Related papers: A Channel-Based Perspective on Conjugate Priors

We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

Weighted Updating generalizes Bayesian updating, allowing for biased beliefs by weighting the likelihood function and prior distribution with positive real exponents. I provide a rigorous foundation for the model by showing that…

Prior elicitation methods for Bayesian analyses transfigure prior information into quantifiable prior distributions. Recently, methods that leverage copulas have been proposed to accommodate more flexible dependence structures when…

Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…

Databases often contain corrupted, degraded, and noisy data with duplicate entries across and within each database. Such problems arise in citations, medical databases, genetics, human rights databases, and a variety of other applied…

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This…

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized…

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop…

This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first…

We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…

A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…

The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…