Bayesian astrostatistics: a backward look to the future

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in "Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in 2012), the inaugural volume for the Springer Series in Astrostatistics. Version 2 has minor clarifications and an additional referenc

Bayesian Hierarchical Modelling for Tailoring Metric Thresholds

Software is highly contextual. While there are cross-cutting `global' lessons, individual software projects exhibit many `local' properties. This data heterogeneity makes drawing local conclusions from global data dangerous. A key research challenge is to construct locally accurate prediction models that are informed by global characteristics and data volumes. Previous work has tackled this problem using clustering and transfer learning approaches, which identify locally similar characteristics. This paper applies a simpler approach known as Bayesian hierarchical modeling. We show that hierarchical modeling supports cross-project comparisons, while preserving local context. To demonstrate the approach, we conduct a conceptual replication of an existing study on setting software metrics thresholds. Our emerging results show our hierarchical model reduces model prediction error compared to a global approach by up to 50%.Comment: Short paper, published at MSR '18: 15th International Conference on Mining Software Repositories May 28--29, 2018, Gothenburg, Swede

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences