Bayesian Statistics in Computational Anatomy∗

Probability , Statistics , and Computational Science Niko

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur ...

1 Bayesian computational methods

If, in the mid 1980’s, one had asked the average statistician about the difficulties of using Bayesian Statistics, his/her most likely answer would have been “Well, there is this problem of selecting a prior distribution and then, even if one agrees on the prior, the whole Bayesian inference is simply impossible to implement in practice!” The same question asked in the 21th Century does not pro...

Non-linear Bayesian prediction of generalized order statistics for liftime models

In this paper, we obtain  Bayesian prediction intervals as well as Bayes predictive estimators under square error loss for generalized order statistics when the distribution of the underlying population belongs to a family which includes several important distributions.

Modified versions of Bayesian Information Criterion for genome-wide association studies

Dynamic Bayesian beta models

We develop a dynamic Bayesian beta model for modeling and forecasting single time series of proportions. This work is related to the class of the so called dynamic generalized linear models (DGLM). We use non-conjugate priors and some forms of approximate Bayesian analysis, including Linear Bayesian estimation. Some applications to both real and simulated data are provided.