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We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace…
Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all…
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…
Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard…
This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…
There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…
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…
The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several…
We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish…
This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…
Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. In this article,…
We show that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable…
Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in some cases efficient, MPL estimation…
This article extends the scope of empirical likelihood methodology in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than $\sqrt{n}$-rates of convergence, and settings in which there…