𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An inverse of Sanov's theorem

✍ Scribed by Ayalvadi Ganesh; Neil O'Connell

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
87 KB
Volume
42
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let X k be a sequence of i.i.d. random variables taking values in a ΓΏnite set, and consider the problem of estimating the law of X1 in a Bayesian framework. We prove that the sequence of posterior distributions satisΓΏes a large deviation principle, and give an explicit expression for the rate function. As an application, we obtain an asymptotic formula for the predictive probability of ruin in the classical gambler's ruin problem.

πŸ“œ SIMILAR VOLUMES

Cramer's condition and Sanov's theorem
Cramer's condition and Sanov's theorem
✍ Alexander Schied πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 305 KB

We discuss whether Sanov's theorem can be extended to a topology that renders the mapping v ~-~ f f dv continuous, for a given measurable function f. We show that this is possible if and only if f possesses all exponential moments with respect to the underlying law #.

An inverse of Bell's theorem
An inverse of Bell's theorem
✍ Kaj B. Hansen πŸ“‚ Article πŸ“… 1995 πŸ› Springer Netherlands 🌐 English βš– 612 KB
An Inverse Function Theorem for Continuo
An Inverse Function Theorem for Continuous Mappings
✍ M. Feckan πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 319 KB

The purpose of this paper is to give conditions under which a continuous mapping admits a local inverse. 1994 Academic Press, Inc.