Displaying similar documents to “Optimal sequential multiple hypothesis testing in presence of control variables”

Stability estimating in optimal sequential hypotheses testing

Evgueni I. Gordienko, Andrey Novikov, Elena Zaitseva (2009)

Kybernetika

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We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X 1 , X 2 , ⋯ when testing two simple hypotheses about their common density f : f = f 0 versus f = f 1 . As a functional to be minimized, it is used a weighted sum of the average (under f 0 ) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by X 1 , X 2 , ⋯ with the density f 0 . For τ * being...

Optimal sequential multiple hypothesis tests

Andrey Novikov (2009)

Kybernetika

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This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.

Optimal sequential procedures with Bayes decision rules

Andrey Novikov (2010)

Kybernetika

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In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss...

A note on control of the false discovery proportion

Marcin Dudziński, Konrad Furmańczyk (2009)

Applicationes Mathematicae

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We consider the problem of simultaneous testing of a finite number of null hypotheses H i , i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned...

A two-disorder detection problem

Krzysztof Szajowski (1997)

Applicationes Mathematicae

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Suppose that the process X = { X n , n ∈ ℕ } is observed sequentially. There are two random moments of time θ 1 and θ 2 , independent of X, and X is a Markov process given θ 1 and θ 2 . The transition probabilities of X change for the first time at time θ 1 and for the second time at time θ 2 . Our objective is to find a strategy which immediately detects the distribution changes with maximal probability based on observation of X. The corresponding problem of double optimal stopping is constructed. The optimal strategy...

Stability and sensitivity analysis for optimal control problems with control-state constraints

Kazimierz Malanowski

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A family of parameter dependent optimal control problems ( O ) h with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of ( O ) h ₀ exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to ( O ) h and the associated Lagrange...

Some results for an optimal control problem with a semilinear state equation

Fausto Gozzi (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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We consider a quadratic control problem with a semilinear state equation depending on a small parameter ϵ . We show that the optimal control is a regular function of such parameter.