williams, C.2
  • 199
    • 18244378520 scopus 로고    scopus 로고
    • On Bayesian analysis of mixtures with an unknown number of components (with discussion)
    • correction, 60 (1998), 661
    • Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Statist. Soc. B, 59, 731-792; correction, 60 (1998), 661
    • (1997) J. R. Statist. Soc. B , vol.59 , pp. 731-792
    • Richardson, S.1    Green, P.J.2
  • 200
    • 34249044465 scopus 로고    scopus 로고
    • Motor unit number estimation using reversible jump Markov chain Monte Carlo (with discussion)
    • Ridall, P. G., Pettitt, A. N., Friel, N., Henderson, R. and McCombe, P. (2007) Motor unit number estimation using reversible jump Markov chain Monte Carlo (with discussion). Appl. Statist., 56, 235-269.
    • (2007) Appl. Statist. , vol.56 , pp. 235-269
    • Ridall, P.G.1    Pettitt, A.N.2    Friel, N.3    Henderson, R.4    Mccombe, P.5
  • 201
    • 0003919677 scopus 로고    scopus 로고
    • Monte Carlo Statistical Methods
    • 1st edn. New York: Springer.
    • Robert, C. and Casella, G. (1999) Monte Carlo Statistical Methods1st edn. New York: Springer.
    • (1999)
    • Robert, C.1    Casella, G.2
  • 202
    • 33645958895 scopus 로고    scopus 로고
    • Bayesian independent component analysis with prior constraints: an application in biosignal analysis, deterministic and statistical methods in machine learning
    • Roberts, S. and Choudrey, R. (2005) Bayesian independent component analysis with prior constraints: an application in biosignal analysis, deterministic and statistical methods in machine learning. Lect. Notes Comput. Sci., 3635, 159-179.
    • (2005) Lect. Notes Comput. Sci. , vol.3635 , pp. 159-179
    • Roberts, S.1    Choudrey, R.2
  • 204
    • 0013037129 scopus 로고    scopus 로고
    • Optimal scaling for various Metropolis-Hastings algorithms
    • Roberts, G. O. and Rosenthal, J. S. (2001) Optimal scaling for various Metropolis-Hastings algorithms. Statist. Sci., 16, 351-367.
    • (2001) Statist. Sci. , vol.16 , pp. 351-367
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 206
    • 85132364916 scopus 로고    scopus 로고
    • Exponential convergence of Langevin distributions and their discrete approximations
    • Roberts, G. O. and Tweedie, R. L. (1996) Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli, 2, 341-363.
    • (1996) Bernoulli , vol.2 , pp. 341-363
    • Roberts, G.O.1    Tweedie, R.L.2
  • 207
    • 78650316383 scopus 로고    scopus 로고
    • Handbook of Markov Chain Monte Carlo
    • (eds S. Brooks, A. Gelman, G. Jones and X.-L. Meng). Boca Raton: Chapman and Hall-CRC Press.
    • Rosenthal, J. S. (2010) Optimal proposal distributions and adaptive MCMC. In Handbook of Markov Chain Monte Carlo (eds S. Brooks, A. Gelman, G. Jones and X.-L. Meng). Boca Raton: Chapman and Hall-CRC Press.
    • (2010) Optimal proposal distributions and adaptive MCMC
    • Rosenthal, J.S.1
  • 208
    • 1842829625 scopus 로고    scopus 로고
    • Iterative Methods for Sparse Linear Systems
    • 2nd edn, ch. 6. Philadelphia: Society for Industrial and Applied Mathematics.
    • Saad, Y. (2003) Iterative Methods for Sparse Linear Systems, 2nd edn, ch. 6. Philadelphia: Society for Industrial and Applied Mathematics.
    • (2003)
    • Saad, Y.1
  • 209
    • 0002505992 scopus 로고    scopus 로고
    • The State of the Art in Numerical Analysis
    • (eds I. S. Duff and G. A. Watson) - Oxford: Clarendon.
    • Sanz-Serna, J. M. (1997) Geometric integration. In The State of the Art in Numerical Analysis (eds I. S. Duff and G. A. Watson), pp. 121-143. Oxford: Clarendon.
