Bayesian networks: exact inference and applications in forensic statistics

Exact inference on Bayesian networks has been developed through sophisticated algorithms. One of which, the variable elimination algorithm, identifies smaller components of the network, called factors, on which local operations are performed. In principle this algorithm can be used on any Bayesian network. However, to make the algorithm work in practice, it is crucial that an appropriate parameterization of the factors exist. Such a parameterization should ideally be closed under the local operations, but in general this is hard to achieve. In this thesis we investigate in detail the variable elimination algorithm, and we extend the class of Bayesian networks on which it can be applied. Bayesian networks are widely used within forensic statistics, especially within familial relationship inference from DNA data. The latter part of this thesis regards applications within forensics in general and relationship inference in particular. In familial relationship cases, it is essential to account for the possibility of mutations. There are a lot of existing methods to model the mutation process, and in the appended paper we investigate one particular property that is desirable for mutation models, namely stationarity