Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm

The paper suggests a procedure to derive stochastic population forecasts adopting an expert-based approach. As in a previous work by Billari et al. (2012), experts are required to provide evaluations, in the form of conditional and unconditional scenarios, on summary indicators of the demographic components determining the population evolution, i.e. fertility, mortality and migration. Here two main purposes are pursued. First, the demographic components are allowed to have some kind of dependence. Second, as a result of the existence of a body of shared information, possible correlations among experts are taken into account. In both cases, the dependence structure is not imposed by the researcher but it is indirectly derived through the scenarios elicited from the experts. To address these issues, the method is based on a mixture model, within the so-called Supra-Bayesian approach according to which expert evaluations are treated as data. The derived posterior distribution for the demographic indicators of interest is used as forecasting distribution and a Markov Chain Monte Carlo algorithm is designed to approximate this posterior. The paper provides the questionnaire which was designed by the authors to collect expert opinions. Finally, an application to the forecast of the Italian Population from 2010 up to 2065 is proposed

Synthesis of Distributions through sets: a unitary approach

This paper suggests a general framework for dealing in a unified way with the problem of the synthesis of a distribution through sets. Following this view, interesting methods and quantities of sinthesis generally discussed separately are seen as particular cases of the general concept of mean of a distribution here presented. Various examples of means, including some based on the use of probabilistic metrics, are discussed

Francesco Paolo Cantelli

A description of the contribution of F. P Cantelli to the theory of Probability at the beginning of the XX centur

Approximating de Finetti's measures for partially exchangeable sequences

We show how to approximate de Finetti's measure of a partially exchangeable sequence by a mixture of products of Dirichlet measures, explicitly built once the approximation error has been fixed. These results are used to give a general method for the elicitation of prior distributions corresponding to partially exchangeable sequences, when prior information essentially derive from available data relative to phenomena similar to that we consider

Some asymptotic results for fiducial and confidence distributions

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations are accurate at least to order O(1/n). For the mean parameter μ=(μ1,…,μk) of an exponential family, our fiducial distribution is asymptotically normal and invariant to the importance ordering of the μi’s

Fiducial Distributions for Real Exponential Families

Abstract The fiducial argument was introduced by Fisher in order to obtain distributions for unknown parameters without the need of a bayesian perspective. In recent years, a certain interest has grown for fiducial inference. In this paper we are using a result obtained by Petrone and Veronese in order to construct a fiducial distribution for the parameter of a discrete or continuous real exponential family in a simple and quite general manner. We identify the families for which a fiducial distribution can be seen as a posterior with respect to a (improper) prior, thus completing previous results by Lindley and we demonstrate that such a prior belongs to the conjugate family. Some further results on the fiducial distribution are discussed

Confidence distribution for the ability parameter of the Rasch model

In this paper we consider the Rasch model and suggest novel point estimators and confidence intervals for the ability parameter. They are based on a proposed confidence distribution (CD) whose construction has required to overcome some difficulties essentially due to the discrete nature of the model. When the number of items is large, the computations due to the combinatorics involved become heavy and thus we provide first and second order approximations of the CD. Simulation studies show the good behavior of our estimators and intervals when compared with those obtained through other standard frequentist and weakly informative Bayesian procedures. Finally, using the expansion of the expected length of the suggested interval, we are able to identify reasonable values of the sample size which lead to a desired length of the interval

Approximating de Finetti's measures for partially exchangeable sequences

We show how to approximate de Finetti's measure of a partially exchangeable sequence by a mixture of products of Dirichlet measures, explicitly built once the approximation error has been fixed. These results are used to give a general method for the elicitation of prior distributions corresponding to partially exchangeable sequences, when prior information essentially derive from available data relative to phenomena similar to that we consider.Partial exchangeability de Finetti's measure Mixtures of products of Dirichlet measures Prior elicitation

Some asymptotic results for fiducial and confidence distributions

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations are accurate at least to order O(1/n). For the mean parameter μ=(μ1,…,μk) of an exponential family, our fiducial distribution is asymptotically normal and invariant to the importance ordering of the μi’s

Some New Results for Dirichlet Priors

Dirichlet Process, Distribution of the Variance, Hypergeometric function