MAP estimation algorithm for phase response curves based on analysis of the observation process |
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Authors: | Keisuke Ota Toshiaki Omori Toru Aonishi |
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Affiliation: | (1) Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G5-17 Nagatsuda-cho, Midori-ku, Yokohama Kanagawa, 226-8502, Japan;(2) The University of Tokyo, Transdisciplinary Sciences Bldg, 5-1-5 Kashiwanoha, Kashiwa Chiba, 277-8561, Japan;(3) Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako Saitama, 351-0198, Japan |
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Abstract: | 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. Action Editor: John Rinzel |
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Keywords: | Phase response curve Liner response theory Fokker-Planck equation Bayesian approach Hyper-parameter estimation |
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