Related papers: Asymptotically optimal nonparametric empirical Bay…
Nonparametric empirical Bayes methods provide a flexible and attractive approach to high-dimensional data analysis. One particularly elegant empirical Bayes methodology, involving the Kiefer-Wolfowitz nonparametric maximum likelihood…
The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter…
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems.…
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration.…
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with…