TY - JOUR
T1 - MAP estimation algorithm for phase response curves based on analysis of the observation process
AU - Ota, Keisuke
AU - Omori, Toshiaki
AU - Aonishi, Toru
N1 - Funding Information:
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research (No.18700299) from MEXT of Japan.
PY - 2009
Y1 - 2009
N2 - Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.
AB - Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.
KW - Bayesian approach
KW - Fokker-Planck equation
KW - Hyper-parameter estimation
KW - Liner response theory
KW - Phase response curve
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U2 - 10.1007/s10827-008-0104-8
DO - 10.1007/s10827-008-0104-8
M3 - Article
C2 - 18751879
AN - SCOPUS:62349136728
VL - 26
SP - 185
EP - 202
JO - Journal of Computational Neuroscience
JF - Journal of Computational Neuroscience
SN - 0929-5313
IS - 2
ER -