Evaluating the performance of a block updating McMC sampler in a simple genetic application

Markov chain Monte Carlo (McMC) methods have provided an enormous breakthrough in the analysis of large complex problems such as those which frequently arise in genetic applications. The richness of the inference and the flexibility of an McMC Bayesian approach in terms of design, data structure that can be analysed, and models that can be posed, is indisputable. However, despite the strengths of the Bayesian approach, it is important to acknowledge that there are other, often easier, ways of tackling a problem. This is so, especially when simpler, qualitative answers are sought, such as presence or absence of a quantitative trait locus. We critically evaluate the behaviour of a Bayesian McMC block sampler for the detection of a quantitative trait locus by linkage with marker data, and compare it with a traditional least squares method. Some practical issues are illustrated by discussing the pros and cons of a Bayesian block updating sampling scheme versus the least squares method in the context of a simple genetic mapping problem. Depending on the focus of analysis, we show that the McMC sampler does not always outperform the simpler approach from a frequentist perspective, and, more to the point, may not always perform appropriately in any particular replication.