Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.

A reinforcement learning approach for sequential mastery testing

Abstract: This paper explores a novel application for reinforcement learning (RL) techniques to sequential mastery testing. In such systems, the goal is to classify each examined person, using the minimal number of test items, as master or non-master. Using RL, an intelligent agent autonomously learns from interactions to administer more informative and effective variable-length tests. Empirical results are also provided to evaluate the performance of the proposed approach as compared to two common approaches for variable-length testing (Bayesian decision and sequential probability ratio test) as well as to the fixed-length testing.

Optimum truncated sequential test of binomial distribution

Abstract: Binomial distribution is very useful in wide fields. And the truncated sequential test theory for the simple null hypothesis vs simple alternative hypothesis is the basis in binomial distribution sequential analysis. In this paper we have defined precise definitions of truncated sequential test of binomial distribution, such as, optimum truncated sequential test, uniformly optimum truncated sequential test (UOTST), nature extended truncated sequential test (NETST) of fixed sample size test, and so on. We also present the sufficient conditions for UOTST, and a lot of relative properties of truncated sequential test. At the end of this paper, we compare the UOTST with IEC1123, sequential mesh test (SMT) methods of truncated sequential test, the results show that UOTST has made significant improvement relatively, and the UOTST presented here is feasible and reliable.

Distributed Sequential Hypothesis Testing with Dependent Sensor Observations

Abstract: In this paper, we consider the problem of distributed sequential detection using wireless sensor networks (WSNs) in the presence of imperfect communication channels between the sensors and the fusion center (FC). We assume that sensor observations are spatially dependent. We propose a copula-based distributed sequential detection scheme that characterizes the spatial dependence. Specifically, each local sensor collects observations regarding the phenomenon of interest and forwards the information obtained to the FC over noisy channels. The FC fuses the received messages using a copula-based sequential test. Moreover, we show the asymptotic optimality of the proposed copula-based sequential test. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

Spectrum Sensing in Cognitive Radio: Bootstrap and Sequential Detection Approaches

Abstract: In this thesis, advanced techniques for spectrum sensing in cognitive radio are addressed. The problem of small sample size in spectrum sensing is considered, and resampling-based methods are developed for local and collaborative spectrum sensing. A method to deal with unknown parameters in sequential testing for spectrum sensing is proposed. Moreover, techniques are developed for multiband sensing, spectrum sensing in low signal to noise ratio, and two-bits hard decision combining for collaborative spectrum sensing. The assumption of using large sample size in spectrum sensing often raises a problem when the devised test statistic is implemented with a small sample size. This is because, for small sample sizes, the asymptotic approximation for the distribution of the test statistic under the null hypothesis fails to model the true distribution. Therefore, the probability of false alarm or miss detection of the test statistic is poor. In this respect, we propose to use bootstrap methods, where the distribution of the test statistic is estimated by resampling the observed data. For local spectrum sensing, we propose the null-resampling bootstrap test which exhibits better performances than the pivot bootstrap test and the asymptotic test, as common approaches. For collaborative spectrum sensing, a resampling-based Chair-Varshney fusion rule is developed. At the cognitive radio user, a combination of independent resampling and moving-block resampling is proposed to estimate the local probability of detection. At the fusion center, the parametric bootstrap is applied when the number of cognitive radio users is large. The sequential probability ratio test (SPRT) is designed to test a simple hypothesis against a simple alternative hypothesis. However, the more realistic scenario in spectrum sensing is to deal with composite hypotheses, where the parameters are not uniquely defined. In this thesis, we generalize the sequential probability ratio test to cope with composite hypotheses, wherein the thresholds are updated in an adaptive manner, using the parametric bootstrap. The resulting test avoids the asymptotic assumption made in earlier works. The proposed bootstrap based sequential probability ratio test minimizes decision errors due to errors induced by employing maximum likelihood estimators in the generalized sequential probability ratio test. Hence, the proposed method achieves the sensing objective. The average sample number (ASN) of the proposed method is better than that of the conventional method which uses the asymptotic assumption. Furthermore, we propose a mechanism to reduce the computational cost incurred by the bootstrap, using a convex combination of the latest K bootstrap distributions. The reduction in the computational cost does not impose a significant increase on the ASN, while the protection against decision errors is even better. This work is motivated by the fact that the sequential probability ratio test produces a smaller sensing time than its counterpart of fixed sample size test. A smaller sensing time is preferable to improve the throughput of the cognitive radio network. Moreover, multiband spectrum sensing is addressed, more precisely by using multiple testing procedures. In a context of a fixed sample size, an adaptive Benjamini-Hochberg procedure is suggested to be used, since it produces a better balance between the familywise error rate and the familywise miss detection, than the conventional Benjamini-Hochberg. For the sequential probability ratio test, we devise a method based on ordered stopping times. The results show that our method has smaller ASNs than the Bonferroni procedure. Another issue in spectrum sensing is to detect a signal when the signal to noise ratio is very low. In this case, we derive a locally optimum detector that is based on the assumption that the underlying noise is Student's t-distributed. The resulting scheme outperforms the energy detector in all scenarios. Last but not least, we extend the hard decision combining in collaborative spectrum sensing to include a quality information bit. In this case, the multiple thresholds are determined by a distance measure criterion. The hard decision combining with quality information performs better than the conventional hard decision combining.

Optimal sequential estimation procedures of a function of a probability of success under LINEX loss

Abstract: In this paper, we investigate the problem of estimating a function g(p), where p is the probability of success in a sequential sample of independent identically Bernoulli distributed random variables. As a loss associated with estimation we introduce a generalized LINEX loss function. We construct a sequential procedure possessing some asymptotically optimal properties in the case when p tends to zero. In this approach to the problem, the conditions are given, under which the stopping time is asymptotically efficient and normal, and the corresponding sequential estimator is asymptotically normal. The procedure constructed guarantees that its sequential risk is asymptotically equal to a prescribed constant.