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In predictive modelling for high‐stake decision‐making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the coverage of prediction results with fewer theoretical assumptions. To obtain the prediction set by so‐called full‐CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split‐CP is often employed where the data is split into two parts: one part for fitting and another for computing the prediction set. Unfortunately, because of the reduced sample size, split‐CP is inferior to full‐CP both in fitting as well as prediction set computation. In this paper, we develop a full‐CP of sparse high‐order interaction model (SHIM), which is sufficiently flexible as it can take into account high‐order interactions among variables. We resolve the computational challenge for full‐CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full‐CP. [ABSTRACT FROM AUTHOR]

Image registration is a widely used tool for matching two images of the same scene with one another. In the literature, several image registration techniques are available to register rigid‐body and non‐rigid‐body transformations. One such important transformation is zooming. There are very few feature‐based methods that address this particular problem. These methods fail miserably when there are only a limited number of point features available in the image. This paper proposes a feature‐based approach that works with a feature that is readily available in almost all images, for registering two images of the same image object where one is a zoomed‐in version of the other. In the proposed method, we first detect the possible edge points which we consider as features in both the reference and the zoomed image. Then, we map these features of the reference and the zoomed image with one another and find the relationship between them using a mathematical model. Finally, we use the relationship to register the zoomed‐in image. This method outperforms some of the state‐of‐the‐art methods in many occasions. Several numerical examples and some statistical properties justify that this method works well in many applications. [ABSTRACT FROM AUTHOR]

Modelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones. [ABSTRACT FROM AUTHOR]

Data science consulting and collaboration units (DSUs) are core infrastructure for research at universities. Activities span data management, study design, data analysis, data visualization, predictive modelling, preparing reports, manuscript writing and advising on statistical methods and may include an experiential or teaching component. Partnerships are needed for a thriving DSU as an active part of the larger university network. Guidance for identifying, developing and managing successful partnerships for DSUs can be summarized in six rules: (1) align with institutional strategic plans, (2) cultivate partnerships that fit your mission, (3) ensure sustainability and prepare for growth, (4) define clear expectations in a partnership agreement, (5) communicate and (6) expect the unexpected. While these rules are not exhaustive, they are derived from experiences in a diverse set of DSUs, which vary by administrative home, mission, staffing and funding model. As examples in this paper illustrate, these rules can be adapted to different organizational models for DSUs. Clear expectations in partnership agreements are essential for high quality and consistent collaborations and address core activities, duration, staffing, cost and evaluation. A DSU is an organizational asset that should involve thoughtful investment if the institution is to gain real value. [ABSTRACT FROM AUTHOR]

The COVID‐19 pandemic led to unprecedented changes in all levels of society, including the statistical consulting field. This paper focuses on the experiences of graduate student consultants and clients at our statistical consulting center (SCC) that operates all year independent of semesters. During the lockdown period, work continued without interruption and was conducted remotely, but there was a temporary reduction in utilization. Advice on statistical methods, help with data analysis and educational offerings are the main appeals to utilize SCC services. We describe our mentoring approach for graduate student research assistants (RAs) and how pandemic changes affected RAs and clients. Based on experiences during the pandemic, we offer practical suggestions for SCCs' approaches to research support, work characteristics and collaborations to improve the experiences of graduate students, both as consultants and clients. Most collaboration meetings are now virtual by request from clients. Telecommuting supports flexible personal schedules and needs. Online educational offerings provide easier access for participants and more opportunities for a wider range of topics and presenters. However, mentoring sessions for RAs are best conducted in‐person, and every effort should be made to encourage in‐person interactions and collaborations between staff members to advance the effectiveness of post‐pandemic SCCs. [ABSTRACT FROM AUTHOR]

Deep learning has achieved unprecedented success in recent years. This approach essentially uses the composition of nonlinear functions to model the complex relationship between input features and output labels. However, a comprehensive theoretical understanding of why the hierarchical layered structure can exhibit superior expressive power is still lacking. In this paper, we provide an explanation for this phenomenon by measuring the approximation efficiency of neural networks with respect to discontinuous target functions. We focus on deep neural networks with rectified linear unit (ReLU) activation functions. We find that to achieve the same degree of approximation accuracy, the number of neurons required by a single‐hidden‐layer (SHL) network is exponentially greater than that required by a multi‐hidden‐layer (MHL) network. In practice, discontinuous points tend to contain highly valuable information (i.e., edges in image classification). We argue that this may be a very important reason accounting for the impressive performance of deep neural networks. We validate our theory in extensive experiments. [ABSTRACT FROM AUTHOR]

In recent years, multi‐response linear models have gained significant popularity in various statistical applications. However, the design aspects of multi‐response linear models with group‐wise considerations have received limited attention in the literature. This paper aims to thoroughly investigate D$$ D $$‐optimal designs for such models. Specifically, we focus on scenarios involving two groups, where the proportions of observations for each group can be arbitrarily selected or not. Two equivalence theorems are presented to elaborate the characterization of D$$ D $$‐optimal designs. Additionally, we delve into the admissibility of approximate designs and establish necessary conditions for a design to be deemed admissible. Several illustrative examples are addressed to demonstrate the application of the derived theoretical results. [ABSTRACT FROM AUTHOR]

Summary: Testing for equivalence, rather than testing for a difference, is an important component of some scientific studies. While the focus of the existing literature is on comparing two groups for equivalence, real‐world applications arise regularly that require testing across more than two groups. This paper reviews the existing approaches for testing across multiple groups and proposes a novel framework for multigroup equivalence testing under a Bayesian paradigm. This approach allows for a more scientifically meaningful definition of the equivalence margin and a more powerful test than the few existing alternatives. This approach also allows a new definition of equivalence based on future differences. [ABSTRACT FROM AUTHOR]

A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes, many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme has received wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships. However, the paper "Conditional extreme value models: fallacies and pitfalls" by Holger Drees and Anja Janßen provides a number of counterexamples to these results. This paper studies these counterexamples in a conditional extremes framework which involves marginal standardisation to a common exponentially decaying tailed marginal distribution. Our calculations show that some of the issues identified can be addressed in this way. [ABSTRACT FROM AUTHOR]

This paper introduces graph‐based mutually exciting processes (GB‐MEP) to model event times in network point processes, focusing on an application to docked bike‐sharing systems. GB‐MEP incorporates known relationships between nodes in a graph within the intensity function of a node‐based multivariate Hawkes process. This approach reduces the number of parameters to a quantity proportional to the number of nodes in the network, resulting in significant advantages for computational scalability when compared with traditional methods. The model is applied on event data observed on the Santander Cycles network in central London, demonstrating that exploiting network‐wide information related to geographical location of the stations is beneficial to improve the performance of node‐based models for applications in bike‐sharing systems. The proposed GB‐MEP framework is more generally applicable to any network point process where a distance function between nodes is available, demonstrating wider applicability. [ABSTRACT FROM AUTHOR]