Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

There are essentially two kinds of approaches for learning the structure of Bayesian Networks (BNs) from data. The first approach tries to find a graph which satis es all the constraints implied by the empirical conditional independencies measured in the data [PV91, SGS00a, Shi00]. The second approach searches through the space of models (either DAGs or PDAGs), and uses some scoring metric (typically Bayesian or some approximation, such as BIC/MDL) to evaluate the models [CH92, Hec95, Hec98, Kra98], typically returning the highest scoring model found. Our main interest is in learning BN structure from gene expression data [FLNP00, HGJY01, MM99, SGS00b]. In domains such as this, where the ratio of the number of observations to the number of variables is low (i.e., when we have sparse data), selecting a threshold for the conditional independence (CI) tests can be tricky, and repeated use of such tests can lead to inconsistencies [DD99]. Bayesian s...

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We present two methodologies for Bayesian model choice and averaging in Gaussian directed acyclic graphs (dags). In both cases model determina-tion is carried out by implementing a reversible jump Markov Chain Monte Carlo sampler. The dimension{changing move involves adding or dropping a (directed) edge from the graph. The rst methodology extends the results in Giudici and Green (1999), by excluding all non{moralized dags and searching in the space of their essential graphs. The second methodology employs the results in Geiger and Heckerman (1999) and searches directly in the space of all dags. To achieve this aim we rely on the concept of adjacency matrices, which provides a relatively inexpensive check for acyclicity. The performance of our procedure is illustrated by means of two simulated datasets.

Fitting a graphical chain model to a multivariate data set consists of di erent steps some of which being rather tedious. The paper outlines the basic features and overall architecture of the computer program GraphFitI which provides the application of a selection strategy for tting graphical chain models and for visualising the resulting models as a graph. It additionally supports the user at the di erent steps of the analysis by an integrated help system.

In this paper we consider the problem of estimating total population size from a series of incomplete census data. We observe that inference is typically highly sensitive to the choice of model and we demonstrate how Bayesian model averaging techniques easily overcome this problem. Using reversible jump MCMC simulation we calculate posterior model probabilities which are used to estimate model averaged statistics of interest. We provide a detailed description of the simulation procedures involved and consider a wide variety of modelling issues, such as the range of models considered, their parameterisation, both prior choice and sensitivity, and computational efficiency. We consider an example in detail concerning adolescent injuries in Pennsylvania on the basis of medical, school and survey data. In the context of this example, we discuss the relationship between posterior model probabilities and the associated information criteria values for model selection. We also discus...

This document is an extension of the talk I gave at the gR meeting in Aalborg on 19 September 2003. It outlines a proposed design for gR, a graphical models library for R. This design is similar to the design of BNT, but is much more general, in that it supports undirected models and chain graphs, and allows parameters to be represented as random variables (Bayesian modeling).

Learning dynamic Bayesian network structures provides a principled mechanism for identifying conditional dependencies in time-series data. An important assumption of traditional DBN structure learning is that the data are generated by a stationary process, an assumption that is not true in many important settings. In this paper, we introduce a new class of graphical model called a nonstationary dynamic Bayesian network, in which the conditional dependence structure of the underlying data-generation process is permitted to change over time. Non-stationary dynamic Bayesian networks represent a new framework for studying problems in which the structure of a network is evolving over time. Some examples of evolving networks are transcriptional regulatory networks during an organism’s development, neural pathways during learning, and traffic patterns during the day. We define the non-stationary DBN model, present an MCMC sampling algorithm for learning the structure of the model from time-series data under different assumptions, and demonstrate the effectiveness of the algorithm on both simulated and biological data.