<title>Sequential detection of targets in distributed systems</title>

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

The virtual bumper is a safeguarding mechanism for autonomous and remotely operated robots to conservatively avoid collisions even in the face of sensor uncertainty. In this paper we take a new approach to the virtual bumper system by applying a powerful but rarely examined statistical test. By using a modified version of Wald's sequential probability ratio test, we demonstrate that we can reduce the number of false positives reported by the virtual bumper, thereby saving valuable mission time. We further use the concept of sequential probability ratio to control vehicle speed in the presence of possible obstacles in order to increase certainty about whether or not obstacles are present. With this principled obstacle certainty measure, our new algorithm reduces the chances of collision by approximately 98% relative to traditional virtual bumper safeguarding without speed control.

Sequential sampling plans based on the negative binomial distribution were developed for egg mass density of spruce budworm, Choristoneura fumiferana (Clemens), in Michigan's Upper Peninsula. Plans developed were modifications of Wald's sequential probability ratio test (SPRT) based on Monte Carlo simulation. Parameters of the negative binomial distribution were estimated by the maximum likelihood method. Sampling models developed classify egg mass populations into low and high categories using the number of egg masses on whole branch samples of balsam fir, Abies balsamifera (L.) Voss. Plans are presented for three pairs of population density hypotheses to give forest pest managers the flexibility to select a plan that best meets management objectives. Monte Carlo estimates indicated that Wald's average sample number (ASN) and operating characteristic (OC) equations underestimated the actual ASN values, and the actual alpha and beta error probabilities were smaller than the values prescribed by Wald's equations. Errors were sufficiently large to have serious economic implications during implementation of plans developed from Wald's approximate procedure. The sequential plans developed by modifying the decision boundaries of Wald's SPRT using the Monte Carlo procedure had error probabilities, OC functions, and ASN values that were approximately equal to those desired.

Sequential sampling plans are appealing because fewer observations are needed than those needed for fixed sampling plans to make a terminating decision when insect populations are sparse or abundant. Wald's Sequential Probability Ratio Test (SPRT) commonly has been used in monitoring insect populations and damages from these populations. At times, particularly for moderate infestations, the SPRT with its parallel boundaries takes longer than a comparable fixed-sample-size method to make a terminating decision. An alternative sequential testing procedure called the 2-SPRT for the negative-binomial parameter P is demonstrated. The value of the exponent k is assumed to be known. In this procedure two one-sided SPRTs are performed simultaneously, which results in the convergent boundary lines. The average number of observations needed for the terminating decision for medium infestations (i.e., for P 1 < P < P 2 ) is observed to be considerably smaller than that for the SPRT with a slight increase in sampling effort when infestations are light or heavy. An application of the 2-SPRT is demonstrated using cotton f1eahopper, Pseudatomoscelis seriatus (Reuter), data obtained in southwestern Oklahoma.

An algorithm is developed for determining exact values of the Operating Characteristic and Average Sample Number functions for Wald's Sequential Probability Ratio Test (SPRT) when observations are drawn from a discrete, Koopman‐Darmois density with positive probability on the nonnegative integers. The sample size distribution and percentiles of sample size are also considered. An example is given for the negative binomial distribution.

Striacosta albicosta (Smith) (Lepidoptera: Noctuidae), is a native pest of dry beans (Phaseolus vulgaris L.) and corn (Zea mays L.). As a result of larval feeding damage on corn ears, S. albicosta has a narrow treatment window; thus, early detection of the pest in the field is essential, and egg mass sampling has become a popular monitoring tool. Three action thresholds for field and sweet corn currently are used by crop consultants, including 4% of plants infested with egg masses on sweet corn in the silking-tasseling stage, 8% of plants infested with egg masses on field corn with approximately 95% tasseled, and 20% of plants infested with egg masses on field corn during mid-milk-stage corn. The current monitoring recommendation is to sample 20 plants at each of five locations per field (100 plants total). In an effort to develop a more cost-effective sampling plan for S. albicosta egg masses, several alternative binomial sampling plans were developed using Wald's sequential probability ratio test, and validated using Resampling for Validation of Sampling Plans (RVSP) software. The benefit-cost ratio also was calculated and used to determine the final selection of sampling plans. Based on final sampling plans selected for each action threshold, the average sample number required to reach a treat or no-treat decision ranged from 38 to 41 plants per field. This represents a significant savings in sampling cost over the current recommendation of 100 plants.

The article presents particulars of developing a plant disease detection system based on analysis of photo-graphic images by deep convolutional neural networks. A original lightweight neural network architecture is used (only 13 480 trained parameters) that is tens and hundreds of times more compact than typical solutions. Real-life field data is used for training and testing, with photographs taken in adverse conditions: variation in hardware quality, angles, lighting conditions, scales (from macro shots of individual fragments of leaf and stem to several rose bushes in one picture), and complex disorienting backgrounds. An adaptive decision-making rule is used, based on the Bayes' theorem and Wald's sequential probability ratio test, in order to improve reliability of the results. A following example is provided: detection of disease on leaves and stems of rose from images taken in the visible spectrum. The authors were able attain the quality of 90.6% on real-life data (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> score, one input image, test dataset).

