Bayesian sequential testing of the drift of a Brownian motion
نویسندگان
چکیده
منابع مشابه
Conditional Frequentist Sequential Tests for the Drift of Brownian Motion
In this paper, we consider the problem of sequentially testing simple hypotheses concerning the drift of a Brownian motion process from a unified Bayesian and frequentist perspective. The conditional frequentist approach to testing statistical hypotheses has been utilized in a variety of settings to produce tests that are virtually equivalent to their objective Bayesian counterparts. Herein, we...
متن کاملOn the Bias of Estimation of a Brownian Motion Drift following Group Sequential Tests
Group sequential tests have been widely used to control the type I error rate at a prespecified level in comparative clinical trials. It is well known that due to the optional sampling effect, conventional maximum likelihood estimates will exaggerate the treatment difference, and hence a bias is introduced. We consider a group sequentially monitored Brownian motion process. An analytical expres...
متن کاملBrownian Motion with Polar Drift
Consider a strong Markov process X° that has continuous sample paths in Rd (d > 2) and the following two properties. (1) Away from the origin X° behaves like Brownian motion with a polar drift given in spherical polar coordinates by n{8)/2r. Here /i is a bounded Borel measurable function on the unit sphere in RJ, with average value Ji. (2) X° is absorbed at the origin. It is shown that X° reach...
متن کاملRange of Brownian motion with drift
Let (Bδ(t))t≥0 be a Brownian motion starting at 0 with drift δ > 0. Define by induction S1 = − inf t≥0 Bδ(t), ρ1 the last time such that Bδ(ρ1) = −S1, S2 = sup 0≤t≤ρ1 Bδ(t), ρ2 the last time such that Bδ(ρ2) = S2 and so on. Setting Ak = Sk + Sk+1 ; k ≥ 1, we compute the law of (A1, · · · , Ak) and the distribution of ((Bδ(t + ρl) − Bδ(ρl) ; 0 ≤ t ≤ ρl−1 − ρl))2≤l≤k for any k ≥ 2, conditionally ...
متن کاملFluctuations of Brownian Motion with Drift
Consider 3 dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators Tt defined by Tt ρ = ρt form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Probability and Statistics
سال: 2015
ISSN: 1292-8100,1262-3318
DOI: 10.1051/ps/2015012