Frequentistic approximations to Bayesian prevision of exchangeable random elements

Given a sequence \xi_1, \xi_2,... of X-valued, exchangeable random elements, let q(\xi^(n)) and p_m(\xi^(n)) stand for posterior and predictive distribution, respectively, given \xi^(n) = (\xi_1,..., \xi_n). We provide an upper bound for limsup b_n d_[[X]](q(\xi^(n)), \delta_\empiricn) and limsup b_n d_[X^m](p_m(\xi^(n)), \empiricn^m), where \empiricn is the empirical measure, b_n is a suitable sequence of positive numbers increasing to +\infty, d_[[X]] and d_[X^m] denote distinguished weak probability distances on [[X]] and [X^m], respectively, with the proviso that [S] denotes the space of all probability measures on S. A characteristic feature of our work is that the aforesaid bounds are established under the law of the \xi_n's, unlike the more common literature on Bayesian consistency, where they are studied with respect to product measures (p_0)^\infty, as p_0 varies among the admissible determinations of a random probability measure

Prima lezione di probabilità soggettiva

L'intento è di fornire gli elementi per giungere a fissare il nesso sostanziale tra significato della probabilità e sua definizione; questa, oltre che ad essere in linea col significato che generalmente si attribuisce a frasi del tipo "la probabilità dell'evento A è p", risulterà, al tempo stesso, adeguatamente precisa da permettere di poggiarvi una teoria matematica della probabilità

Intorno a qualche risultato relativo al processo di Dirichlet

No abstract availabl

Recursive equations for the predictive distributions of some determinantal processes

The paper provides recursive equations for the predictive distributions of one-dependent and two-dependent determinantal processes. Fixed order recursive equations can be applied both to efficiently simulate trajectories and to explore properties of the process

Some New Results for Dirichlet Priors

Dirichlet Process, Distribution of the Variance, Hypergeometric function

Note on “Frequentistic approximations to Bayesian prevision of exchangeable random elements” [Int. J. Approx. Reason. 78 (2016) 138–152]

This note points some ambiguities in the notation adopted in “Frequentistic approximations to Bayesian prevision of exchangeable random elements” [Int. J. Approx. Reason. 78 (2016) 138–152] and provides the correct way to read those statements and proofs which are affected by the aforesaid ambiguities

VaR as a risk measure for multiperiod static inventory models

This paper explores the possibility to use value-at-risk (VaR) in the context ofinventory management. VaR is being used more and more in financial management as a natural measure ofthe risk taken with a given position. In the framework of inventory management it can work as well. After having built a decision model, where the choice concerns the quantity to be ordered to face a random demand, in order to optimize the expected result (an expected cost to be minimized or an expected profit to be maximized) the model explores the probability distribution ofthe result, both via analytical methods and via simulation methods. The analytical exploration ofthis problem has originated a general method to deduce from inequalities for distribution functions, which are based on the expected value, related tail inequalities, which are particularly useful for VaR problems, where only one tail is involved

On generalized semi-Pareto and semi-Burr distributions and random coefficinet minification process

No abstract availabl