Related papers: Universality of Bayesian mixture predictors
We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases---either a discrete alternative or a continuous…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…
Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…
Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function.…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…
Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood…
This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous…
We consider an interacting bipartite network through a Bayesian game-theoretic framework and demonstrate that weak measurements introduce an inherent asymmetry that is not present when using standard projective measurements. These…
We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics,…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…
Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data…
As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…