Sequential Probability Ratio Test Research Articles

Sequential probability ratio test for zero inflation in counting data

In this paper, we will discuss the sequential probability ratio test to test the zero inflation in counting data with the sample size being a random variable with specified Type I and Type II errors. We will introduce the zero-inflated non-central negative binomial distribution, and explain how its operating characteristic and average sample number functions are derived. Simulations are studied to indicate the performances of the proposed tests with different scenarios. A real application is also discussed to explain the process of the sequential probability ratio test.

Testing traffic density of a heterogeneous stochastic queueing system using SPRT

We aim to determine the traffic density of the system as a control method in queuing systems and to keep it at the desired level. This article expands the sequential probability ratio test (SPRT) method in the heterogeneous server queuing system, which gives more accurate results in modeling a real-life case. Controlling the traffic density of the heterogeneous server queuing system can be used to determine optimal policies for the system.

Sensor Fault Diagnosis of Locomotive Electro‐Pneumatic Brake Using an Adaptive Unscented Kalman Filter

Normal operation of the pressure sensor is important for the safe operation of the locomotive electro‐pneumatic brake system. Sensor fault diagnosis technology facilitates detection of sensor health. However, the strong nonlinearity and variable process noise of the brake system make the sensor fault diagnosis become challenging. In this paper, an adaptive unscented Kalman filter‐ (UKF‐) based fault diagnosis strategy is proposed, aimed at detecting bias faults and drift faults of the equalizing reservoir pressure sensor in the brake system. Firstly, an adaptive UKF based on the Sage‐Husa method is applied to accurately estimate the pressure transients in the equalizing reservoir of the brake system. Then, the residual is generated between the estimated pressure by the UKF and the measured pressure by the sensor. Afterwards, the Sequential Probability Ratio Test is used to evaluate the residual so that the incipient and gradual sensor faults can be diagnosed. An experimental prototype platform for diagnosis of the equalizing reservoir pressure control system is constructed to validate the proposed method.

Employing Keyed Hash Algorithm, Sequential Probability Ratio Test, and Temperature Comparison Test as Security Against Node Capture Attacks of IoT-Based WSNs

The emergence of IoT opened new opportunities for development in various fields. With all the information that it gathers, it became an interesting target for multiple attackers. Thus, this study will enforce security solutions to IoT-based devices specifically in the perception layer by incorporating a Temperature Comparison Test, Keyed Hash Algorithm and evaluating it using SPRT especially in the defense against malicious activities detected in the nodes of a network namely for Mobile and Immobile attacks. For immobile attacks, using the keyed hash algorithm and the SPRT, the hash key of the passcodes was compared to determine the safety of the nodes. Hence, from the functionality test that was conducted, and evaluating the data gathered using SPRT and Bernoulli’s equation, the reliability of the protocol to detect Immobile attacks is concluded to have a 100% detection rate. For mobile node attacks, the study assumes the environment to be under normal, warm, and cold room temperatures. where both mobile and without mobile attack is simulated, the result shows that there is only an overall 3% difference from the temperature measure by the sensor to the ambient temperature. Hence, combining these protocols that are applied in the study eliminates the single points of failure in the nodes that are either applicable only to a distributed scheme or mobility support, the study also compared the tested protocol to the other existing protocols.

Double-Channel Sequential Probability Ratio Test for Failure Detection in Multisensor Integrated Systems

This article proposes a double-channel sequential probability ratio test (DCSPRT) failure detection algorithm for improving the fault-tolerant ability of the multisensor system. It develops a horizon-based sequential probability ratio test (HSPRT) using the horizon technique for the detection of slowing-growing failures and a current sample-based probability ratio test (CSPRT) for the detection of abrupt failures. Subsequently, the DCSPRT is established by combining HSPRT with CSPRT for the detection of both slow-growing and abrupt failures. Simulation and experimental results together with comparison analysis demonstrate that the proposed DCSPRT can effectively detect both slow-growing failures and abrupt failures to improve the capability of failure tolerance for multisensor integrated systems.