    • (1997) Geometric integration , pp. 121-143
    • Sanz-Serna, J.M.1
  • 210
    • 47649119838 scopus 로고    scopus 로고
    • Nonnegative matrix factorization with Gaussian process priors
    • Schmidt, M. N. and Laurberg, H. (2008) Nonnegative matrix factorization with Gaussian process priors. Computnl Intell. Neursci., 1-10.
    • (2008) Computnl Intell. Neursci. , pp. 1-10
    • Schmidt, M.N.1    Laurberg, H.2
  • 211
    • 57049083998 scopus 로고    scopus 로고
    • Nesting forward-mode AD in a functional framework
    • Siskind, M. and Pearlmutter, B. (2008) Nesting forward-mode AD in a functional framework. High. Ord. Symbol. Computn, 21, 361-376.
    • (2008) High. Ord. Symbol. Computn , vol.21 , pp. 361-376
    • Siskind, M.1    Pearlmutter, B.2
  • 212
    • 29544451379 scopus 로고    scopus 로고
    • Monte Carlo computation of the Fisher information matrix in nonstandard settings
    • Spall, J. (2005) Monte Carlo computation of the Fisher information matrix in nonstandard settings. J. Comput. Graph. Statist., 14, 889-909.
    • (2005) J. Comput. Graph. Statist. , vol.14 , pp. 889-909
    • Spall, J.1
  • 213
    • 34547248473 scopus 로고    scopus 로고
    • New Riemannian metrics for speeding-up the convergence of over-and underdetermined ICA
    • Kos New York: Institute of Electrical and Electronics Engineers.
    • Squartini, S., Piazza, F. and Theis, F. (2006) New Riemannian metrics for speeding-up the convergence of over-and underdetermined ICA. In Proc. Int. Symp. Circuits and Systems Kos New York: Institute of Electrical and Electronics Engineers.
    • (2006) Proc. Int. Symp. Circuits and Systems
    • Squartini, S.1    Piazza, F.2    Theis, F.3
  • 214
    • 0001697792 scopus 로고    scopus 로고
    • A Bayesian approach to geometric subspace estimation
    • Srivastava, A. (2000) A Bayesian approach to geometric subspace estimation. IEEE Trans Signal Process., 48, 1390-1400.
    • (2000) IEEE Trans Signal Process. , vol.48 , pp. 1390-1400
    • Srivastava, A.1
  • 215
    • 0037090016 scopus 로고    scopus 로고
    • Jump-diffusion markov processes on orthogonal groups for objects recognition
    • Srivastava, A., Grenander, U., Jensen, G. R. and Miller, M. I. (2002) Jump-diffusion markov processes on orthogonal groups for objects recognition. J. Statist. Planng Inf., 103, 15-37.
    • (2002) J. Statist. Planng Inf. , vol.103 , pp. 15-37
    • Srivastava, A.1    Grenander, U.2    Jensen, G.R.3    Miller, M.I.4
  • 216
    • 0036475030 scopus 로고    scopus 로고
    • Monte Carlo extrinsic estimators for manifold-valued parameters
    • Srivastava, A. and Klassen, E. (2001) Monte Carlo extrinsic estimators for manifold-valued parameters. IEEE Trans. Signal Process., 50, 299-308.
    • (2001) IEEE Trans. Signal Process. , vol.50 , pp. 299-308
    • Srivastava, A.1    Klassen, E.2
  • 217
    • 0000231847 scopus 로고    scopus 로고
    • Langevin-type models I: diffusions with given stationary distributions, and their discretizations
    • Stramer, O. and Tweedie, R. (1999a) Langevin-type models I: diffusions with given stationary distributions, and their discretizations. Methodol. Comput. Appl. Probab., 1, 283-306.
    • (1999) Methodol. Comput. Appl. Probab. , vol.1 , pp. 283-306
    • Stramer, O.1    Tweedie, R.2
  • 218
    • 0000231847 scopus 로고    scopus 로고
    • Langevin-type models II: self-targeting candidates for Hastings-Metropolis algorithms
    • Stramer, O. and Tweedie, R. (1999b) Langevin-type models II: self-targeting candidates for Hastings-Metropolis algorithms. Methodol. Comput. Appl. Probab., 1, 307-328.
    • (1999) Methodol. Comput. Appl. Probab. , vol.1 , pp. 307-328
    • Stramer, O.1    Tweedie, R.2
  • 219
    • 71449110790 scopus 로고    scopus 로고
    • Gradients on matrix manifolds and their chain rule
    • Theis, F. (2005) Gradients on matrix manifolds and their chain rule. Neur. Inform. Process., 9, 1-13.
