Sequential Probability Ratio Test Research Articles

Chen Software Reliability Growth Model

Software reliability analysis is very vital in software development. Software manufacturers assess the quality of their developed software through this analysis. This has triggered the development of reliability models. Software reliability growth models have been used extensively to examine the quality of manufactured software before they are sent to the market. This study presents a new software reliability growth model using Chen distribution. The Chen software reliability growth model is then used to establish sequential probability ratio test limits for determining whether a manufactured software is reliable or unreliable. The applications of the proposed model revealed that it performs better than some of the existing software reliability growth models for the given datasets.

Quick cooperative spectrum sensing in cognitive unmanned aerial vehicles networks

AbstractIn cognitive unmanned aerial vehicles (UAVs) networks (CUAVNs), cooperative spectrum sensing (CSS) has been recognized as a key technology to enable UAVs to detect spectrum holes and opportunistically access primary licensed spectrum band without harmful interference. Considering that the location flexibility of flying UAV spectrum sensors makes the collaborative working mode of multiple UAVs difficult to achieve, this article establishes an easy‐to‐implement intraframe CSS mode by considering the cooperation within the microsensing time slots of a single UAV. On the basis of this, we adopt sequential probability ratio test (SPRT) as the fusion criterion of sensing decisions from microsensing slots to implement quick CSS for multiple channels under the sensing delay limit and make an investigation the achievable throughput of truncated‐SPRT for CUAVNs. Due to the uncertainty of the sensing decision number required in SPRT, we further propose a soft truncation (ST) way to terminate SPRT process and further evaluate the global CSS performance. At last, numerical simulation results show that the CSS efficiency of the proposed intraframe CSS outperforms that of the traditional interframe CSS, and the performance of ST‐SPRT is also better than hard truncation (HT)‐SPRT, in terms of the detection performance and throughput, especially in the multichannel spectrum sensing scenario.

A Quantum-Inspired Classifier for Early Web Bot Detection

This paper introduces a novel approach, inspired by the principles of Quantum Computing, to address web bot detection in terms of real-time classification of an incoming data stream of HTTP request headers, in order to ensure the shortest decision time with the highest accuracy. The proposed approach exploits the analogy between the intrinsic correlation of two or more particles and the dependence of each HTTP request on the preceding ones. Starting from the a-posteriori probability of each request to belong to a particular class, it is possible to assign a Qubit state representing a combination of the aforementioned probabilities for all available observations of the time series. By leveraging the underlying mathematical details of superposition and entanglement on specific subsequences, it is possible to devise a measure of membership to each class, thus enabling the system to take a reliable decision when a sufficient level of confidence is met or to continue with additional observations. The results reported in this paper objectively show the effectiveness of our quantum-inspired algorithm which outperforms other state-of-the-art approaches, including our own one based on the Sequential Probability Ratio Test.

Sequential sampling plan for Ceratitis capitata (Diptera: Tephritidae) in guava orchards.

This study aimed to elaborate a sequential sampling plan for C. capitata in commercial orchards of guava. 90 McPhail traps were randomly installed in three guava orchards in a transverse direction for 23 weeks. The data were submitted to sequential probability ratio test. Adopted the average of 0.3 C. capitata for the level of security and 0.7 for the control action. In this sequential sampling plan was defined the average number of 0.40 adults of C. capitata for each trap McPhail (sample). The sequential plan generated is unprecedented and will contribute to the rapid and safe decision making in the control of C. capitata population in guava farming.

