MAP estimation algorithm for phase response curves based on analysis of the observation process

Keisuke Ota, Toshiaki Omori, Toru Aonishi

Research output: Contribution to journalArticle

20 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)185-202
Number of pages18
JournalJournal of Computational Neuroscience
Volume26
Issue number2
DOIs
Publication statusPublished - 2009 Jan 1

Keywords

  • Bayesian approach
  • Fokker-Planck equation
  • Hyper-parameter estimation
  • Liner response theory
  • Phase response curve

ASJC Scopus subject areas

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience

Fingerprint Dive into the research topics of 'MAP estimation algorithm for phase response curves based on analysis of the observation process'. Together they form a unique fingerprint.

  • Cite this