Minimax optimal sequential hypothesis tests for Markov processes

Fauß, Michael; Zoubir, Abdelhak M.; Poor, H. Vincent

doi:10.1214/19-aos1899

Cited by 11 publications

(35 citation statements)

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“…This leads into the territory of sequential tests, which adapt the sample size to the observed data. The existence of strictly minimax optimal sequential tests has recently been shown in [104]. Combining the benefits of adaptive procedures with strict robustness guarantees makes them a promising choice for future applications that require both efficiency and reliability.…”

Section: B Characterizing Least Favorable Distributionsmentioning

confidence: 99%

“…Similar optimality properties of the SPRT also hold for Bayesian cost functions [180]. Sequential tests for multiple hypotheses are covered in [184] and [104]. While an in-depth discussion is beyond the scope of this paper, the underlying concepts can be understood without going into technical details.…”

Section: Minimax Sequential Detectionmentioning

confidence: 99%

“…In general, it makes sense to assume that the conditional distribution X n |X n−1 is subject to uncertainty. For random processes with Markovian representations this problem has been studied in [104]. However, in order to reduce the technicalities, (X 1 , X 2 , .…”

Section: Minimax Sequential Detectionmentioning

confidence: 99%

“…While the underlying theory is well-understood by now, designing and implementing minimax sequential tests still requires a considerable computational effort. The procedure proposed in [104] designs a minimax sequential test by alternatingly updating ρ and (Q 0 , . .…”

Section: : Loopmentioning

confidence: 99%

“…The example presented here is taken from [104], and the reader is referred to this reference for a more detailed discussion. In addition, [104] also presents an example with dependent observations, which is beyond the scope of this overview.…”

Section: A a Numerical Examplementioning

confidence: 99%

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Minimax Robust Detection: Classic Results and Recent Advances

Fauß

Zoubir

Poor

2021

IEEE Trans. Signal Process.

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This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and giving a brief recount of the most prominent developments. Subsequently, the minimax principle is introduced and its strengths and limitations are discussed. The first part of the paper focuses on the two-hypothesis case. After briefly reviewing the basics of statistical hypothesis testing, uncertainty sets are introduced as a generic way of modeling distributional uncertainty. The design of minimax detectors is then shown to reduce to the problem of determining a pair of least favorable distributions, and different criteria for their characterization are discussed. Explicit expressions are given for least favorable distributions under three types of uncertainty: ε-contamination, probability density bands, and f -divergence balls. Using examples, it is shown how the properties of these least favorable distributions translate to properties of the corresponding minimax detectors. The second part of the paper deals with the problem of robustly testing multiple hypotheses, starting with a discussion of why this is fundamentally different from the binary problem. Sequential detection is then introduced as a technique that enables the design of strictly minimax optimal tests in the multi-hypothesis case. Finally, the usefulness of robust detectors in practice is showcased using the example of ground penetrating radar. The paper concludes with an outlook on robust detection beyond the minimax principle and a brief summary of the presented material.

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Section: B Characterizing Least Favorable Distributionsmentioning

confidence: 99%

Section: Minimax Sequential Detectionmentioning

confidence: 99%

Section: Minimax Sequential Detectionmentioning

confidence: 99%

Section: : Loopmentioning

confidence: 99%

Section: A a Numerical Examplementioning

confidence: 99%

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