Related papers: On the non-arbitrary assignment of equi-probable p…

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…

There are things we know, things we know we don't know, and then there are things we don't know we don't know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

Bayesian statistics emphasizes the importance of prior distributions, yet finding an appropriate one is practically challenging. When multiple sample results are taken regarding the frequency of the same event, these samples may be…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…

In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…

This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…

As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…

This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). Indirect inference (II) is a classical likelihood-free approach that pre-dates the main developments of ABC and relies on simulation from a…

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…