Related papers: Inferential models: A framework for prior-free pos…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
A great deal of interest has recently focused on conducting inference on the parameters in a high-dimensional linear model. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
In the past two decades, there has been a fast-growing literature on fiducial inference since it was first proposed by R. A. Fisher in the 1930s. However, most of the fiducial inference based methods and related approaches have been…
Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…
High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. When coupled with machine learning, a simulator makes it possible to infer the parameters of a theoretical model directly…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
Dempster-Shafer theory of imprecise probabilities has proved useful to incorporate both nonspecificity and conflict uncertainties in an inference mechanism. The traditional Bayesian approach cannot differentiate between the two, and is…