Statistical Data Assimilation: Formulation and Examples From Neurobiology

Anna Miller,Henry D I Abarbanel,Jason Platt,Arij Daou,Daniel Margoliash,Dawei Li

doi:10.3389/fams.2018.00053

Abstract

For the Research Topic Data Assimilation and Control: Theory and Applications in Life Sciences we first review the formulation of statistical data assimilation (SDA) and discuss algorithms for exploring variational approximations to the conditional expected values of biophysical aspects of functional neural circuits. Then we report on the application of SDA to (1) the exploration of properties of individual neurons in the HVC nucleus of the avian song system, and (2) characterizing individual neurons formulated as very large scale integration (VLSI) analog circuits with a goal of building functional, biophysically realistic, VLSI representations of functional nervous systems. Networks of neurons pose a substantially greater challenge, and we comment on formulating experiments to probe the properties, especially the functional connectivity, in song command circuits within HVC.

Highlights

A broad class of “inverse” problems presents itself in many scientific and engineering inquiries
The penultimate topic we address is the use of statistical data assimilation (SDA) to calibrate very large scale integration (VLSI) analog chips designed and built as components of a developing instantiation of the full songbird song command network, called HVC
We take our examples of the use of SDA in neurobiology from experiments on the avian song system

Summary

Introduction

A broad class of “inverse” problems presents itself in many scientific and engineering inquiries. The existence of large, information rich, well curated data sets from increasingly sophisticated observations on complicated nonlinear systems has set new challenges to the information transfer task. Assisting with this challenge are new substantial computational capabilities. Together they have provided an arena in which principled formulation of this information transfer along with algorithms to effect the transfer have come to play an essential role. This paper reports on some efforts to meet this class of challenge within neuroscience. Many of the ideas are applicable much more broadly than our focus, and we hope the reader will find this helpful in their own inquiries

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