BAYSM2016

Drawing inferences about causal effects of treatments, interventions and actions is central to decision making in many research disciplines. We review the Bayesian approach to causal inference under the potential outcome approach, which defines a causal effect as the comparison of potential outcomes under different treatment conditions for the same units. Focus will be on settings with intermediate variables, that is, post-treatment variables potentially affected by the treatment and also affecting the response, where Principal Stratification is used to define causal estimands and formally express structural and distributional assumptions. Bayesian inference is natural for causal inference, and PS analysis in particular, inherently a missing data problem under the potential outcome approach. The general structure of Bayesian inference will be presented and specific scientific applications will be illustrated, such as the analysis of clustered encouragement designs and trials with treatment switching. Important open questions will be discussed.
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We discuss an application of feature allocation models to inference for tumor heterogeneity. We use a variation of Indian buffet process models to facilitate model-based imputation of hypothetical subpopulations of tumor cells, characterized by unique sets of somatic mutations and/or structural variants like copy number variations. Implementing posterior inference in this problem gives rise to several computational challenges. We discuss solutions based on fractional Bayes factors, MAD Bayes small variance asymptotics, and a reversible jump implementation for a determinantal point process.
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An A/B test is really just another name for an experiment that happens to be conducted online. However, the mechanics of an online experiment are dramatically different than those of a medical, agricultural, or manufacturing experiment. In particular, the cost of a type-I error is much lower. The standard playbook for experimental design mandates that you control for type-I errors before doing anything else. This results in experiments that are needlessly conservative, sometimes by multiple orders of magnitude. An alternative approach is to run the A/B test as an optimization problem, where the goal is to minimize regret. A technique known as "Thompson sampling" is a simple, intuitive heuristic based on Bayesian reasoning that also happens to outperform all similar heuristics. Thompson sampling uses "probability matching" to manage the explore-exploit tradeoff in multi-armed bandit problems. Each new observation is assigned to an arm according to the probability of that arm being "the best". The heuristic can be applied across a very broad class of reward distributions, making it easy to incorporate many of the "good" ideas from classical experimental design into an online A/B test.
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Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. In this talk I will describe Bayesian spatiotemporal models that detect task-related activation patterns as well as Bayesian hierarchical models for the estimation of brain connectivity.

We will interpret the usual Bayesian approach via the notion of exchangeability. In particular, we will see how the Bayesian nonparametric approach can be understood as the most natural generalization of Bayesian parametric models when the prior does not select finite-dimensional families of distribution (as in the parametric case).
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