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Volumn 99, Issue 4-5, 2008, Pages 253-262

A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models

Author keywords

Feller process; First passage times; Fortets integral equation; Interspike intervals; Laplace transform; Maximum likelihood; Moment method; Ornstein Uhlenbeck; Statistical inference

Indexed keywords

CELL MEMBRANES; DIFFUSION; ENZYME ACTIVITY; INTEGRATION; KNOWLEDGE BASED SYSTEMS; LAPLACE EQUATION; LAPLACE TRANSFORMS; MATHEMATICAL TRANSFORMATIONS; MAXIMUM LIKELIHOOD ESTIMATION; METHOD OF MOMENTS; MODAL ANALYSIS; SEMICONDUCTOR DOPING; STOCHASTIC MODELS; TRAJECTORIES;

EID: 56549129789     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-008-0237-x     Document Type: Review
Times cited : (81)

References (50)
  • 1
    • 14844315957 scopus 로고    scopus 로고
    • Survival models based on the Ornstein-Uhlenbeck process
    • O Aalen H Gjessing 2004 Survival models based on the Ornstein-Uhlenbeck process Lifetime Data Anal 10 407 423
    • (2004) Lifetime Data Anal , vol.10 , pp. 407-423
    • Aalen, O.1    Gjessing, H.2
  • 2
    • 33644971385 scopus 로고    scopus 로고
    • Representations of the first hitting time density of an Ornstein-Uhlenbeck process
    • L Alili P Patie J Pedersen 2005 Representations of the first hitting time density of an Ornstein-Uhlenbeck process Stochastic Models 21 967 980
    • (2005) Stochastic Models , vol.21 , pp. 967-980
    • Alili, L.1    Patie, P.2    Pedersen, J.3
  • 3
    • 0002166622 scopus 로고    scopus 로고
    • On estimation for discretely observed diffusions: A review
    • B Bibby M Sørensen 1996 On estimation for discretely observed diffusions: A review Theory Stochastic Process 2 49 56
    • (1996) Theory Stochastic Process , vol.2 , pp. 49-56
    • Bibby, B.1    Sørensen, M.2
  • 5
    • 0023686914 scopus 로고
    • Maximum likelihood analysis of spike trains of interacting nerve cells
    • D Brillinger 1988 Maximum likelihood analysis of spike trains of interacting nerve cells Biol Cybern 59 189 200
    • (1988) Biol Cybern , vol.59 , pp. 189-200
    • Brillinger, D.1
  • 6
    • 40749088917 scopus 로고    scopus 로고
    • Lapicque's 1907 paper: From frogs to integrate-and-fire
    • N Brunel M van Rossum 2008 Lapicque's 1907 paper: from frogs to integrate-and-fire Biol Cybern 97 337 339
    • (2008) Biol Cybern , vol.97 , pp. 337-339
    • Brunel, N.1    Van Rossum, M.2
  • 7
    • 0001302849 scopus 로고    scopus 로고
    • Cooperative behavior in periodically driven noisy integrate-and-fire models of neuronal dynamics
    • A Bulsara T Elston C Doering S Lowen K Lindberg 1996 Cooperative behavior in periodically driven noisy integrate-and-fire models of neuronal dynamics Phys Rev E 53 3958 3969
    • (1996) Phys Rev e , vol.53 , pp. 3958-3969
    • Bulsara, A.1    Elston, T.2    Doering, C.3    Lowen, S.4    Lindberg, K.5
  • 8
    • 33745712258 scopus 로고    scopus 로고
    • A review of the integrate-and-fire neuron model: I. homogeneous synaptic input
    • A Burkitt 2006 A review of the integrate-and-fire neuron model: I. homogeneous synaptic input Biol Cybern 95 1 19
    • (2006) Biol Cybern , vol.95 , pp. 1-19
    • Burkitt, A.1
  • 9
    • 34247491502 scopus 로고    scopus 로고
    • Predicting neuronal activity with simple models of the threshold type: Adaptive exponential integrate-and-fire model with two compartments
    • C Clopath R Jolivet A Rauch HR Luscher W Gerstner 2007 Predicting neuronal activity with simple models of the threshold type: Adaptive exponential integrate-and-fire model with two compartments Neurocomput 70 1668 1673
    • (2007) Neurocomput , vol.70 , pp. 1668-1673
