Sensitivity analysis of discrete Markov chains via matrix calculus

Linear Algebra and Its Applications

Volumn 438, Issue 4, 2013, Pages 1727-1745

  Caswell, Hal ^a,b  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

^b MAX PLANCK INSTITUTE FOR DEMOGRAPHIC RESEARCH   (Germany)

Author keywords

Community dynamics; Demography; Elasticity; Life expectancy; Life lost to mortality; Population models; Sensitivity

Indexed keywords

COMMUNITY DYNAMICS; DEMOGRAPHY; LIFE EXPECTANCIES; LIFE LOST TO MORTALITY; POPULATION MODEL; SENSITIVITY;

CALCULATIONS; ELASTICITY; MATHEMATICAL MODELS; POPULATION DYNAMICS; POPULATION STATISTICS; PROBABILITY DISTRIBUTIONS; SENSITIVITY ANALYSIS;

MARKOV PROCESSES;

EID: 84872112996     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.07.046     Document Type: Conference Paper

References (45)

1. K.M. Abadir, and J.R. Magnus Matrix Algebra Econometric Exercises 1 2005 Cambridge University Press Cambridge, United Kingdom
2. H. Caswell Matrix Population Models: Construction, Analysis, and Interpretation second ed. 2001 Sinauer Associates Sunderland, Massachusetts, USA
3. H. Caswell, Applications of Markov chains in demography, in: A.N. Langville, W.J. Stewart (Eds.), MAM2006: Markov Anniversary Meeting, Boson Books, Raleigh, North Carolina, USA, 2006, pp. 319-334.
4. H. Caswell Sensitivity analysis of transient population dynamics Ecol. Lett. 10 2007 1 15
5. H. Caswell Perturbation analysis of nonlinear matrix population models Demogr. Res. 18 2008 59 116
6. H. Caswell Stage, age, and individual stochasticity in demography Oikos 118 2009 1763 1782
7. H. Caswell, Perturbation analysis of continuous-time absorbing Markov chains, Numer. Linear Algebra Appl. (2011), doi:10.1002/nla.791.
8. H. Caswell, M.G. Neubert, and C.M. Hunter Demography and dispersal: invasion speeds and sensitivity analysis in periodic and stochastic environments Theor. Ecol. 2010 10.1007/s12080-010-0091-z
9. G.E. Cho, and C.D. Meyer Comparison of perturbation bounds for the stationary distribution of a Markov chain Linear Algebra Appl. 335 2000 137 150
10. J. Conlisk Comparative statics for Markov chains J. Econom. Dynam. Control 19 1985 139 151
11. J.N. Darroch, and E. Seneta On quasi stationary distributions in absorbing discrete time finite Markov chains J. Appl. Probab. 2 1965 88 100
12. R.D. Edwards, and S. Tuljapurkar Inequality in life spans and a new perspective on mortality convergence across industrialized countries Popul. Develop. Rev. 31 2005 645 674
13. R.E. Funderlic, and C.D. Meyer Jr. Sensitivity of the stationary distribution vector for an ergodic Markov chain Linear Algebra Appl. 76 1986 1 17
14. R.P. Gillespie Partial Differentiation second ed. 1954 Oliver and Boyd Edinburgh, United Kingdom
15. G.H. Golub, and C.D. Meyer Jr. Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains SIAM J. Algebraic Discrete Methods 7 1986 273 281
16. C.M. Grinstead, and J.L. Snell Introduction to Probability second ed. 2003 American Mathematical Society
17. M.F. Hill, J.D. Witman, and H. Caswell Spatio-temporal variation in Markov chain models of subtidal community succession Ecol. Lett. 5 2002 665 675
18. M.F. Hill, J.D. Witman, and H. Caswell A Markov chain model of a rocky subtidal community: succession and species interactions in a complex assemblage Am. Nat. 164 2004 E46 E61
19. H.S. Horn Markovian properties of forest succession M.L. Cody, J.M. Diamond, Ecology and Evolution of Communities 1975 Harvard University Press Cambridge, MA 196 211
20. Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available from: or .
21. J.J. Hunter Stationary distributions and mean first passage times of perturbed Markov chains Linear Algebra Appl. 410 2005 217 243
22. J.J. Hunter Mixing times with applications to perturbed Markov chains Linear Algebra Appl. 417 2006 108 123
23. M. Iosifescu Finite Markov Processes and their Applications 1980 Wiley New York, USA
24. J.G. Kemeny Generalization of a fundamental matrix Linear Algebra Appl. 38 1981 193 206
25. J.G. Kemeny, and J.L. Snell Finite Markov Chains 1960 Van Nostrand New York, NY, USA
26. S. Kirkland Conditioning properties of the stationary distribution for a Markov chain Electron. J. Linear Algebra 10 2003 1 15
27. S.J. Kirkland, M. Neumann, and N-S. Sze On optimal condition numbers for Markov chains Numer. Math. 110 2008 521 537
28. J.R. Magnus, and H. Neudecker Matrix differential calculus with applications to simple, Hadamard, and Kronecker products J. Math. Psych. 29 1985 474 492
29. J.R. Magnus, and H. Neudecker Matrix Differential Calculus with Applications in Statistics and Econometrics 1988 John Wiley & Sons New York, NY, USA
30. C.D. Meyer The role of the group generalized inverse in the theory of finite Markov chains SIAM Rev. 17 1975 443 464
31. C.D. Meyer Sensitivity of the stationary distribution of a Markov chain SIAM J. Matrix Anal. Appl. 15 1994 715 728
32. C.D. Meyer, and G.W. Stewart Derivatives and perturbations of eigenvectors SIAM J. Numer. Anal. 25 1982 679 691
33. A.Y. Mitrophanov Stability and exponential convergence of continuous time Markov chains J. Appl. Probab. 40 2003 970 979
34. A.Y. Mitrophanov Reversible Markov chains and spanning trees Math. Sci. 29 2004 107 114
35. A.Y. Mitrophanov Sensitivity and convergence of uniformly ergodic Markov chains J. Appl. Probab. 42 2005 1003 1014
36. A.Y. Mitrophanov, A. Lomsadze, and M. Borodovsky Sensitivity of hidden Markov models J. Appl. Probab. 42 2005 632 642
37. L.C. Nelis, and J.T. Wootton Treatment-based Markov chain models clarify mechanisms of invasion in an invaded grassland community Proc. B Roy. Soc. London 277 2010 539547 10.1098/rspb.2009.1564
38. W.E. Roth On direct product matrices Bull. Amer. Math. Soc. 40 1934 461 468
39. P.A. Samuelson Foundations of Economic Analysis 1947 Harvard University Press Cambridge, Massachusetts, USA
40. P.J. Schweitzer Perturbation theory and finite Markov chains J. Appl. Probab. 5 1968 401 413
41. G.A.F. Seber A Matrix Handbook for Statisticians 2008 Wiley New York, NY, USA
42. E. Seneta Perturbation of the stationary distribution measured by ergodicity coefficients Adv. Appl. Probab. 20 1988 228 230
43. E. Seneta Sensitivity of finite Markov chains under perturbation Stat. Probab. Lett. 17 1993 163 168
44. J.W. Vaupel, and V. Canudas Romo Decomposing change in life expectancy: a bouquet of formulas in honor of Nathan Keyfitz's 90th birthday Demography 40 2004 201 216
45. J.R. Wilmoth, and S. Horiuchi Rectangularization revisited: variability of age at death within human populations Demography 36 1999 475 495