On general conditional random quantities

Giuseppe Sanfilippo, Angelo Gilio, Giuseppe Sanfilippo, Veronica Biazzo

Risultato della ricerca: Other

2 Citazioni (Scopus)

Abstract

In the first part of this paper, recalling a general discussion on iterated conditioning given by de Finetti in the appendix of his book, vol. 2, we give a representation of a conditional random quantity $X|HK$ as $(X|H)|K$. In this way, we obtain the classical formula $\pr{(XH|K)} =\pr{(X|HK)P(H|K)}$, by simply using linearity of prevision. Then, we consider the notion of general conditional prevision $\pr(X|Y)$, where $X$ and $Y$ are two random quantities, introduced in 1990 in a paper by Lad and Dickey. After recalling the case where $Y$ is an event, we consider the case of discrete finite random quantities and we make some critical comments and examples. We give a notion of coherence for such more general conditional prevision assessments; then, we obtain a strong generalized compound prevision theorem. We study the coherence of a general conditional prevision assessment $\pr(X|Y)$ when $Y$ has no negative values and when $Y$ has no positive values. Finally, we give some results on coherence of $\pr(X|Y)$ when $Y$ assumes both positive and negative values. In order to illustrate critical aspects and remarks we examine several examples.
Lingua originaleEnglish
Pagine51-60
Numero di pagine10
Stato di pubblicazionePublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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    Sanfilippo, G., Gilio, A., Sanfilippo, G., & Biazzo, V. (2009). On general conditional random quantities. 51-60.