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In many fields, researchers are interested in discovering features with substantial effect on the response from a large number of features and controlling the proportion of false discoveries. By incorporating the knockoff procedure in the Bayesian framework, we develop the Bayesian knockoff filter (BKF) for selecting features that have important effect on the response. In contrast to the fixed knockoff variables in the frequentist procedures, we allow the knockoff variables to be continuously updated in the Markov chain Monte Carlo. Based on the posterior samples and elaborated greedy selection procedures, our method can distinguish the truly important features as well as controlling the Bayesian false discovery rate at a desirable level. Numerical experiments on both synthetic and real data demonstrate the advantages of our method over existing knockoff methods and Bayesian variable selection approaches, i.e., the BKF possesses higher power and yields a lower false discovery rate.
We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algorithm is shown to be geometrically ergodic regardless of whether the n
In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In
The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often used for the regression coefficients in Bayesian logistic regression models. The resulting int
As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zeldovic
For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of our adapti