This thesis considers graphical models that are represented by families of probability distributions having sets of conditional independence constraints specified by an influence diagram. Chapter 1 introduces the notion of a directed acyclic graph, a particular type of independence graph, which is used to define the influence diagram. Examples of such structures are given, and of how they are used in building a graphical model. Models may contain discrete or continuous variables, or both. Local computational schemes using exact probabilistic methods on these models are then reviewed. Chapter 2 presents a review of the use of graphical models in legal reasoning literature. The use of likelihood ratios to propagate probabilities through an influence diagram is investigated in this chapter, and a method for calculating LRs in graphical models is presented. The notion of recovering the structure of a graphical model from observed data is studied in Chapter 3. An established method on discrete data is described, and extended to include continuous variables. Kernel methods are introduced and applied to the probability estimation needed in these methods. Chapters 4 and 5 describe the use of stochastic simulation on mixed graphical association models. Simulation methods, in particular the Gibbs sampler, can be used on a wider range of models than exact probabilistic methods. Also estimates of marginal density functions of continuous variables can be obtained by using kernel estimates on the simulated values; exact methods generally only provide the marginal means and variances of continuous variables.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:641931 |
| Date | January 1994 |
| Creators | Brewer, Mark John |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/10836 |
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