Item response theory (IRT) has most often been used in research on computerized adaptive testing (CAT). Depending on the model used, IRT requires between 200 and 1,000 examinees for estimating item parameters. Thus, it is not practical for instructional designers to develop their own CAT based on the IRT model. Frick improved Wald's sequential probability ratio test (SPRT) by combining it with normative expert systems reasoning, referred to as an EXSPRT-based CAT. While previous studies were based on re-enactments from historical test data, the present study is the first to examine how well these adaptive methods function in a real-time testing situation. Results indicate that the EXSPRT-I significantly reduced test lengths and was highly accurate in predicting mastery. EXSPRT is apparently a viable and practical alternative to IRT for assessing mastery of instructional objectives.

The use of the cumulative sum (CUSUM) charting procedure in process monitoring is first described. The relationship between the CUSUM charting procedure and Wald's sequential probability ratio test is then explained. This is followed by three main approaches of determining the average run length. The strengths and weaknesses of the CUSUM charting procedure, with respect to the Shewhart charting procedure, are illustrated with simulated data sets. Various other aspects of the CUSUM chart are also discussed. These include estimation of process mean using the CUSUM, weighting of samples for signaling, fast initial response for a newly start‐up process, simultaneous CUSUM schemes, design of CUSUM chart, multivariate CUSUM schemes, and risk‐adjusted CUSUM charts.

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.

The banana root borer, Cosmopolites sordidus Germar (Coleoptera: Curculionidae), is a major pest in many banana (Musa spp.)‐producing regions of the world, causing yield losses of up to 100%. The aims of this study were to define the spatial distribution pattern of C. sordidus in banana plantations, to determine the probability distribution model that best describes the sampling data, and to develop a sequential sampling plan for this pest. Aggregation was investigated using aggregation indices and theoretical frequency distributions. To quantify the number of insects, 80 traps were distributed in a commercial banana plantation with an area of 4 ha and inspections were performed every 2 wk from 2005 to 2008. The sequential sampling plan was based on Wald's sequential probability ratio test. The calculated indices indicated moderate aggregation, with a common k parameter of the negative binomial distribution equal to 3.29. The best model for predicting the spatial distribution of the insects was the negative binomial distribution, which fit 93% of the inspections, followed by the Neyman Type A distribution, which fit 90% of the surveys, and Poisson's distribution, which fit only one survey. A sequential sampling plan was generated with Type I and II error rates of 5%, for which 19 was the maximum expected number of samples required to reach a decision for an infestation mean of approximately 3.7 insects per trap. The validation showed that the constructed plan is reliable and provides correct recommendations for decision‐making in pest control. The banana root borer has an aggregated spatial distribution in the field. Negative binomial distribution is the best model to explain species spatial pattern. A sequential sampling plan was developed and validated. The sequential sampling plan showed reliable decision rates. The sequential sampling plan showed a reasonable number of required sample units.

Chapter 6 - Stopping Time of Invariant Sequential Probability Ratio Testst

We consider a single-hop, random-access, wireless sensor network (WSN) performing sequential distributed detection under a bandwidth constraint. At each time slot, the sensor nodes will make their decisions on whether the observed event is happening. The sensor censoring strategy is applied such that only the local decisions equal to one (i.e., the event happens) will be sent to the fusion center (FC). Because only one transmission channel between the FC and the sensor nodes is assumed, if two or more local decisions are sent at a time slot, a packet collision happens. We design a sequential probability ratio test (SPRT) at the FC that is aware of the collisions. The performance measures of the collision-aware SPRT are analyzed based on a Markov chain. In addition, we derive the asymptotic relative efficiency of the collision-aware SPRT relative to another SPRT. Numerical results show some interesting characteristics of the collision-aware SPRT. For example, the collision-aware SPRT prefers the scenario that many local decisions are likely to be sent per time slot.

We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.

A significant problem nowadays is detection of Web traffic generated by automatic software agents (Web bots). Some studies have dealt with this task by proposing various approaches to Web traffic classification in order to distinguish the traffic stemming from human users' visits from that generated by bots. Most of previous works addressed the problem of offline bot recognition, based on available information on user sessions completed on a Web server. Very few approaches, however, have been proposed to recognize bots online, before the session completes. This paper proposes a novel approach to binary classification of a multivariate data stream incoming on a Web server, in order to recognize ongoing user sessions as generated by bots or humans. The present approach uses deep neural networks combined with Wald's Sequential Probability Ratio Test to express the relationship between subsequent HTTP requests in an ongoing session and to assess the likelihood of each session being generated by a bot or human before it ends. Experimental results showed the ability of the proposed approach to detect Web bots online with high performance scores and a small number of false negatives, as evidenced by the Recall index, minimizing the impact on human visitors. Another valuable indicator is the speed of decision: the present method allows very quick classification of nearly all sessions, leaving only very few of them undecided.