Fall Detection System on Smart Walker Based on Multisensor Data Fusion and SPRT Method

Traditional walkers are commonly used for the elderly in social life, which solves the basic problem of walking, but it is difficult to ensure safety when a fall occurs, and the human-computer interaction is poor. The image recognition method or the IMU sensor method fixed on the user, such as a wearable watch, is used by most of the current fall detection methods. Wearable sensors require the user’s wearing operation, which is a little troublesome, and the detection accuracy is related to the way of wearing. The image recognition method requires a high-priced camera and a fixed installation position, which is unable to adapt to outdoor activities. We investigated a low-cost method of mounting the sensor on the body of the walker. We propose in this paper an improved fall detection method, namely Precondition and Limit Threshold SPRT (PLT-SPRT), and a novel fall detection system on the smart walker based on PLT-SPRT. The signals of the upper and lower limb sensors are fused based on the Kalman filter algorithm, and the admittance control parameters are obtained through the system identification method. In this study, the improved sequential probability ratio test algorithm is used to set the null hypothesis and the alternative hypothesis, construct the likelihood ratio and optimize the decision function, which is used to judge whether falls occur. The system is simulated by Matlab software, the user intention after fusion is more accurate, and the optimized decision function is judged accurately. Verified by the embedded system based on STM32 of the smart walker equipment in the real world, it can accurately identify the fallen state, with low detection delay, and the fallen state is detected about 160ms earlier than the traditional threshold-based detection algorithm, at the same time, the accuracy is higher than 94.9%, which meets the high real-time requirements of fall detection and is the ideal solution for smart walkers.

A Sequential Probability Ratio Test for Sparse Gaussian Mixtures

A Sequential Probability Ratio Test for Sparse Gaussian Mixtures

Improving test efficiency for a grid multidimensional computerized classification test by the application of a conditional latent-trait distribution to a sequential probability ratio test.

The measurement efficiency of a multidimensional computerized adaptive testing (MCAT) can be improved by taking the correlations between the dimensions into account during the item selection and latent-trait estimation procedures (Segall, 1996; Wang & Chen, 2004). Although a multidimensional computerized classification test (MCCT), which was based on a multidimensional itemresponse model, was previously found more efficient than its unidimensional counterpart, the difference was negligible (Seitz & Frey, 2013); the researchers had adopted a sequential probability ratio test (SPRT) as the termination criterion in this MCCT study. To make a classification decision on each dimension, which is called a grid classification (Wang et al., 2019), only items that loaded on that dimension were used to calculate the likelihood ratio, which squandered the available information of the correlations between the dimensions. The current study utilizes such useful information to improve the measurement efficiency of the MCCT by applying a conditional distribution of the latent-trait estimates and then including all the administered items to calculate the likelihood ratio in the SPRT. The performance of this newly proposed method was evaluated through a series of simulation studies. The results showed that the proposed method can sizably improve the measurement efficiency of an MCCT by saving 1% to 32% of the test length in comparison with the SPRT when the two test dimensions are at least moderately correlated. The findings and further applications of this study are discussed.

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.

Improved probability hypothesis density filter for multi‐target tracking of non‐cooperative bistatic radar

Non-cooperative bistatic radar refers to the passive bistatic radar using a non-cooperative radar as the illuminator of opportunity. Limited by the non-cooperation and bistatic configuration, multi-target tracking of the non-cooperative bistatic radar is confronted with challenges of low detection probability and high clutter. Based on the sequential Monte Carlo implementation of probability hypothesis density (PHD) filter, this study proposes an improved PHD (I-PHD) filter. Similar to the tracking gate in data association, whether each candidate target is detected at each time is determined and recorded, and the sequential probability ratio test distinguishes a real target and false target based on this record. To distinguish miss detection and target death, a new survival probability dependent on target position is defined, and the survival probability of a specific target drops rapidly when it is located near the boundary and moves outwards. To label targets and extract their states, a new method of track identification and state estimation is proposed. The simulation results illustrate that the proposed I-PHD filter can effectively track multiple targets of non-cooperative bistatic radar under low detection probability and high clutter and has superior performance than competing methods.

