统计计算

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.…

This paper proposes Incremental Seeded Expectation Maximization, an algorithm that improves upon the traditional Expectation Maximization computational flow for clusterwise or finite mixture linear regression tasks. The proposed method…

Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…

Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…

Background and Objective: Variables collected over time, or longitudinally, such as biologic measurements in electronic health records data, are not simple to summarize with a single time-point, and thus can be more holistically…

As mobile phones become ubiquitous, high-frequency smartphone positioning data are increasingly being used by researchers studying the mobility patterns of individuals as they go about their daily routines and the consequences of these…

Sampling algorithms drive probabilistic machine learning, and recent years have seen an explosion in the diversity of tools for this task. However, the increasing sophistication of sampling algorithms is correlated with an increase in the…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

The weighted multiplier method (WMM) is an extension of the traditional method of back-calculation method to estimate the size of a target population, which synthesizes available evidence from multiple subgroups of the target population…

We introduce a novel and flexible framework for constructing locally adaptive Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For…

We make two closely related theoretical contributions to the use of importance sampling schemes. First, for independent sampling, we prove that the minimax optimal trial distribution coincides with the target if and only if the target…

Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of the integration time…

Ratio statistics and distributions are fundamental in various disciplines, including linear regression, metrology, nuclear physics, operations research, econometrics, biostatistics, genetics, and engineering. In this work, we introduce two…

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can…

A Bayesian coreset is a small, weighted subset of a data set that replaces the full data during inference to reduce computational cost. The state-of-the-art coreset construction algorithm, Coreset Markov chain Monte Carlo (Coreset MCMC),…

Modern implementations of Hamiltonian Monte Carlo and related MCMC algorithms support sampling of probability functions that embed numerical root-finding algorithms, thereby allowing fitting of statistical models involving analytically…

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…

Simulating mixtures of distributions with signed weights proves a challenge as standard simulation algorithms are inefficient in handling the negative weights. In particular, the natural representation of mixture variates as associated with…

Bayesian inference is conceptually elegant, but calculating posterior expectations can entail a heavy computational cost. Monte Carlo methods are reliable and supported by strong asymptotic guarantees, but do not leverage smoothness of the…