title: MAP estimation algorithm for phase response curves based on analysis of the observation process.
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.
authors.affiliation: Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G5-17 Nagatsuda-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan. keisuke@acs.dis.titech.ac.jp
authors.forename: Keisuke
authors.initials: K
authors.lastname: Ota
authors.forename: Toshiaki
authors.initials: T
authors.lastname: Omori
authors.forename: Toru
authors.initials: T
authors.lastname: Aonishi