A real-time fault diagnosis method for hypersonic air vehicle with sensor fault based on the auto temporal convolutional network

In this paper, a fault diagnosis problem for Hypersonic Air Vehicle (HAV) with sensor fault is concerned. Existing fault diagnosis models pay less attention to the problems of high-performance real-time diagnosis and Artificial Intelligence (AI) algorithm autonomous optimization. Therefore, a smart real-time fault diagnosis algorithm is put forward to automatically build a more accurate and rapid model in a short time. Based on the Temporal Convolutional Network (TCN) with tuning parameters optimizing by Strengthen Elitist Genetic Algorithm (SEGA), the Auto Temporal Convolutional Network (AutoTCN) is first proposed. To better diagnose the time-sequence sensor fault signal, the Sequential Probability Ratio Test (SPRT) method is introduced afterwards. Additionally, the Wavelet Packet Translation (WPT) is combined with TCN to enhance the mechanism and sensitivity of the extracted fault features. Experimental results from the HAV model with the Reaction Control System (RCS) control simulated under sensor fault are obtained. It is demonstrated that, for typical sensor faults greater than 8.89%, the real-time fault diagnosis accuracy of the proposed method may exceed 96%. The diagnosis delay is less than 0.05 s. Moreover, on the computer equipped with an 8-core CPU, over 87.5% of the working time can be saved.

Early Stopping in Experimentation With Real-Time Functional Magnetic Resonance Imaging Using a Modified Sequential Probability Ratio Test.

Introduction: Functional magnetic resonance imaging (fMRI) often involves long scanning durations to ensure the associated brain activity can be detected. However, excessive experimentation can lead to many undesirable effects, such as from learning and/or fatigue effects, discomfort for the subject, excessive motion artifacts and loss of sustained attention on task. Overly long experimentation can thus have a detrimental effect on signal quality and accurate voxel activation detection. Here, we propose dynamic experimentation with real-time fMRI using a novel statistically driven approach that invokes early stopping when sufficient statistical evidence for assessing the task-related activation is observed.Methods: Voxel-level sequential probability ratio test (SPRT) statistics based on general linear models (GLMs) were implemented on fMRI scans of a mathematical 1-back task from 12 healthy teenage subjects and 11 teenage subjects born extremely preterm (EPT). This approach is based on likelihood ratios and allows for systematic early stopping based on target statistical error thresholds. We adopt a two-stage estimation approach that allows for accurate estimates of GLM parameters before stopping is considered. Early stopping performance is reported for different first stage lengths, and activation results are compared with full durations. Finally, group comparisons are conducted with both early stopped and full duration scan data. Numerical parallelization was employed to facilitate completion of computations involving a new scan within every repetition time (TR).Results: Use of SPRT demonstrates the feasibility and efficiency gains of automated early stopping, with comparable activation detection as with full protocols. Dynamic stopping of stimulus administration was achieved in around half of subjects, with typical time savings of up to 33% (4 min on a 12 min scan). A group analysis produced similar patterns of activity for control subjects between early stopping and full duration scans. The EPT group, individually, demonstrated more variability in location and extent of the activations compared to the normal term control group. This was apparent in the EPT group results, reflected by fewer and smaller clusters.Conclusion: A systematic statistical approach for early stopping with real-time fMRI experimentation has been implemented. This dynamic approach has promise for reducing subject burden and fatigue effects.

On designing efficient sequential schemes to monitor non‐normal processes

AbstractThe process monitoring techniques play an essential role to improve the overall performance of processes. The control chart is an essential monitoring tool used to detect changes in the process parameters. The Shewhart charts are famous for detecting larger shifts, while exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are famous for detecting small‐to‐moderate shifts. The separate control schemes are required for the quick identification of the changes in the process parameters because sometimes testing is too expensive or time taking and a practitioner may not afford any kind of defects or loss. With this motivation, the dynamic feature of this article is to introduce an efficient sequential probability ratio test (SPRT) decision‐based Tukey CUSUM design. The performance of the proposal is judged by using several run lengths (RLs) performance measures such as average, median, standard deviation, and percentile RLs. Based on the comparative analysis, it is revealed that the proposed chart offers more sensitivity towards the changes in process location than its competitor's charts for several probability models. The study proposal may find applications in packaging, manufacturing, decision‐making, finance and economics modeling, image processing and automation. A case study from steel rods manufacturing is included to demonstrate the application of the proposed design.

