Publication Summary and Abstract
Caballero JA (2012), Multi-alternative sequential analysis as a realistic model of biological decision-making, PhD thesis, The University of Sheffield, UK.
What is the decision-making mechanism in the nervous system? The recurrent circuits interconnecting the cortex, basal ganglia and thalamus have long been regarded as the key vertebrate substrate for this function. Sequential analysis is a statistical inference method that does not assume that the number of observations available is fixed beforehand; conversely, it makes one observation after another, only stopping when a desired accuracy is reached. This makes sequential tests ideal tools to model biological decision-making processes and their time course, and so they have been proposed to map into the mentioned circuitry. Nevertheless, the examination of the compatibility of these algorithms with the known properties of the substrate, is just beginning. In this dissertation we contribute to this effort by presenting generalisations/extensions of the multi-alternative sequential analysis theory, that accommodate neuro-biological properties like: realistic variability of the evidence for a decision (i.e. of neural events), membrane dynamics, connection weights, latencies and the multiple recursions found within the substrate. Such properties were incorporated one by one to analyse the implications of each addition. This undertaking yielded many insights on various aspects of biological decision-making and suggested that the properties of the nervous system are indeed amenable with sequential analysis. Most of this work is based on a well known asymptotically optimal multi-alternative sequential test. Here we also point out the existence of a Bayesian (optimal) multi-alternative sequential test. Apart from being optimal, it enables us to model the impact of the costs inherent to a decision process carried out over time. We therefore finally produce a recursive generalisation of this test, and propose such generalisation as the actual pattern/mechanism that the nervous system might be approximating during decision-making.