This monograph is based on lectures presented at a 1999 CBMS Summer Research Conference. It develops the probability models for genetic data on related individuals, from the meiosis level to data on extended pedigrees. The focus is on simple Mendelian traits, such as DNA markers, but on joint models for data at multiple genetic loci, such as arise in modern genome scan studies. The statistical approach is that of likelihood, maximum likelihood estimation, and methods for the analysis of latent-variable and hidden-Markov models including the EM algorithm, the Baum algorithm, and Monte Carlo imputation methods.

The first half of the monograph develops the basic concepts and approaches, focusing on the ideas of gene identity by descent and the tracing of gene descent in pedigrees using meiosis indicators or inheritance vectors. This material should be accessible to first-year graduate students in statistics or biostatistics. Only a basic understanding of discrete probability and mathematical statistics (likelihood inference) are assumed. No genetic knowledge is presupposed, although some familiarity with basic terminology will be helpful.

Building on these foundations, the second half of the monograph develops Markov chain Monte Carlo (MCMC) and Monte Carlo likelihood methods for the analysis of data on individuals in a known pedigree structure. This material is more specialized, but should be accessible to those who have mastered the earlier chapters, or who have studied hidden Markov models and MCMC methods. The objective is Monte Carlo estimation of likelihood surfaces and conditional probabilities, rather than Bayesian sampling of parameter spaces and posterior distributions. The penultimate chapter illustrates the methods presented, through detailed analysis of two examples, using recently implemented MCMC samplers and likelihood estimation procedures. The final chapter discusses related research areas and the potential for further development of methods.