Title: Conditional Baum-Welch, Dynamic Model Surgery, and the three-Poisson Dempster-Shafer model
Description: I present a Dempster-Shafer approach to estimating limits from Poisson counting data with nuisance parameters and two new methods, Conditional Baum-Welch and Dynamic Model Surgery, for achieving maximum-likelihood or maximum a-posteriori estimates of the parameters of Profile hidden Markov Models. Dempster-Shafer (DS) is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the event space. This eliminates the Bayesian dependence on prior distributions while allowing the incorporation of prior information when it is available. I use the Poisson Dempster-Shafer model (DSM) to derive a posterior DSM for the "Banff upper limits challenge" three-Poisson model. Profile hidden Markov Models (Profile HMMs) are widely used for protein sequence family modeling. The algorithm commonly used to estimate the parameters of Profile HMMs, Baum-Welch (BW), is prone to prematurely converge to local optima. I provide a description and proof of the Conditional Baum-Welch (CBW) algorithm, and show that it is able to parameterize Profile HMMs better than BW under a range of conditions including both protein and DNA sequence family models. I also introduce the Dynamic Model Surgery (DMS) method, which can be applied to either BW or CBW to help them achieve higher maxima by dynamically altering the structure of the Profile HMM during BW or CBW training. I conclude by describing the results of an application of these methods to the transposon (interspersed repeat) modeling problem that originally inspired the research.