Porta Mana, P. | bioRxiv Science

bioRxiv2018

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

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.

neuroscience↗

bioRxiv2018

Inferring health conditions from fMRI-graph data

Automated classification methods for disease diagnosis are currently in the limelight, especially for imaging data. Classification does not fully meet a clinicians needs, however: in order to combine the results of multiple tests and decide on a course of treatment, a clinician needs the likelihood of a given health condition rather than binary classification yielded by such methods. We illustrate how likelihoods can be derived step by step from first principles and approximations, and how they can be assessed and selected, using fMRI data from a publicly available data set containing schizophrenic and healthy control subjects, as a working example. We start from the basic assumption of partial exchangeability, and then the notion of sufficient statistics and the \"method of translation\" (Edgeworth, 1898) combined with conjugate priors. This method can be used to construct a likelihood that can be used to compare different data-reduction algorithms. Despite the simplifications and possibly unrealistic assumptions used to illustrate the method, we obtain classification results comparable to previous, more realistic studies about schizophrenia, whilst yielding likelihoods that can naturally be combined with the results of other diagnostic tests.

neuroscience↗