Related papers: Horseshoe Priors and MDP
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…
A central challenge for intelligent agents in an uncertain world is striking the right balance between utility maximization and resource use, not only for external movement but also for internal computation. Existing theories of control…
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…
Over the past two decades, shrinkage priors have become increasingly popular, and many proposals can be found in the literature. These priors aim to shrink small effects to zero while maintaining true large effects. Horseshoe-type priors…
Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the…
Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
We examine the effect of a prior that favours low values of fine-tuning on Bayesian multi-dimensional fits of the constrained minimal supersymmetric standard model (CMSSM or mSUGRA) to current data. The dark matter relic density, the…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
Currently several Bayesian approaches are available to estimate large sparse precision matrices, including Bayesian graphical Lasso (Wang, 2012), Bayesian structure learning (Banerjee and Ghosal, 2015), and graphical horseshoe (Li et al.,…
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question.…
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…
We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has…
Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…
The new class of Markov processes is proposed to realize the flexible shrinkage effects for the dynamic models. The transition density of the new process consists of two penalty functions, similarly to Bayesian fused LASSO in its functional…
We propose Bayesian Univariate-Guided Sparse Regression (BUGS), a novel global-local shrinkage framework that incorporates marginal association information directly into the prior through a continuous modulation of shrinkage. Unlike…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
Choosing between classical and Bayesian sparse regression methods involves a real trade-off: penalized estimators like Lasso run in milliseconds but give no uncertainty estimates,while Horseshoe and Spike-and-Slab priors produce full…