Related papers: Optimal compromise between incompatible conditiona…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…
The target measure $\mu$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $\mu$. A ``coupling from the past'' construction of the…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of…
Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and…
Parametric portfolio policies may experience estimation risk. I develop a generalized Bayesian framework that updates priors, delivering a posterior distribution over characteristic tilts and out-of-sample returns that is the unique…
Maximum likelihood estimates (MLEs) are asymptotically normally distributed, and this property is used in meta-analyses to test the heterogeneity of estimates, either for a single cluster or for several sub-groups. More recently, MLEs for…
We present a Bayesian mixture model for estimating the joint distribution of mixed ordinal, nominal, and continuous data conditional on a set of fixed variables. The model uses multivariate normal and categorical mixture kernels for the…
We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…
We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry breaking binary direction $\bm{B}\in\{-1,+1\}^{N}$, onto which the projections have a Gaussian…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current…
Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation…