ABSTRACT In an era of increasingly complex data, three‐way arrays capturing information across units, variables and occasions are ubiquitous in fields from chemometrics to finance. However, extracting meaningful and interpretable patterns from such data remain a significant challenge. To address this, we introduce the Explainable Tucker3 Clustering (XT3Clus) methodology. XT3Clus performs clustering on units while simultaneously identifying explainable components for variables and/or occasions, significantly enhancing model interpretability. This approach functions as a constrained Tucker3 model, where each dimension is forced to contribute to a single component. The framework supports fully confirmatory, exploratory or hybrid analytical strategies. The optimization of the objective function is carried out by an efficient Alternating Least Squares algorithm. Finally, we propose a novel quantitative metric to evaluate the interpretability of a solution and confirm the practical utility of XT3Clus in three real‐world scenarios.

ABSTRACT This article develops a valuation model for mortgages with partial prepayment risk under the equal principal payment method. To model partial prepayment, we assume prepayment events occur at the jump times of a point process. The proportion of the prepayment amount to the outstanding principal balance is characterized by a stochastic process. By defining specific forms for the point process and stochastic process, we derive explicit valuation formulas for the mortgage loan. Finally, after resolving the computational challenge of multiple integrals via matrix exponentiation techniques, numerical results are presented to investigate the impact of some parameters on the valuation.

ABSTRACT A new sparse recursive filtering is suggested for the efficient inference of the joint posterior of the number of change points and their locations. The computational and storage costs of the sparse recursive filtering are quadratic to the number of uniformisation times generated by the uniformisation scheme, which can be scaled down to the number of change points. This new version of sparse recursive filtering is generally applicable for either conjugate or nonconjugate priors. It is also applicable when either cross‐segment dependence or cross‐segment independence occurs. Its good performance in some complicated circumstances is demonstrated through examples from robust Bayesian change point detection using ‐models, Bayesian change point detection with dependence cross‐segment, objective Bayesian change point detection and simulation studies, in which the marginal likelihood of the model is often difficult to obtain or intractable.

ABSTRACT In this article analysis of a simple step‐stress accelerated life test is considered under progressive type‐II censoring. A cumulative exposure model is considered when the latent lifetimes of test units follow the Gompertz distribution with different shape parameters and a common scale parameter. We explore the study by estimating all unknown parameters using classical and Bayesian techniques. The model parameters are estimated using maximum likelihood and Bayesian methods. Subsequently, interval estimates are derived based on the observed Fisher information matrix. Bayesian estimates are obtained using squared error and linear exponential loss functions. Subsequently highest posterior density intervals are also constructed. We examine the efficiency of all estimators through simulation studies. Finally, we provide a real‐life example in support of the considered model.

ABSTRACTThis paper contributes a modelling approach for prediction of subsequent injury risk using longitudinal wearable data in the sports industry. Understanding subsequent injury events in sport, namely injuries that follow an initial injury, will assist athletes, support staff, and coaches to quantify the risk of future injury and better inform risk mitigation strategies. Traditionally, such modelling has relied on logistic regression and survival analysis, which can have limited ability to capture time‐varying and cumulative effects, differing exposures, and surveillance periods associated with training and injury history. Athletes and their injuries constitute a complex system. We develop a novel set of modelling tools combining survival modelling for feature selection of longitudinal wearable sensor and injury data, and a two‐state Hidden Markov Model (HMM) for predicting injury risk. Using data from a club in the Australian Football League (AFL), the quality of model fit was high with an Area Under the Curve (AUC) of 0.93 (77% sensitivity, 90% specificity). This HMM enables personalised analysis of risk given individual training and game loads and injury history, as well as cohort‐level insight into risk factors. Specifically, factors relating to the number of efforts exceeding the 95th percentile in terms of speed, rating of perceived exertion, and acceleration had order(s) of magnitude greater impact on risk than other features. This methodology is applicable to subsequent event modelling for a broad range of complex systems and industries, and highlights opportunities for better decision support for practitioners.

ABSTRACTIndustrial statistics grew up in an era when manufacturing was the primary engine of commerce. Today, the driver is information technology. This paper discusses how statisticians need to adapt to contribute to this new business model, with particular emphasis upon computational advertising, autonomous vehicles, operations management, and large language models. Remarkably, many of our old tools are still relevant, even as the new problem space poses fresh research challenges for our employment and educational systems.

ABSTRACTThis article compares the information content of a sample for two competing Bayesian approaches. One approach follows Dennis Lindley's Bayesian standpoint, where one begins by formulating a prior for a parameter related to the problem in question and incorporates a likelihood to transition to a posterior. This contrasts with the usual Bayesian approach, where one starts with a likelihood model, formulates a prior distribution for its parameters, and derives the corresponding posterior. In both cases, the sample information content is measured using the difference between the prior and posterior entropies. We investigate this contrast in the context of learning about the moments of a variable. The maximum entropy principle is used to construct the likelihood model consistent with the given moment parameters. This likelihood model is then combined with the prior information on the parameters to derive the posterior. The model parameters are the Lagrange multipliers for the moment constraints. A prior for the moments induces a prior for the model parameters; however, the data provides differing amounts of information about them. The results obtained for several problems show that the information content using the two formulations can differ significantly. Additional information measures are derived to assess the effects of operating environments on the lifetimes of system components.