    • Clopath, C.1    Jolivet, R.2    Rauch, A.3    Luscher, H.R.4    Gerstner, W.5
  • 10
    • 0001205798 scopus 로고
    • A theory of the term structure of interest rates
    • J Cox J Ingersoll S Ross 1985 A theory of the term structure of interest rates Econometrica 53 385 407
    • (1985) Econometrica , vol.53 , pp. 385-407
    • Cox, J.1    Ingersoll, J.2    Ross, S.3
  • 11
    • 35548977214 scopus 로고    scopus 로고
    • A result on the first-passage time of an Ornstein-Uhlenbeck process
    • S Ditlevsen 2007 A result on the first-passage time of an Ornstein-Uhlenbeck process Stat Probab Lett 77 1744 1749
    • (2007) Stat Probab Lett , vol.77 , pp. 1744-1749
    • Ditlevsen, S.1
  • 12
    • 41549100101 scopus 로고    scopus 로고
    • Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process
    • S Ditlevsen O Ditlevsen 2008 Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process Prob Eng Mech 23 170 179
    • (2008) Prob Eng Mech , vol.23 , pp. 170-179
    • Ditlevsen, S.1    Ditlevsen, O.2
  • 13
    • 37649030460 scopus 로고    scopus 로고
    • Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model
    • Art
    • Ditlevsen S, Lansky P (2005) Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys Rev E 71:Art. No. 011,907
    • (2005) Phys Rev e , vol.71 , Issue.11 , pp. 907
    • Ditlevsen, S.1    Lansky, P.2
  • 14
    • 33745189627 scopus 로고    scopus 로고
    • Estimation of the input parameters in the Feller neuronal model
    • Art
    • Ditlevsen S, Lansky P (2006) Estimation of the input parameters in the Feller neuronal model. Phys Rev E 73:Art. No. 061,910
    • (2006) Phys Rev e , vol.73 , Issue.61 , pp. 910
    • Ditlevsen, S.1    Lansky, P.2
  • 15
    • 35248883957 scopus 로고    scopus 로고
    • Parameters of stochastic diffusion processes estimated from observations of first hitting-times: Application to the leaky integrate-and-fire neuronal model
    • Art
    • Ditlevsen S, Lansky P (2007) Parameters of stochastic diffusion processes estimated from observations of first hitting-times: application to the leaky integrate-and-fire neuronal model. Phys Rev E 76:Art. No. 041,906
    • (2007) Phys Rev e , vol.76 , Issue.41 , pp. 906
    • Ditlevsen, S.1    Lansky, P.2
  • 16
    • 51549102021 scopus 로고    scopus 로고
    • Comparison of statistical methods for estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model from first-passage times data
    • (to appear)
    • Ditlevsen S, Lansky P (2008) Comparison of statistical methods for estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model from first-passage times data. American Institute of Physics Proceedings Series (to appear)
    • (2008) American Institute of Physics Proceedings Series
    • Ditlevsen, S.1    Lansky, P.2
  • 17
    • 0001208970 scopus 로고
    • Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test
    • J Durbin 1971 Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test J Appl Prob 8 431 453
    • (1971) J Appl Prob , vol.8 , pp. 431-453
    • Durbin, J.1
  • 19
    • 0001556572 scopus 로고
    • Les fonctions aléatories du type de markoff associées à certaines équations lineáires aux dérivées partiell es du type parabolique
    • R Fortet 1943 Les fonctions aléatories du type de markoff associées à certaines équations lineáires aux dérivées partiell es du type parabolique J Math pures Appl 22 177 243
    • (1943) J Math Pures Appl , vol.22 , pp. 177-243
    • Fortet, R.1
  • 20
    • 0002338948 scopus 로고
    • Random walk models for the spike activity of a single neuron
    • G Gerstein B Mandelbrot 1964 Random walk models for the spike activity of a single neuron Biophys J 4 41 68
    • (1964) Biophys J , vol.4 , pp. 41-68
    • Gerstein, G.1    Mandelbrot, B.2
