Related papers: An MCMC Approach to Classical Estimation

We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…

An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…

Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…

Objectives: Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML).…

Efficient Bayesian model selection relies on the model evidence or marginal likelihood, whose computation often requires evaluating an intractable integral. The harmonic mean estimator (HME) has long been a standard method of approximating…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

Current state-of-the-art Quality Estimation (QE) in machine translation relies on massive, proprietary LLMs, raising data privacy concerns. We demonstrate that smaller, open-source LLMs (<30B parameters) are a viable, cost-effective and…

It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…

We develop a Laplace's method to compute the asymptotic expansions of sums of sharply peaked sequences. These series arise as discretizations (Riemann sums) of sharply-peaked integrals, whose asymptotic behavior can be computed by the…

We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior…

In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…

The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE:…

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In…

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…

Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…

The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust…

The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…