Related papers: Bayesian interpretation of Generalized empirical l…

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

We demonstrate how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (ME). A general example of updating with data and moments is shown. A specific econometric…

The generalized maximum entropy method (GMEM) is a special modification of the standard maximum entropy method (MEM) which seeks solutions in the space of complex functions. In this work a reduced version of the GMEM intended for…

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…

Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSS) whose lifetime increases with the system size. In the paradigmatic Hamiltonian Mean-field Model (HMF) out-of-equilibrium phase…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…

Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for…

The maximum likelihood estimation is computationally demanding for large datasets, particularly when the likelihood function includes integrals. Subsampling can reduce the computational burden, but it often results in efficiency loss.This…

We introduce estimation and test procedures through divergence minimiza- tion for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with…

Parameter ensembles or sets of random effects constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where several decision theoretic frameworks can be deployed. The…

Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE),…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex…

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…