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This paper proposes a novel extended object tracking (EOT) approach with embedded classification. Traditionally, for extended objects, only tracking is addressed without considering classification. This has serious defects: On the one hand, some practical EOT problems require classification as an embedded subproblem; on the other hand, with the assistance of classification, the tracking performance can be improved. Therefore, we propose a systematic EOT method with embedded classification, which is desired to satisfy the practical demands and also enjoys superior tracking performance. Specifically, we first formulate the EOT problem with embedded classification by kinematic models and attribute models. Then, we explore a random-matrix-based, multiple model EOT method with embedded classification. Two strategies are creatively provided in which soft classification and hard classification are embedded, respectively. Especially for the EOT with hard classification, a sequential probability ratio-test-based classification scheme is explored due to its nice properties and adaptability to our problem. In both methods, classification assist tracking is used. The simulation results demonstrate the superiority of the proposed EOT method with embedded classification, which can not only satisfy the practical requirements for classification but can also improve the tracking performance by utilizing the assistant of classification.

Data Drift refers to the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory similar in structure to the neocortex and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is their independence from training and testing cycles; all the learning takes place online with streaming data, and no separate training and testing cycle is required. In the sequential learning paradigm, the Sequential Probability Ratio Test (SPRT) offers unique benefits for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in a multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each data dimension, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

Monitoring patient safety during clinical trials is a critical component throughout the drug development life-cycle. Pharmaceutical sponsors must work proactively and collaboratively with all stakeholders to ensure a systematic approach to safety monitoring. The regulatory landscape has evolved with increased requirements for risk management plans, risk evaluation and minimization strategies. As the industry transitions from passive to active safety surveillance activities, there will be greater demand for more comprehensive and innovative approaches that apply quantitative methods to accumulating data from all sources, ranging from the discovery and preclinical through clinical and post-approval stages. Statistical methods, especially those based on the Bayesian framework, are important tools to help provide objectivity and rigor to the safety monitoring process.

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.

The sequential probability ratio test (SPRT) chart is a very effective control chart. It is much faster to detect mean shifts compared with the and CUSUM charts, even their VSSI (variable sample sizes and sampling intervals) versions. This article proposes an SPRT scheme, called the VSI SPRT chart, which uses the variable sampling intervals (VSI) scheme to further increase the effectiveness of the SPRT chart for detecting process mean shifts. This VSI SPRT chart employs a long sampling interval d 1 when the process is likely to be in control and adopts a short sampling interval d 2 when the process seems close to an out-of-control condition. The results of the case studies show that the adaptive feature has the potential to further increase the overall detection effectiveness of the SPRT chart compared with the fixed sampling interval SPRT chart and, therefore, to reduce the manufacturing costs. This new chart is particularly effective when mean shift is moderate.

The sequential probability ratio test (SPRT) chart is a desirable tool for monitoring manufacturing processes due to its high effectiveness. It is especially suitable for applications where testing is very expensive or destructive, such as the automobile airbags test and unaxial tensile test. This article proposes a design algorithm for the SPRT chart in which the reference value ( γ ) of the SPRT chart is optimized. The design algorithm increases the overall effectiveness of the SPRT chart by more than 10% on average. Moreover, the improvement in detection effectiveness is achieved without any additional difficulty in implementation. A design table is also provided to facilitate quality engineers to design the SPRT chart.

We present the explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the intensity of an observed Poisson process. The method of proof consists of reducing the initial problem to a free-boundary differential-difference Stephan problem and solving the latter by use of the principles of smooth and continuous fit. A rigorous proof of the optimality of the Wald's sequential probability ratio test in the variational formulation of the problem is obtained as a consequence of the solution of the Bayesian problem.

Sequential analysis of safety data ensure early detection of safety issues while minimizing the risk for patients who are exposed to the unsafe medical products. Wald presented the sequential probability ratio tests (SPRTs) in the framework of testing a simple null hypothesis against a simple alternative hypothesis. SPRT approach maximizes the (log) likelihood ratio by posting a constraint on the maximum likelihood estimate (MLE) of the parameter of interest within the domain of the alternative hypothesis, while the sequential generalized likelihood ratio (GLR) approach of Lai calculates the (log) likelihood ratio without any constraint and its stopping rule is determined jointly by the magnitude of the (log) likelihood ratio and the MLE of the parameter. The sequential GLR approach has smaller expected sample size (earlier detection of safety signals) as compared with either the SPRT or the maximized SPRT method, while still maintaining satisfactory power under a variety of circumstances.