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Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…
Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different…
In latent variable models the parameter estimation can be implemented by using the joint or the marginal likelihood, based on independence or conditional independence assumptions. The same dilemma occurs within the Bayesian framework with…
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…
We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…
Neural posterior estimation (NPE) and neural likelihood estimation (NLE) are machine learning approaches that provide accurate posterior, and likelihood, approximations in complex modeling scenarios, and in situations where conducting…
In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally…
Semiparametric estimators admitting a von Mises expansion often reduce inference to the influence-function variance. This reduction is justified when the second-order remainder is negligible in variance, a condition that is stronger than…
Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved…
Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…
Misclassified variables used in regression models, either as a covariate or as the response, may lead to biased estimators and incorrect inference. Even though Bayesian models to adjust for misclassification error exist, it has not been…