Related papers: Functional Uniform Priors for Nonlinear Modelling
Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
We study prior distributions for Poisson parameter estimation under $L^1$ loss. Specifically, we construct a new family of prior distributions whose optimal Bayesian estimators (the conditional medians) can be any prescribed increasing…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
This paper is concerned with the construction of prior free posterior distributions which rely on the use of one step ahead predictive distribution functions. These are typically more straightforward to motivate than prior distributions.…
Consider binary observations whose response probability is an unknown smooth function of a set of covariates. Suppose that a prior on the response probability function is induced by a Gaussian process mapped to the unit interval through a…
We propose a prior distribution for the number of components of a finite mixture model. The novelty is that the prior distribution is obtained by considering the loss one would incur if the true value representing the number of components…
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…
The Bayesian treatment of neural networks dictates that a prior distribution is specified over their weight and bias parameters. This poses a challenge because modern neural networks are characterized by a large number of parameters, and…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion…
We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals, to be called "regression functionals'', defined on large…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…