Bayesian inference for detection problems in biology

This thesis is about different kinds of detection problems in biology: detection of DNA sequences in crime scene samples, detection of harmful bacteria in feed and food stuff and detection of epidemical diseases in animal populations. In each case, biological data is produced or collected in order to determine which DNA sequences, bacteria types or diseases are present, if any. However, the state of nature will often remain uncertain due to limited amounts of samples, low quality samples and imperfect methods for detection and classification. For correct and efficient interpretation of such data it is therefore often necessary to use statistical methods, taking the different sources of uncertainty into account. Several Bayesian models for analysis of such data, for determining the performance of detection methods, and for deciding on the optimal analysis procedure are developed and implemented. In paper I of this thesis it is investigated how the quality in forensic DNA profiles, such as allele dropout rates, changes with different analysis settings, and how the results depend on features in the DNA sample, such as the DNA concentration and marker type. Regression models are developed and the better analysis setting is determined. In paper II Bayesian decision theory is used to determine the optimal forensic DNA analysis procedure, after the DNA concentration and level of degradation in the sample have been estimated. It is assumed the alternatives for DNA analysis are 1) using a standard assay, 2) using the standard assay and a complementary assay, or 3) the analysis is cancelled. In paper III detection models for bacteria are developed. It is shown how heterogeneous experimental data can be used to learn about the sensitivity of detection methods for specific bacteria types, such as Bacillus anthracis. As exemplified in the paper, such results are useful e.g. when evaluating negative analysis results. Finally, in paper IV a Bayesian method for early detection of disease outbreaks in animal populations is developed and implemented. Based on reported neurological syndromes in horses, connected e.g. with the West Nile Virus, the probability of an outbreak is computed using a Gibbs sampling procedure