An exact predictive recursion for Bayesian nonparametric analysis of incomplete data

Exact solution of the (approximated) well-known Newton\u27s computational procedure to the bayesian nonparamertric approach to censored data

Tolstoy\u27s dream and the quest for statistical equilibrium in economics and the social sciences

The meaning of the notion of statistical equilibrium in economics is discussed as well as its relevance for economic theory. A simple agent-based model of taxation and redistribution is presented. Its invariant equilibrium distribution is the generalized P?lya sampling distribution. It turns out that the expected wealth distribution is the dichotomous P?lya whose continuous limit is the Beta distribution and whose appropriate thermodynamic limit is the Gamma distribution, often found in describing empirical data. The shape parameter of the Gamma distribution is the inverse of the wealth preferential attachment α−1

Interplay of simple stochastic games as models for the economy

summary:Using the interplay among three simple exchange games, one may give a satisfactory representation of a conservative economic system where total wealth and number of agents do not change in time. With these games it is possible to investigate the emergence of statistical equilibrium in a simple pure-exchange environment. The exchange dynamics is composed of three mechanisms: a decentralized interaction, which mimics the pair-wise exchange of wealth between two economic agents, a failure mechanism, which takes into account occasional failures of agents and includes wealth redistribution favoring righer agents, and a centralized mechanism, which describes the result of a redistributive effort. According to the interplay between these three mechanisms, their relative strength, as well as the details of redistribution, different outcomes are possible

Realistic interpretations of de Finetti's Theorem

Mixtures of binomial distributions have been recently introduced in Statistical Physics both in theoretical and in experimental frames in order to explain physical correlations. The physical interpretation of the mixing distribution is realistic, in contrast with the subjective mood originally attached by De Finetti to his celebrated "Representation Theorem". Inductive and physical correlations, despite different in meaning, obey the same mathematical rules. Hence the logical status of the Theorem is worth of reconsideration by non-bayesian statisticians

A general solution of the problem of repeated birthdays

We solve the well-known problem of repeated birthdays by an exact and complete method due to L.Boltzmann

On association

In the present paper we face, from a general perspective, the problems posed by statistical inferences in the case of two modalities. The analysis of the association is performed both from the ipotetical-deductive point of view (tests of significance) and from the inductive one (predictive inferences). That analysis is performed with the view of the foundational aspects of statistical inferences not caring too mach about the mathematical subtleties

Una formulazione probabilistica del principio di esclusione di Pauli nel contesto delle inferenze predittive

A unified derivation of Elementary Particle Statistics is hindered by Pauli's Exclusion Principle, that limits the possible states of the physical system in a peculiar way. It follows that if the Principle does not hold (Maxwell-Boltzmann e di Bose-Einstein cases) all occupation vectors are regular, so long as they are allowed by the macroscopic parameters. On the contrary, if the Principe holds (Fermi-Dirac case), the regularity domain of the probabilistic description is narrowed by the Principle itself. In this paper a recursive definition of regularity is proposed, able to unify the three Statistics. In this general formulation Pauli's Exclusion Principle can be found as a particular case. The paper is based on the notion of stochastic process with exchangeable increments. It can be considered as an unified approach to predictive inductive inferences from the particular point of view of Statistical Physics

Finitary probabilistic methods in econophysics

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