  • 21
    • 0023939939 scopus 로고
    • Diffusion approximation and first-passage-time problem for a model neuron
    • V Giorno P Lansky A Nobile L Ricciardi 1988 Diffusion approximation and first-passage-time problem for a model neuron Biol Cybern 58 387 404
    • (1988) Biol Cybern , vol.58 , pp. 387-404
    • Giorno, V.1    Lansky, P.2    Nobile, A.3    Ricciardi, L.4
  • 22
    • 0000340275 scopus 로고
    • Diffusion approximations for neuronal activity including synaptic reversal potentials
    • F Hanson H Tuckwell 1983 Diffusion approximations for neuronal activity including synaptic reversal potentials J Theor Neurobiol 2 127 153
    • (1983) J Theor Neurobiol , vol.2 , pp. 127-153
    • Hanson, F.1    Tuckwell, H.2
  • 23
    • 0029355301 scopus 로고
    • On the parameter estimation for diffusion models of single neurons activity
    • J Inoue S Sato L Ricciardi 1995 On the parameter estimation for diffusion models of single neurons activity Biol Cybern 73 209 221
    • (1995) Biol Cybern , vol.73 , pp. 209-221
    • Inoue, J.1    Sato, S.2    Ricciardi, L.3
  • 25
    • 33745833056 scopus 로고    scopus 로고
    • Predicting spike timing of neocortical pyramidal neurons by simple threshold models
    • R Jolivet A Rauch HR Luscher W Gerstner 2006 Predicting spike timing of neocortical pyramidal neurons by simple threshold models J Comput Neurosci 21 35 49
    • (2006) J Comput Neurosci , vol.21 , pp. 35-49
    • Jolivet, R.1    Rauch, A.2    Luscher, H.R.3    Gerstner, W.4
  • 29
    • 34047238964 scopus 로고    scopus 로고
    • Randomness and variability of the neuronal activity described by the Ornstein-Uhlenbeck model
    • L Kostal P Lansky C Zucca 2007 Randomness and variability of the neuronal activity described by the Ornstein-Uhlenbeck model Netw Comput Neural Syst 18 63 75
    • (2007) Netw Comput Neural Syst , vol.18 , pp. 63-75
    • Kostal, L.1    Lansky, P.2    Zucca, C.3
  • 31
    • 0023130393 scopus 로고
    • Diffusion approximations of the neuronal model with synaptic reversal potentials
    • P Lansky V Lanska 1987 Diffusion approximations of the neuronal model with synaptic reversal potentials Biol Cybern 56 19 26
    • (1987) Biol Cybern , vol.56 , pp. 19-26
    • Lansky, P.1    Lanska, V.2
  • 32
    • 0029394120 scopus 로고
    • On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity
    • P Lansky L Sacerdote F Tomasetti 1995 On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity Biol Cybern 73 457 465
    • (1995) Biol Cybern , vol.73 , pp. 457-465
    • Lansky, P.1    Sacerdote, L.2    Tomasetti, F.3
  • 33
    • 33747272940 scopus 로고    scopus 로고
    • The parameters of the stochastic leaky integrate-and-fire neuronal model
    • P Lansky P Sanda J He 2006 The parameters of the stochastic leaky integrate-and-fire neuronal model J Comput Neurosci 21 211 223
    • (2006) J Comput Neurosci , vol.21 , pp. 211-223
    • Lansky, P.1    Sanda, P.2    He, J.3
  • 35
    • 41249095433 scopus 로고    scopus 로고
    • Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data
    • P Mullowney S Iyengar 2008 Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data J Comput Neurosci 24 179 194
    • (2008) J Comput Neurosci , vol.24 , pp. 179-194
    • Mullowney, P.1    Iyengar, S.2
  • 36
    • 0022082682 scopus 로고
    • Exponential trends of Ornstein-Uhlenbeck 1st-passage-time densities
    • A Nobile L Ricciardi L Sacerdote 1985 Exponential trends of Ornstein-Uhlenbeck 1st-passage-time densities J Appl Prob 22 360 369
    • (1985) J Appl Prob , vol.22 , pp. 360-369
    • Nobile, A.1    Ricciardi, L.2    Sacerdote, L.3
  • 37
    • 9744239998 scopus 로고    scopus 로고
    • Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model