Binomial early stopping times

Sequential analysis for the purposes of possibly stopping a trial early is important whenever a result must be obtained as quickly as possible for public health, economic, or other reasons. A dominant research stream since the middle of the 20th century has been the challenge of generalizing Wald’s sequential probability ratio test (SPRT) to include composite alternative hypotheses. This article offers an alternative for a binomial distribution by constructing a single-parameter family of triangular rejection regions for the null hypothesis using a generation function argument in the two-dimensional space of successes versus failures. The result is algebraically equivalent to one line of the SPRT with unit power and with the second value of the binomial parameter as the undetermined parameter. Rounding then discretizes the line to the grid of two-dimensional integers and classical results for arbitrary stopping conditions are used to give expressions for the estimator, of the binomial parameter and its variance The choice can be made by the practitioner in terms of their appetite for risk or more formally via a power analysis. An example is given of an ecological study where a quick binary decision was required and this desire had to be weighed against robustness of the results.

The SPRT Sign Chart for Process Dispersion

Abstract A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example.

An Adaptive Authenticated Model for Big Data Stream SAVI in SDN-Based Data Center Networks

With the rapid development of data-driven and bandwidth-intensive applications in the Software Defined Networking (SDN) northbound interface, big data stream is dynamically generated with high growth rates in SDN-based data center networks. However, a significant issue faced in big data stream communication is how to verify its authenticity in an untrusted environment. The big data stream traffic has the characteristics of security sensitivity, data size randomness, and latency sensitivity, putting high strain on the SDN-based communication system during larger spoofing events in it. In addition, the SDN controller may be overloaded under big data stream verification conditions on account of the fast increase of bandwidth-intensive applications and quick response requirements. To solve these problems, we propose a two-phase adaptive authenticated model (TAAM) by introducing source address validation implementation- (SAVI-) based IP source address verification. The model realizes real-time data stream address validation and dynamically reduces the redundant verification process. A traffic adaptive SAVI that utilizes a robust localization method followed by the Sequential Probability Ratio Test (SPRT) has been proposed to ensure differentiated executions of the big data stream packets forwarding and the spoofing packets discarding. The TAAM model could filter out the unmatched packets with better packet forwarding efficiency and fundamental security characteristics. The experimental results demonstrate that spoofing attacks under big data streams can be directly mitigated by it. Compared with the latest methods, TAAM can achieve desirable network performance in terms of transmission quality, security guarantee, and response time. It drops 97% of the spoofing attack packets while consuming only 9% of the controller CPU utilization on average.

811 WHETHER 10 WATER SWALLOWS NECESSARY TO OBTAIN REPRODUCIBLE RESULTS OF HIGH-RESOLUTION OESOPHAGEAL MANOMETRY?

Abstract Not less than ten wet swallows assessment in the primary test position is recommended by Chicago classification 4.0 for high-resolution oesophageal manometry (HREM); however, the required number of measurements are not sufficiently supported. Aim to evaluate the number of wet swallows necessary for correct interpretation of the results of lower esophageal sphincter integrated relaxation pressure (IRP) with low probability of type I and II errors. Methods Patients referred to perform HREM were enrolled. Solid-state 10Fr catheter and Solar (Laborie) software were used. Minimum 10 swallows by 5 mL water were obtained. These were analysed for cumulative means of IRP after 1…9 measurements. Conclusion made at each moment was compared with one based on 10 measurements. The results were characterized as true/false positive/negative for calculation of diagnostic accuracy. To exclude sample influence, Monte-Carlo simulation of sequential decision-making was performed with the use of sequential probability ratio test. Association of the diagnostic accuracy from recall was studied with the use of receiver operating characteristic curve (ROC) analysis. Results One hundred subjects were enrolled (25 with disorders of EGJ outflow). During the simulation, the probability of matching the decisions based on the 10 measurements and lower number of them was high. ROC analysis showed that actual probability to obtain false-positive results was twice as lower then ‘allowed’ rate of 5%. The probability to make false-negative results did not exceed 10% in any number of measurements. The probability that the conclusions made after 2 and after 10 measurements match was 0.9584 in those with disorders of EGJ outflow and 0.9652 in those without (figure 1). Conclusion The standard number of measurements required to support the presence of disorders of EGJ outflow during evaluation of 5 mL wet swallows in the primary position is excessive. Values of the IRP after 2 swallows allows to make similar decision to that after 10 swallows with >95% probability. This allows to reduce the number of wet swallows to assess in the primary position and save time for assessments in alternative position or perform provocation tests.