Towards Real-Time Detection of Auditory Steady-State Responses: A Comparative Study

To objectively evaluate weak neural responses such as auditory steady-state responses (ASSRs) often involves repetitive measurements, after which the accumulated trials are averaged or analyzed by statistical methods to detect a significant response. Such detection methods are often performed off-line on all measured trials. However, the number of required trials, and therefore the measurement time, is often heuristically chosen, and might be suboptimal. In this work, we compared three real-time signal-detection algorithms that could yield improved detection performance, at reduced measurement time. The classical Neyman-Pearson (NP) detector was evaluated by quantifying the signal-to-noise ratio (SNR), and detection probability of ASSRs, as a function of accumulated trial number. We also analyzed the performance of the Bayes factor (BF) to detect ASSRs at different thresholds. Finally, we modified the sequential probability ratio test (SPRT), with a cropped maximum likelihood (ML) estimator, such that it can detect ASSRs (with unknown SNRs) sequentially. We compared the three real-time detectors by using Monte Carlo simulation, and evaluated their performance on detecting ASSRs, generated from the superposition of a pair of amplitude-modulated (AM) tones near 40 Hz in the EEG of nine subjects with normal hearing. The low-order ASSRs (i.e., envelope frequency-following responses) have been sufficiently evaluated in the literature. However, the higher-order ASSRs might reflect further nonlinear mechanisms in the upper ascending auditory pathway. Results show that the real-time detectors can detect not only all low-order ASSRs but also higher-order ASSRs at frequencies with lower SNR. The NP detector yielded the best simulation and actual detection performance. For all subjects, the second-order ASSRs could already be detected with the NP and BF detectors within five trials, but more trials were needed for the modified SPRT detector. In general, higher-order ASSRs require more trials to detect, with the exception of ASSRs near 40 Hz and 80 Hz. In conclusion, compared with traditional off-line detectors, both (real-time) NP and BF detectors showed improved detection performance, and their application in EEG experiments can save valuable measurement time.

Online Estimation of Degradation State Under Random Change of Mode

Due to the changes in the surrounding environment, the dynamic of one degradation process may change at a random time, and it follows different modes before and after the change point. For solving online degradation state estimation problems subject to random change of mode, a novel state estimation method is proposed in this article based on the degradation models and the related monitored data. The proposed method employs the sequential probability ratio test (SPRT) based on the log-likelihood ratio to detect the unknown change time of the degradation mode and particle filtering to estimate the degradation states given observations and also evaluate the decision functions of the SPRT. Two case studies referring to a pneumatic valve considering single- and multiple-change times of the degradation mode are presented to illustrate the accuracy and effectiveness of the proposed method.

Sequential Decision Fusion for Abnormality Detection via Diffusive Molecular Communications

This letter considers the task of abnormality detection in a fluid medium, employing a molecular communications (MC) based network of nanoscale sensors. This task entails sensing, detection and reporting of abnormal changes in the environment that may characterize a disorder or an abnormal event. Such distributed detection (DD) problems are of paramount interest, especially in applications such as health monitoring, disease diagnosis, targeted drug delivery, environmental sensing and monitoring, contaminant detection and removal, and environmental remediation. This letter proposes, for the first time in the literature, to employ a sequential probability ratio test based approach to the decision fusion in diffusive MC based DD. The proposed approach leads to considerable gains in the average number of samples required for the decision compared to its fixed-sample size counterparts, resulting in a significant improvement in the average decision delay. In the investigated DD scenarios, we observe savings of up to 50% in the number of samples required for decision fusion.

