| Issue |
ESAIM: PS
Volume 26, 2022
|
|
|---|---|---|
| Page(s) | 265 - 282 | |
| DOI | https://doi.org/10.1051/ps/2022005 | |
| Published online | 20 May 2022 | |
Bayesian Sequential Composite Hypothesis Testing in Discrete Time*
Department of Mathematics, Uppsala University, Box 256, 75105 Uppsala, Sweden
** Corresponding author: ekstrom@math.uu.se
Received:
14
October
2021
Accepted:
11
April
2022
We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using the conditional probability of one of the hypotheses as the underlying spatial variable, we show that the cost function is concave and that the posterior distribution becomes more concentrated as time goes on. Moreover, we study time monotonicity of the value function. For a large class of model specifications, the cost function is non-decreasing in time, and the optimal stopping boundaries are thus monotone.
Mathematics Subject Classification: 62L10 / 60G40 / 62C10
Key words: Sequential analysis / hypothesis testing / exponential family / optimal stopping
© The authors. Published by EDP Sciences, SMAI 2022
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