    • L Paninski J Pillow E Simoncelli 2004 Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model Neural Comput 16 2533 2561
    • (2004) Neural Comput , vol.16 , pp. 2533-2561
    • Paninski, L.1    Pillow, J.2    Simoncelli, E.3
  • 38
    • 43449123054 scopus 로고    scopus 로고
    • Parameters of spike trains observed in a short time window
    • (in press)
    • Pawlas Z, Klebanov L, Prokop M, Lansky P (2008) Parameters of spike trains observed in a short time window. Neural Comput (in press)
    • (2008) Neural Comput
    • Pawlas, Z.1    Klebanov, L.2    Prokop, M.3    Lansky, P.4
  • 39
    • 55749107079 scopus 로고    scopus 로고
    • Parameters of the diffusion leaky integrate-and fire neuronal model for a slowly fluctuating signal
    • (to appear)
    • Picchini U, Lansky P, De Gaetano A, Ditlevsen S (2008) Parameters of the diffusion leaky integrate-and fire neuronal model for a slowly fluctuating signal. Neural Comput (to appear)
    • (2008) Neural Comput
    • Picchini, U.1    Lansky, P.2    De Gaetano, A.3    Ditlevsen, S.4
  • 41
    • 0141565240 scopus 로고    scopus 로고
    • Neocortical pyramidal cells respond as integrate-and fire neurons in vivo-like input currents
    • A Rauch L G HR Luscher W Senn S Fusi 2003 Neocortical pyramidal cells respond as integrate-and fire neurons in vivo-like input currents J Neurophysiol 90 1598 1612
    • (2003) J Neurophysiol , vol.90 , pp. 1598-1612
    • Rauch A.La Camera, G.1    Luscher, H.R.2    Senn, W.3    Fusi, S.4
  • 43
    • 0018606356 scopus 로고
    • The Ornstein-Uhlenbeck process as a model of neuronal activity
    • L Ricciardi L Sacerdote 1979 The Ornstein-Uhlenbeck process as a model of neuronal activity Biol Cybern 35 1 9
    • (1979) Biol Cybern , vol.35 , pp. 1-9
    • Ricciardi, L.1    Sacerdote, L.2
  • 44
    • 0000711915 scopus 로고
    • First-passage-time density and moments of the Ornstein-Uhlenbeck process
    • L Ricciardi S Sato 1988 First-passage-time density and moments of the Ornstein-Uhlenbeck process J Appl Prob 25 43 57
    • (1988) J Appl Prob , vol.25 , pp. 43-57
    • Ricciardi, L.1    Sato, S.2
  • 45
    • 0001571879 scopus 로고    scopus 로고
    • An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling
    • 2
    • L Ricciardi A Di Crescenzo V Giorno A Nobile 1999 An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling Math Japonica 50 2 247 322
    • (1999) Math Japonica , vol.50 , pp. 247-322
    • Ricciardi, L.1    Di Crescenzo, A.2    Giorno, V.3    Nobile, A.4
  • 46
    • 0033561846 scopus 로고    scopus 로고
    • The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex
    • S Shinomoto Y Sakai S Funahashi 1999 The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex Neural Comput 11 935 951
    • (1999) Neural Comput , vol.11 , pp. 935-951
    • Shinomoto, S.1    Sakai, Y.2    Funahashi, S.3
  • 47
    • 36149019489 scopus 로고
    • On the first passage time probability problem
    • A Siegert 1951 On the first passage time probability problem Phys Rev 81 617 623
    • (1951) Phys Rev , vol.81 , pp. 617-623
    • Siegert, A.1
  • 49
    • 0017799081 scopus 로고
    • Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters
    • H Tuckwell W Richter 1978 Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters J Theor Biol 71 167 180
    • (1978) J Theor Biol , vol.71 , pp. 167-180
    • Tuckwell, H.1    Richter, W.2
  • 50
    • 0019983720 scopus 로고
    • Neuronal firing and input variability
    • F Wan H Tuckwell 1982 Neuronal firing and input variability J Theoret Neurobiol 1 197 218
    • (1982) J Theoret Neurobiol , vol.1 , pp. 197-218
    • Wan, F.1    Tuckwell, H.2


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