The Annals of Applied Statistics

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Yuriy Mishchenko, Joshua T. Vogelstein, and Liam Paninski

Full-text: Open access

Abstract

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network’s connectivity matrix. We derive a Monte Carlo Expectation–Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1 penalization methods.

Article information

Source
Ann. Appl. Stat., Volume 5, Number 2B (2011), 1229-1261.

Dates
First available in Project Euclid: 13 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1310562720

Digital Object Identifier
doi:10.1214/09-AOAS303

Mathematical Reviews number (MathSciNet)
MR2849773

Zentralblatt MATH identifier
1223.62162

Keywords
Sequential Monte Carlo Metropolis–Hastings spike train data point process generalized linear model

Citation

Mishchenko, Yuriy; Vogelstein, Joshua T.; Paninski, Liam. A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data. Ann. Appl. Stat. 5 (2011), no. 2B, 1229--1261. doi:10.1214/09-AOAS303. https://projecteuclid.org/euclid.aoas/1310562720


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