A Linear Programming Approach to Sequential Hypothesis Testing

Fauß, Michael; Zoubir, Abdelhak M.

doi:10.1080/07474946.2015.1030981

Cited by 38 publications

(30 citation statements)

References 26 publications

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“…In this section, a strategy how to obtain the coefficients based on linear programming is presented. It adopts the approach given in Fauß and Zoubir (2015) for the sequential joint detection and estimation problem. Recall the problem formulation: design a sequential procedure which uses on average as few samples as possible and fulfills constraints on the error probabilities and the estimation quality.…”

Section: Optimal Coefficients Of the Loss Functionmentioning

confidence: 99%

“…In order to solve the optimization problem in Eq. (5.4), we proceed, as in Fauß and Zoubir (2015), by relaxing the equality constraints to inequality constraints and adding the cost function ρ n to the set of free variables.…”

Section: Optimal Coefficients Of the Loss Functionmentioning

confidence: 99%

“…The proof of Theorem 3.1 follows from the fundamental results of optimal stopping theory. We follow here the proofs stated in Fauß and Zoubir (2015); Novikov (2009);Poor and Hadjiliadis (2009). In this proof, a truncated optimal stopping problem with finite horizon N ≥ 1 is considered with the cost c n for stopping at time n. Let V n = min{c n , E [V n+1 | t n ]} , n < N be the cost for stopping at the optimal time instant between n and N with basis V N = c N .…”

Section: A Proof Of Theorem 31mentioning

confidence: 99%

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Bayesian sequential joint detection and estimation

Reinhard

Fauß

Zoubir

2018

Sequential Analysis

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Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.2. The hypothesis H i , i = 0, 1, as well as the random parameter Θ i do not change during the observation period of X N .3. A sufficient static t n (x n ) in a state space (E t , E t ) exists such thatThe sufficient statistic has a transition kernel of the formand some initial statistic t 0 .4. The two hypotheses are separable, i.e.,5. The second order moment of the random parameter Θ exists and is finite, i.e., E[Θ 2 ] <∞ .Note that this implies, that the conditional second order moment E[Θ 2 | A] exist and is finite for all events A with non-zero probability.

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Section: Optimal Coefficients Of the Loss Functionmentioning

confidence: 99%

Section: Optimal Coefficients Of the Loss Functionmentioning

confidence: 99%

Section: A Proof Of Theorem 31mentioning

confidence: 99%

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Bayesian sequential joint detection and estimation

Reinhard

Fauß

Zoubir

2018

Sequential Analysis

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“…to the two thresholds (17) and (18). Moreover, the ASN of such a sequential test can be approximated along (19) and (20) by using…”

Section: Sequential Tests In the Exponential Familymentioning

confidence: 99%

In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

Stein

Faub

2018

2018 IEEE Statistical Signal Processing Workshop (SSP)

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Detecting the presence of a random wireless source with minimum latency utilizing an array of radio sensors is considered. The problem is studied under the constraint that the analog-to-digital conversion at each sensor is restricted to reading the sign of the analog received signal. We formulate the resulting digital signal processing task as a sequential hypothesis test in simple form. To circumvent the intractable probabilistic model of the multivariate binary array data, a reduced model representation within the exponential family in conjunction with a log-likelihood ratio approximation is employed. This approach allows us to design a likelihood-based sequential test and to analyze its analytic performance along Wald's classical arguments. In the context of wireless spectrum monitoring for satellite-based navigation and synchronization systems, we study the achievable processing latency, characterized by the average sample number, as a function of the binary sensors in use. The practical feasibility and potential of the discussed low-complexity sensing and decision-making technology is demonstrated via simulations.

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“…where ρ k ∈ P. Following the techniques developed in [22], [23], (14) can be straightforwardly solved as follows, where we omit the details in the interest of space: Let m0 and m1 denote the number of 0's and 1's observed. The likelihood-ratios of the corresponding observations under P0 and Pρ k , with respect to Pρ * are given by…”

Section: Joint Detection and Estimationmentioning

confidence: 99%

Sequential joint signal detection and signal-to-noise ratio estimation

Fauß

Nagananda

Zoubir

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.

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A Linear Programming Approach to Sequential Hypothesis Testing

Cited by 38 publications

References 26 publications

Bayesian sequential joint detection and estimation

Bayesian sequential joint detection and estimation

In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

Sequential joint signal detection and signal-to-noise ratio estimation

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