Exact boundaries in sequential testing for phase-type distributions

Multi-dimensional sequential testing and detection

We study extensions to higher dimensions of the classical Bayesian sequential testing and detection problems for Brownian motion. In the main result we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.

Bayesian sequential testing of the drift of a Brownian motion

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing in time, which enables us to prove monotonicity and continuity of the optimal stopping boundaries as …

序贯检验的平均场博弈

A Mean Field Game of Sequential Testing

本文针对布朗运动漂移序贯检验问题提出首个带停止和未观测公共噪声的平均场滤波博弈，证明了其适定性并建立了均衡存在性，同时给出了数值研究。

布朗运动漂移的贝叶斯序贯软分类问题

A Bayesian sequential soft classification problem for a Brownian motion's drift

本文提出并求解了布朗运动漂移的贝叶斯序贯软分类问题，证明值函数为自由边界问题的唯一非平凡解，并刻画了停止边界对信噪比的依赖关系。

Bayesian sequential composite hypothesis testing in discrete time

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…

具有信号控制的序贯检验问题

A Sequential Testing Problem with Signal Control

本文研究带信号强度控制的贝叶斯序贯检验问题，证明当成本结构决定的函数存在全局极小点时最优控制为常数且可显式计算，否则最优控制不存在但值函数仍显式，从而在引入内生信息流控制后保持完全可处理性。