1035COVID-19: Boom or bust?

Abstract Background In the final weeks of 2019, a SARS-CoV-2 virus slipped furtively from animal to human in China. As of March 13, there have been 1,34,918 confirmed cases, out of which 4,990 is the death count. We are predicting extinction or explosion of the virus from the current realization of a Galton Watson process. Methods Based on the region wise reported number of cases, total was calculated. The observed offspring distribution was found by calculating the difference between the total number of cases in consecutive days. Hence the distribution modelled using Sequential Probability Ratio Tests (SPRT) to predict whether extinction or explosion will occur for the current realization of the process. Kolmogorov-Smirnov test was performed on the data to check the distribution of fit. Results We assume conservative approach of SPRT. The geometric distribution fits to the data taken from January 2020 to March 12, 2020. The SPRT on the offspring distribution predicts extinction of the disease if the number of cases reported on a new day are less than 58 then the disease will extinct, and will explode if more than 9,990 cases. Conclusions Our results show that if COVID-19 transmission is established, understanding the effectiveness of control measures in different settings will be crucial for understanding the likelihood that transmission can eventually be effectively mitigated. Key messages Our analysis highlights the value of recording individual cases and analyzing geographically heterogeneous data of COVID-19. Our results also have implications for estimation of transmission dynamics using the number of exported cases from a specific area.

Two new termination rules for multidimensional computerized classification testing