    • (2005) Neur. Inform. Process. , vol.9 , pp. 1-13
    • Theis, F.1
  • 220
    • 79952288057 scopus 로고    scopus 로고
    • Geodesics in Monte Carlo sampling. Unpublished.
    • Transtrum, M. K., Chen, Y.-J. and Sethna, J. P. (2010) Geodesics in Monte Carlo sampling. Unpublished.
    • (2010)
    • Transtrum, M.K.1    Chen, Y.-J.2    Sethna, J.P.3
  • 221
    • 76649138302 scopus 로고    scopus 로고
    • Why are nonlinear fits to data so challenging?
    • Transtrum, M. K., Machta, B. B. and Sethna, J. P. (2010a). Why are nonlinear fits to data so challenging? Phys. Rev. Lett., 104, 1060201.
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 1060201
    • Transtrum, M.K.1    Machta, B.B.2    Sethna, J.P.3
  • 222
    • 79952294722 scopus 로고    scopus 로고
    • The geometry of nonlinear least squares with applications to sloppy models and optimization. To be published.
    • Transtrum, M. K., Machta, B. B. and Sethna, J. P. (2010b) The geometry of nonlinear least squares with applications to sloppy models and optimization. To be published.
    • (2010)
    • Transtrum, M.K.1    Machta, B.B.2    Sethna, J.P.3
  • 223
    • 0003462953 scopus 로고
    • Detection, Estimation and Modulation Theory, Part 1
    • New York: Wiley.
    • van Trees, H. L. (1968) Detection, Estimation and Modulation Theory, Part 1. New York: Wiley.
    • (1968)
    • van Trees, H.L.1
  • 224
    • 77953768713 scopus 로고    scopus 로고
    • Approximate inference for disease mapping with sparse Gaussian processes
    • Vanhatalo, J., Pietiläinen, V. and Vehtari, A. (2010) Approximate inference for disease mapping with sparse Gaussian processes. Statist. Med., 29, 1580-1607.
    • (2010) Statist. Med. , vol.29 , pp. 1580-1607
    • Vanhatalo, J.1    Pietiläinen, V.2    Vehtari, A.3
  • 225
    • 38949117814 scopus 로고    scopus 로고
    • Sparse log Gaussian processes via MCMC for spatial epidemiology
    • Vanhatalo, J. and Vehtari, A. (2007) Sparse log Gaussian processes via MCMC for spatial epidemiology. J. Mach. Learn. Res. Wrkshp Conf. Proc., 1, 73-89.
    • (2007) J. Mach. Learn. Res. Wrkshp Conf. Proc. , vol.1 , pp. 73-89
    • Vanhatalo, J.1    Vehtari, A.2
  • 226
    • 84255165453 scopus 로고    scopus 로고
    • Learning and Inference in Computational Systems Biology
    • (eds N. Lawrence, M. Girolami, M. Rattray and G. Sanguinetti) - Cambridge: MIT Press.
    • Wilkinson, D. J. and Golightly, A. (2010) Markov chain Monte Carlo algorithms for SDE parameter estimation. In Learning and Inference in Computational Systems Biology (eds N. Lawrence, M. Girolami, M. Rattray and G. Sanguinetti), pp. 253-275. Cambridge: MIT Press.
    • (2010) Markov chain Monte Carlo algorithms for SDE parameter estimation , pp. 253-275
    • Wilkinson, D.J.1    Golightly, A.2
  • 227
    • 85041123735 scopus 로고    scopus 로고
    • Divergence function, duality, and convex analysis
    • Zhang, J. (2004) Divergence function, duality, and convex analysis. Neur. Computn, 16, 159-195.
    • (2004) Neur. Computn , vol.16 , pp. 159-195
    • Zhang, J.1
  • 229
    • 0040333774 scopus 로고    scopus 로고
    • Manifold stochastic dynamics for Bayesian Learning
    • Zlochin, M. and Baram, Y. (2001) Manifold stochastic dynamics for Bayesian Learning. Neur. Computn, 13, 2549-2572.
    • (2001) Neur. Computn , vol.13 , pp. 2549-2572
    • Zlochin, M.1    Baram, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.