Related papers: Divide-and-conquer with finite sample sizes: valid…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…
Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a…
Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
Computational validation is vital for all large-scale quantum computers. One needs computers that are both fast and accurate. Here we apply precise, scalable, high order statistical tests to data from large Gaussian boson sampling (GBS)…
The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…
The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing…