Related papers: Monte Carlo Confidence Sets for Identified Sets

This paper introduces quasi-Monte Carlo latent variable models (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard…

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating…

A confidence sequence (CS) is a sequence of confidence sets that contains a target parameter of an underlying stochastic process at any time step with high probability. This paper proposes a new approach to constructing CSs for means of…

Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…

This research leverages Conformal Prediction (CP) in the form of Conformal Predictive Systems (CPS) to accurately estimate uncertainty in a suite of machine learning (ML)-based radio metric models [1] as well as in a 2-D map-based ML path…

Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

This paper studies the Model Selection Confidence Set (MSCS) methodology for univariate time series models involving autoregressive and moving average components, and applies it to study model selection uncertainty in the Italian…

Economic models produce moment inequalities, which can be used to form tests of the true parameters. Confidence sets (CS) of the true parameters are derived by inverting these tests. However, they often lack analytical expressions,…

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

We use approximate Bayesian computation (ABC) combined with an "improved" Markov chain Monte Carlo (IMCMC) method to estimate posterior distributions of model parameters in subgrid-scale (SGS) closures for large eddy simulations (LES) of…

Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…

We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…

A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…

Most scientific domains elicit the development of efficient algorithms and accessible scientific software. This thesis unifies our developments in three broad domains: Quasi-Monte Carlo (QMC) methods for efficient high-dimensional…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the…