CIF: Small: Controlling Uncertainty: On the Sequential Refinement of Belief

University Of California-San Diego, La Jolla CA

Investigators

Abstract

Controlling Uncertainty: On the Sequential Refinement of Belief This research focuses on a variety of information acquisition and sensing applications in which a decision maker, by carefully controlling a sequence of actions with uncertain outcomes, dynamically refines his belief about a phenomenon of interest in a speedy, accurate, and efficient manner. The model includes a class of applications in communications, design of experiments, cognitive science, and sensor management. In particular, the following three problems are tackled. ? Active Sequential Hypothesis Testing: There are a set of hypotheses, one of which is true. A decision maker is asked to identify the correct hypothesis by sequentially employing either one of available sensing actions. Actions costs differently and produce statistically distinct observations. Given a penalty for error in declaration, the work investigates the optimal selection of sensing actions. ? Feedback Schemes for Joint Source-Channel Coding with Bandwidth Expansion: A message is to be conveyed to a receiver over a noisy memoryless channel with feedback. The expected distortion between the message and the receiver?s construction is sought to be minimized over the choice of causal encoding functions as well as the decoding function. ? Joint Source-Channel Coding over a Multiple Access Channel with Feedback: Multiple transmitters convey messages to a common receiver over a noisy memoryless multiple access channel with perfect output feedback. These problems boil down to the sequential control of a dynamical system whose system is the conditional distribution of the unknown (true hypothesis, message, etc) and whose dynamics is dictated by the Bayes? rule. In particular, the optimal choice of actions, i.e. refinement in the conditional distribution and reduction of uncertainty, is investigated.