Related papers: Approximation of improper priors
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
In this article we study the limiting empirical measure of zeros of higher derivatives for sequences of random polynomials. We show that these measures agree with the limiting empirical measure of zeros of corresponding random polynomials.…
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective…
I propose a novel approach to simultaneous inference that alleviates the need to specify a correlational structure among marginal errors. The vacuous orientation assumption retains what the normal i.i.d. assumption implies about the…
In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance. This study leverages ideas from…
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…
In this paper we introduce a new notion of convergence of sparse graphs which we call Large Deviations or LD-convergence and which is based on the theory of large deviations. The notion is introduced by "decorating" the nodes of the graph…
Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with…
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…
Parameter estimates in misspecified models converge to pseudo-true parameter values, which minimize a population objective function. Pseudo-true values often differ from quantities of economic interest, raising questions of how, if at all,…
In this brief research note I present a generalized version of the Savage-Dickey Density Ratio for representation of the Bayes factor (or marginal likelihood ratio) of nested statistical models; the new version takes the form of a…
Let L_1 be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in L_1 converges to 0 in measure if and only if each of its subsequences admits another subsequence which converges to 0 in…
Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…
For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the…
Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…