Assessing debris strikes in spacecraft telemetry: Development and comparison of various techniques

Debris strikes on operational spacecraft are becoming more common due to increasing numbers of space objects. Sample return missions indicate hundreds of minor strikes, but rigorous analysis is often only performed when a strike causes an anomaly in spacecraft performance. Developing techniques to identify and assess minor strikes that do not immediately cause anomalous behavior can help to validate models for debris populations, perform risk assessments, and aid in the attribution of future anomalies. This study introduces debris strikes to a spacecraft dynamics simulation and assesses the effect on spacecraft telemetry. Various signal processing and change detection techniques are used to identify strikes in noisy telemetry and estimate strike parameters. Matched filter wavelets are developed to identify the effects on state telemetry, where errors are autonomously corrected by the spacecraft attitude control system. A bank of matched filters is used to estimate the parameters of the strike based on a priori knowledge of the spacecraft's response characteristics. A sequential probability ratio test is used to highlight abrupt changes in the spacecraft's angular momentum. Monte-Carlo analyses are conducted to characterize the performance of these algorithms. The results of the various techniques are compared in terms of correctly identifying the debris strikes and accurately estimating the strike parameters. Developing the capability to catalog and characterize minor debris strikes allows any spacecraft to be used as an in situ debris sensor.

Sequential probability ratio tests: conservative and robust

Because computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs. However, until now simulation analysts have ignored SPRTs. To change this situation, we review SPRTs for the simplest case; namely, the case of choosing between two hypothesized values for the mean simulation output. For this case, the classic SPRT of Wald (Wald A. Sequential tests of statistical hypotheses. Ann Math Stat 1945; 16: 117–186) allows general types of distribution, including normal distributions with known variances. A modification permits unknown variances that are estimated. Hall (Hall WJ. Some sequential analogs of Stein’s two-stage test. Biometrika 1962; 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. A modification uses a fully sequential variance estimator. In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. In experiment #1, simulation outputs are normal. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative”; that is, the actual error rates are smaller than those prespecified (nominal). Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. For these two experiments, we provide details on their design and analysis; these details may also be useful for simulation experiments in general.

Path Planning Under Malicious Injections and Removals of Perceived Obstacles: A Probabilistic Programming Approach

An autonomous mobile robot may encounter adversarial environments in which an attacker tries to influence its decisions. Through physical or software-level attacks, some of the robot's sensors might be compromised-a special concern for self-driving vehicles. Motivated by this scenario, this letter introduces and studies the problem of planning kinematically feasible (and possibly efficient) paths with bounded collision probability in adversarial settings where the obstacles perceived online by the robot display two layers of uncertainty. The first is the “usual” Gaussian uncertainty one would obtain from a standard object tracker (e.g., an Extended Kalman Filter); the second is an additional layer of uncertainty that captures possible sensor attacks and describes the actual existence of groups of obstacles in the environment. We study the complexity of the problem and propose a general sampling-based solution framework that uses the Sequential Probability Ratio Test (SPRT) to check collision probability constraints along the computed trajectory. We also show how probabilistic programming languages (PPLs) can simplify programming common algorithms (such as RRT and Hybrid A*) for mixed uncertainty. In addition to providing an easy-to-use programming framework, our approach is shown to plan safer paths compared to a Naive Monte Carlo baseline when both approaches are allowed to use at most the same given number of samples to perform collision checks.

A Sequential Target Existence Statistic for Joint Probabilistic Data Association

A sequential probability ratio test (SPRT) is introduced as a track management (TM) mechanism for the joint probabilistic data association (JPDA) multitarget tracking algorithm. The SPRT is based on an approximate target likelihood ratio that is derived from the JPDA event and association probabilities. SPRT-based TM functions are defined and compared to the joint integrated probabilistic data association (JIPDA) algorithm, including a discussion of parameter tuning for both approaches. Simulation experiments are reported for multiple closely spaced constant-velocity targets over a range of values for detection probability and clutter density. The SPRT-based algorithm achieves performance similar to JIPDA for this data, but with fewer TM parameters and a more straightforward parameter-tuning process.

