Related papers: On the Asymptotic Efficiency of Approximate Bayesi…
In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo…
This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). The conceptual and methodological framework that underpins approximate Bayesian computation (ABC) is targetted primarily towards problems in…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
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…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
Background: We proposed approximate Bayesian computation with single distribution selection (ABC-SD) for estimating mean and standard deviation from other reported summary statistics. The ABC-SD generates pseudo data from a single…
We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows…
Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is…
We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…