Related papers: Bayesian interpretation of Generalized empirical l…
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…
High-precision measurements require optimal setups and analysis tools to achieve continuous improvements. Systematic corrections need to be modeled with high accuracy and known uncertainty to reconstruct underlying physical phenomena. To…
We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…
A problem of a new physical model test given observed experimental data is a typical one for modern experiments of high energy physics (HEP). A solution of the problem may be provided with two alternative statistical formalisms, namely…
Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true signal. Our estimators approximate certain…
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…
Many scientifically well-motivated statistical models in natural, engineering, and environmental sciences are specified through a generative process. However, in some cases, it may not be possible to write down the likelihood for these…
This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…
The Method of Moments [Pea94] is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially…
Capture-recapture experiments are widely used to estimate the abundance of a finite population. Based on capture-recapture data, the empirical likelihood (EL) method has been shown to outperform the conventional conditional likelihood (CL)…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in…