Software Reliability Model with Dependent Failures and SPRT

Software reliability and quality are crucial in several fields. Related studies have focused on software reliability growth models (SRGMs). Herein, we propose a new SRGM that assumes interdependent software failures. We conduct experiments on real-world datasets to compare the goodness-of-fit of the proposed model with the results of previous nonhomogeneous Poisson process SRGMs using several evaluation criteria. In addition, we determine software reliability using Wald’s sequential probability ratio test (SPRT), which is more efficient than the classical hypothesis test (the latter requires substantially more data and time because the test is performed only after data collection is completed). The experimental results demonstrate the superiority of the proposed model and the effectiveness of the SPRT.

Decision-making system for the management of Frankliniella schultzei thrips in commercial melon fields

The common blossom thrips, Frankliniella schultzei (Thysanoptera: Thripidae) (Trybom), is an important pest of melons (Cucumis melo). This species is found on all continents, but especially in tropical and subtropical regions. Decision-making systems are essential parts of Integrated Pest Management (IPM) programs. Sampling plans and decision-making indices are two critical components for an effective and successful IPM program. Sequential sampling plans have a variable number of samples as a function of pest density. Economic Injury Level (EIL) is the most commonly used decision-making index in IPM programs. Despite the importance of the impact of Frankliniella schultzei on Cucumis melo, economic injury levels and sequential sampling plans for this pest have not yet been determined. Thus, this study aimed to determine the control decision-making system for F. schultzei. To this end, research was conducted over two years in 39 commercial melon fields. The EIL was calculated based on control costs and melon production value as a function of F. schultzei density. The sequential sampling plan was developed based on the binomial sequential probability ratio test. Attack up to 9 thrips. sample−1 reduced the yield of melon fields by 46%. The cost of thrips control represented 1.85% of the production value of the melon fields. The EIL for F. schultzei was 0.36 thrips per sample. The sequential sampling plan made correct decisions in 100% of situations and saved more than 85% of sampling time and cost. In conclusion, this decision-making system can be incorporated into melon field IPM programs to help farmers make correct decisions when the monitoring this pest, as well as reduce the costs and sampling times.

Early detection of anomalous degradation behavior in lithium-ion batteries

• Identifying ongoing reliability testing samples with anomalous degradation behavior at the earliest stage. • User-dependent confidence levels to determine the anomaly thresholds. • Evaluation of five data-driven methods on two datasets with 35 samples. • Development of an anomaly detection approach that considers an ensemble of methods. Before lithium-ion batteries are purchased in volume, they are typically tested (qualified) to determine if they meet the life-cycle reliability requirements for the targeted applications. To ensure that subsequent production lots of batteries continue to meet the reliability requirements, ongoing reliability testing is often conducted on production lot samples. However, a key challenge is how to quickly determine if the samples have substantially similar reliability as those batteries that were initially qualified, and, in particular, how to detect early signs of unacceptable degradation. This paper uses five data-driven methods (regression model with prediction bound, one-class support vector machine, local outlier factor, Mahalanobis distance, and sequential probability ratio test) to detect anomalous degradation behavior of samples from actual production lots subjected to ongoing reliability tests. An ensemble approach was then developed because it was observed that no single method always gave the earliest warning. The approach can be used by device companies for warranty, recall, and technical decisions.

Data-driven fault diagnosis based on coal-fired power plant operating data

This paper discusses data-driven fault diagnosis of the power plant reheater tube leakage based on their operating data. From the temperature sensors, fault data and normal data are measured. Mahalanobis distance (MD) analysis was performed to quantitatively analyze whether the distribution of fault data differed from that of the normal data. Then, sequential probability ratio test (SPRT) was performed to determine the time to anomalies (TTAs). To verify detected TTAs, power-generation data was used. This paper demonstrated the feasibility of the proposed approach to detect reheater tube leakage prior to the failure.