<p id="p00005">Computerized classification testing (CCT) is a subset of computerized adaptive testing (CAT), and it aims to classify examinees into one of at least two possible categories that denote results such as pass/fail or non-mastery/partial mastery/mastery. Therefore, CCTs focus on increasing the accuracy of classification which is different from CATs designed for precise measurement. The termination rule is one of the key components of CCT. However, as pointed out by Nydick (<xref xml:base="bibr" rid="b17">2013</xref>), most CCTs (i.e., UCCTs) were designed under unidimensional item response theory (IRT), in which the unidimensionality assumption is easily violated in practice. Thus, researchers then began to construct multidimensional CCT termination rules (i.e., MCCT) based on multidimensional IRT. To date, however, these rules still have some deficiencies in terms of classification accuracy or test efficiency. <p id="p00010">Most current studies on termination rules of MCCT are based on termination rules of UCCT. In UCCTs, termination rules require setting a cut point, <inline-formula>${{\theta }_{0}}$</inline-formula>, of the latent trait to calculate the statistics; and when they are extended from UCCT to MCCT, the cut point will become a classification bound curve or even a surface (i.e., <inline-formula>$g(\theta )=0$</inline-formula>). At this time, a question is how to convert the curve or surface into <inline-formula>${{\theta }_{0}}$</inline-formula>. To this end, the projected sequential probability ratio test (P-SPRT), constrained SPRT (C-SPRT; Nydick, <xref xml:base="bibr" rid="b17">2013</xref>), and multidimensional generalized likelihood ratio (M-GLR) were respectively proposed to solve the problem in different ways. Among them, P-SPRT and C-SPRT choose specific points on g(<italic>θ</italic>) as the approximate cut point, <inline-formula>${{\hat{\theta }}_{0}}$</inline-formula>, by projecting into Euclidean space or constraining on g(<italic>θ</italic>) respectively; as for M-GLR, because the generalized likelihood ratio statistic can be calculated without a cut point, it can be directly employed in MCCT. To overcome the limitation that P-SPRT may lead to unstable results at the beginning of the test, this study proposed the Mahalanobis distance-based SPRT (Mahalanobis-SPRT). <p id="p00015">In addition, stochastic curtailment is a technique for shortening the test length by predicting whether the classification of participants will change as the test continues. This article also combined M-GLR with the stochastic curtailment and proposed M-GLR with stochastic curtailment (M-SCGLR). <p id="p00020">A full-scale simulation study was conducted to (1) compare both the Mahalanobis-SPRT and M-SCGLR with the P-SPRT, C-SPRT, M-GLR, and multidimensional stochastically curtailed SPRT (M-SCSPRT) under varying conditions; (2) compare the classification performance of the above six termination rules for participants with specific abilities to explore whether there is a significant difference in the sensitivity of various rules to classify specific participants. To achieve the first research objective, three levels of correlation between dimensions (<italic>ρ</italic>=0, 0.5, and 0.8), two item bank structures (within-item multidimensionality and between-item multidimensionality), and two kinds of classification boundary (compensatory boundary and non-compensatory boundary) were considered; to achieve the second objective, 36 specific ability points <inline-formula>$({{\theta }_{1}},{{\theta }_{2}})$</inline-formula> were generated where <inline-formula>${{\theta }_{1}},{{\theta }_{2}}\in \{-0.5,-0.3,-0.1,0.1,0.3,0.5\}$</inline-formula>. The results showed that: (1) when the compensatory classification function was used, the Mahalanobis-SPRT led to higher classification accuracy and similar test length to the rules without stochastic curtailment; (2) under almost all conditions, the M-SCGLR not only possessed higher precision but also maintained the short test length, compared to M-SCSPRT that also uses stochastic curtailment; (3) the six termination rules showed a consistent change in the sensitivity of the precision and test length to specific participants. <p id="p00025">To sum up, two new MCCT termination rules (Mahalanobis-SPRT and M-SCGLR) are put forward in this article. Although the simulation results are very promising, several research directions merit further investigation, such as the development of MCCT termination rules for more than two categories, and the construction of MCCT termination rules by incorporating process data like the response time.

Neurally-constrained modeling of human gaze strategies in a change blindness task.

Despite possessing the capacity for selective attention, we often fail to notice the obvious. We investigated participants' (n = 39) failures to detect salient changes in a change blindness experiment. Surprisingly, change detection success varied by over two-fold across participants. These variations could not be readily explained by differences in scan paths or fixated visual features. Yet, two simple gaze metrics-mean duration of fixations and the variance of saccade amplitudes-systematically predicted change detection success. We explored the mechanistic underpinnings of these results with a neurally-constrained model based on the Bayesian framework of sequential probability ratio testing, with a posterior odds-ratio rule for shifting gaze. The model's gaze strategies and success rates closely mimicked human data. Moreover, the model outperformed a state-of-the-art deep neural network (DeepGaze II) with predicting human gaze patterns in this change blindness task. Our mechanistic model reveals putative rational observer search strategies for change detection during change blindness, with critical real-world implications.

Online neutron/gamma discrimination and source detection using CLYC(Ce) scintillator: A sequential approach

We develop a sequential approach for online neutron/gamma discrimination and source detection using CLYC(Ce) scintillator. This approach consists of a dynamic k-means clustering algorithm, a density-based filter and a sequential probability ratio test. Compared to traditional methods, the proposed one has three advantages: (a) it does not require a prior threshold value for pulse shape parameter (PSP), (b) it automatically drops troublesome pulses which cannot be easily classified as neutron or gamma-ray, (c) it makes decision of whether a source exists during the detection (when the received pulses are adequate) instead of after a rigid detecting period. Experiment results show that under a neutron flux density of 11.16/cm2 s, the average detection time for a239Pu–Be source is 0.56 s for 95% confidence coefficient and 0.91 s for 99% confidence coefficient.