Eugenio Regazzini

Finitely additive conditional probabilities

SuntoSi fornisce una breve rassegna delle ricerche tese ad estendere la condizione di coerenza di B. de Finetti alla previsione di numeri aleatori subordinati. Si studiano alcune conseguenze di tale estensione in relazione alla impostazione assiomatica delle probabilità subordinate finitamente additive. Si analizza, infine, il fenomeno della non conglomerabilità e si discute un ulteriore rafforzamento della condizione di coerenza che, in particolari condizioni, conduce alla più usuale teoria della speranza matematica subordinata secondo A. N. Kolmogorov.SummaryThis paper includes a concise survey of the work done in order to extend de Finettis coherence condition to the prevision of conditional random quantities. Sections 1 and 2 deal with the equivalence among different formulations of the extended condition and analyse the relations between it and the usual axiomatic treatment of finitely additive probabilities and previsions. Sections 3 and 4 include some results and remarks about the extensibility of a coherent conditional prevision. Finally, Sections 5 and 6 consider conglomerative previsions in order to frame Kolmogorovs theory of conditional probability and expectation into the more general approach sketched in the previous sections.

Means of a Dirichlet process and multiple hypergeometric functions

The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and the parameter of a Dirichlet process, a characterization of the family of Cauchy distributions as the set of the fixed points of this correspondence, and an extension of the Markov-Krein identity. Moreover, an expression of the characteristic function of the mean of a Dirichlet process is obtained by resorting to an integral representation of a confluent form of the fourth Lauricella function. This expression is then employed to prove that the distribution of the mean of a Dirichlet process is symmetric if and only if the parameter of the process is symmetric, and to provide a new expression of the moment generating function of the variance of a Dirichlet process.

Reaching the best possible rate of convergence to equilibrium for solutions of Kac’s equation via central limit theorem

Let

Central limit theorem for the solution of the Kac equation

f(\cdot,t)

The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation

be the probability density function which represents the solution of Kacs equation at time

Polyandry Is a Common Event in Wild Populations of the Tsetse Fly Glossina fuscipes fuscipes and May Impact Population Reduction Measures

t

On mixtures of distributions of Markov chains

, with initial data

Priors for Exponential Families Which Maximize the Association between Past and Future Observations

f_0

Strong previsions of random elements

, and let

WELL CALIBRATED, COHERENT FORECASTING SYSTEMS

g_{\sigma}