On Wald’s sequential test for vector mean under multivariate normal distribution and correlated data

In this article Wald’s sequential probability ratio test (SPRT) is implemented for multivariate normal distribution, for independent and autocorrelated data and known covariance matrix. The methodology based on residuals from the vector autoregressive moving average (VARMA) class models is presented for autocorrelated data. In this approach the average sample size required to take a decision in the sequential test is based on the Mahalanobis distance between the vectors of the intercept constants with respect to the error covariance matrix. Monte Carlo simulations were performed considering different scenarios for bivariate normal distribution. For fixed probabilities of type I and II errors, the results showed that the estimated average sample sizes to stop the sequential test were a little larger than those expected by Wald’s theory for autocorrelated and independent data. Under independence assumption the SPRT estimated sample sizes were also smaller than the sample sizes required by Hotelling’s test. It was shown that the omission of the correlation structure of the data strongly affects the type I and II errors of the sequential test. An example in the quality control field is presented using real data from a pig iron production process and the multivariate VAR(1) model.

Optimal Stopping and Worker Selection in Crowdsourcing: an Adaptive Sequential Probability Ratio Test Framework

In this study, we solve a class of multiple testing problems under a Bayesian sequential decision framework. Our work is motivated by binary labeling tasks in crowdsourcing, where a requestor needs to simultaneously choose a worker to provide a label and decide when to stop collecting labels, under a certain budget constraint. We begin by using a binary hypothesis testing problem to determine the true label of a single object, and provide an optimal solution by casting it under an adaptive sequential probability ratio test framework. Then, we characterize the structure of the optimal solution, that is, the optimal adaptive sequential design, which minimizes the Bayes risk using a log-likelihood ratio statistic. We also develop a dynamic programming algorithm to efficiently compute the optimal solution. For the multiple testing problem, we propose an empirical Bayes approach for estimating the class priors, and show that the average loss of our method converges to the minimal Bayes risk under the true model. Experiments on both simulated and real data show the robustness of our method, as well as its superiority over existing methods in terms of its labeling accuracy.

Is trust in government really declining? Evidence using the sequential probability ratio test

Evidence for declining trust in government is often presented as the difference between the present day and an idealized period of high trust in government. The fact is, though, trust in government, in many OECD countries, was relatively low historically and remains so now. This questions whether one can definitively state that trust is declining. If trust in government is not declining but instead fluctuating, then the effects of declining trust on political and policy outcomes may be overstated. Additionally, if trust is relatively stable, then it suggests that marginal shifts in trust may be affected by specific policy actions rather than large shifts in citizens’ attitudes. Using a simple yet powerful tool, the Sequential Probability Ratio Test, this analysis tests whether trust is in general decline. This test works in a manner that is different from traditional hypothesis testing. Rather than using fixed samples, one chooses a single measure—such as trust at an idealized time or average trust within a given period, and then tests whether individual observations are different than that observation. The findings provide evidence that in all but a few cases, one cannot find statistically significant evidence for declining trust in government in OECD countries. Therefore, statements of general decline in trust may be overstated and relying on declining trust as an explanatory variable may require consideration of the events that preceded those declines.

Enhancing the Robustness and Security Against Various Attacks in a Scale: Free Network

The development of the wireless sensor networks (WSNs) in the recent years is mainly due to the readily obtainable low-cost and short-range sensors. The objective of the WSN system is to both sense and transmit the real-time sense contents belonging to a particular monitoring environment for the back-end system for performing the necessary processing and analysis tasks. One of the most significant tasks of prime consideration is to ensure the safety and privacy aspects of the WSN in a wireless channel. The ultimate idea of the wireless sensor network is to preserve the limited node energy and thereby process the huge volume of data without affecting the robustness. The main objective of this work is to strengthen the robustness of the wireless sensor network that particularly relies on a scale-free type of network. The ability of the Scale-free WSNs in tolerating the random attacks efficiently have made them appear significant; on the other hand, they may be vulnerable to certain malicious attacks, that specifically targets the significant nodes in the system. This limitation has been addressed in this work by means of introducing a new modelling strategy called sequential probability ratio test (SPRT) that assists in the generation of scale-free network topologies. SPRT, a unique robustness improvising algorithm for the scale free type of WSNs, has been designed in this work and also the proposed SPRT is compared with the existing EROSE technique. The wide range of experimental results thus ensure that the introduced SPRT modelling methodology can achieves robustness and enhances the security of WSN.