Maximum-entropy and representative samples of neuronal activity: a dilemma

TL;DR

This paper explores two different applications of the maximum-entropy method to neuronal data samples, highlighting their differences and discussing which approach is preferable for neuroscience sampling problems.

Contribution

It clarifies the implications of applying maximum-entropy directly to samples versus larger populations, proposing the second approach as more advantageous.

Findings

The two routes yield inequivalent results.

Applying to the larger population and marginalizing is generally preferable.

Probability formulas relate knowledge about populations and samples.

Abstract

The present work shows that the maximum-entropy method can be applied to a sample of neuronal recordings along two different routes: (1) apply to the sample; or (2) apply to a larger, unsampled neuronal population from which the sample is drawn, and then marginalize to the sample. These two routes give inequivalent results. The second route can be further generalized to the case where the size of the larger population is unknown. Which route should be chosen? Some arguments are presented in favour of the second. This work also presents and discusses probability formulae that relate states of knowledge about a population and its samples, and that may be useful for sampling problems in neuroscience.