Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given data sets. This procedure is well-developed in the Bayesian perspective, in which one infers probability distributions describing to what extent various possible parameters agree with the data. In this paper we motivate and review probabilistic modeling for adaptive immune receptor repertoire data then describe progress and prospects for future work, from germline haplotyping to adaptive immune system deployment across tissues. The relevant quantities in immune sequence analysis include not only continuous parameters such as gene use frequency, but also discrete objects such as B cell clusters and lineages. Throughout this review, we unravel the many opportunities for probabilistic modeling in adaptive immune receptor analysis, including settings for which the Bayesian approach holds substantial promise (especially if one is optimistic about new computational methods). From our perspective the greatest prospects for progress in probabilistic modeling for repertoires concern ancestral sequence estimation for B cell receptor lineages, including uncertainty from germline genotype, rearrangement, and lineage development.
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