Sequential Design of Experiments

Chernoff, Herman

doi:10.1214/aoms/1177706205

Cited by 414 publications

(462 citation statements)

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“…From the asymptotic viewpoint, however, the thresholds a and b in δ * cen (c) satisfy a ≈ b ≈ | log c| as c → 0, as shown in [4], [24]. To see this, note that as c → 0, both a and b are large and it is well-known [24] that SPRT in the centralized setting satisfies…”

Section: Problem (P1)mentioning

confidence: 94%

“…Note that such a lower bound can be established by the optimality of SPRT in the centralized version, and it turns out this bound will be sufficient for our purpose in the system with full local memory. The following theorem was a slight modification of Theorem 2 in [4]. While this theorem follows at once from the optimality of the centralized SPRT and its asymptotic property established in (16), an alternative proof, due to Chernoff [4], is given in the Appendix so that parts of the argument can be applied conveniently in the proof of Theorem 4.…”

Section: B Asymptotic Optimalitymentioning

confidence: 98%

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Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks

Mei

2008

IEEE Trans. Inform. Theory

106

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Abstract-The decentralized sequential hypothesis testing problem is studied in sensor networks, where a set of sensors receive independent observations and send summary messages to the fusion center, which makes a final decision. In the scenario where the sensors have full access to their past observations, the first of asymptotically Bayes sequential tests is developed, and the proposed test has same asymptotic performance as the optimal centralized test that has access to all sensor observations. Next, in the scenario where the sensors do not have full access to their past observations, a simple but asymptotically Bayes sequential tests is developed, in which sensor message functions are what we call tandem quantizer, where each sensor only uses two different sensor quantizers with at most one switch between these two quantizers. Moreover, a new minimax formulation of finding optimal stationary sensor quantizers is proposed and is studied in detail in the case of additive Gaussian sensor noises. Finally, our results show that the feedback from the fusion center does not improve asymptotic performance in the scenario with full local memory, however, even a one-shot one-bit feedback can significantly improve asymptotic performance in the scenario with limited local memory.

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Section: Problem (P1)mentioning

confidence: 94%

Section: B Asymptotic Optimalitymentioning

confidence: 98%

Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks

Mei

2008

IEEE Trans. Inform. Theory

106

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“…The problems of sequential testing of two or more hypotheses under different conditions have been studied in [22][23][24].…”

Section: Choice Of Suitable Parametersmentioning

confidence: 99%

Information‐based algorithm for moving object detection

Andrić

Todorović

2013

IET Radar, Sonar & Navigation

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An algorithm for moving object detection using the information entropy is proposed and analysed. The proposed algorithm is applied on Doppler radar signal and it represents an alternative approach to Doppler radar signal analysis using the Fourier transform. The algorithm is tested using data obtained in real measurements by ground surveillance Doppler radar. The numerical results are compared with those obtained by the method using the Fourier transform. It is shown that the ground clutter due to windblown vegetation, which is the main challenge for radar to detect moving object, does not affect the information entropy. The impact of two main parameters of the algorithm on information entropy is analysed. The authors discuss on choice of the detector structure, threshold setting and decision rule. The computational complexity of the proposed algorithm is calculated and compared with the complexity of the method using Fourier transform. It is shown that the computational complexity of the proposed algorithm is one order of magnitude lower than the computational complexity of the method using Fourier transform.

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“…Robbins and Monro (1951) proposed a sequential design scheme (known as stochastic approximation) for this problem, in which the dose for each experimental run is determined by the dose and the outcome of the previous run. Much subsequent work has continued to exploit a sequential approach (see, for example, Wetherill 1963, Tsutakawa 1972, Chernoff 1975, Owen 1975, and Anbar 1978. Other authors have developed non-sequential design schemes for quanta1 response experiments.…”

Section: Nonlinear Modelsmentioning

confidence: 99%

Experimental Design: Review and Comment

Steinberg¹,

Hunter²

1984

Technometrics

240

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We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.

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Sequential Design of Experiments

Cited by 414 publications

References 0 publications

Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks

Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks

Information‐based algorithm for moving object detection

Experimental Design: Review and Comment

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