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In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often associated with Gaussian processes. However, when considering non-linear prediction for non-Gaussian and categorical data, the Kriging prediction is no longer optimal, and the associated variance is often overly optimistic. Although deep neural networks (DNNs) are widely used for general classification and prediction, they have not been studied thoroughly for data with spatial dependence. In this work, we propose a novel DNN structure for spatial prediction, where the spatial dependence is captured by adding an embedding layer of spatial coordinates with basis functions. We show in theory and simulation studies that the proposed DeepKriging method has a direct link to Kriging in the Gaussian case, and it has multiple advantages over Kriging for non-Gaussian and non-stationary data, i.e., it provides non-linear predictions and thus has smaller approximation errors, it does not require operations on covariance matrices and thus is scalable for large datasets, and with sufficiently many hidden neurons, it provides the optimal prediction in terms of model capacity. We further explore the possibility of quantifying prediction uncertainties based on density prediction without assuming any data distribution. Finally, we apply the method to predicting PM2.5 concentrations across the continental United States.

We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel representations of FGM copulas based on symmetric multivariate Bernoulli distributions and order statistics. First, we detail families of multivariate distributions with closed-form solutions for the cumulative distribution function or moments of the aggregate random variables. We order aggregate random variables under the convex order and provide methods to compute the cumulative distribution function of aggregate rvs when the marginals are discrete. Finally, we discuss risk-sharing and capital allocation, providing numerical examples for each.

In most circumstances, probability sampling is the only way to ensure unbiased inference about population quantities where a complete census is not possible. As we enter the era of 'big data', however, nonprobability samples, whose sampling mechanisms are unknown, are undergoing a renaissance. We explain why the use of nonprobability samples can lead to spurious conclusions, and why seemingly large nonprobability samples can be (effectively) very small. We also review some recent controversies surrounding the use of nonprobability samples in biodiversity monitoring. These points notwithstanding, we argue that nonprobability samples can be useful, provided that their limitations are assessed, mitigated where possible and clearly communicated. Ecologists can learn much from other disciplines on each of these fronts., Comment: Two tables, two boxes

Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging modalities, and (c) testing independence between brain regions across different modalities. Considering a general form for all the three tests, we develop a global testing procedure and a multiple testing procedure controlling the false discovery rate. We study theoretical properties of the proposed tests and develop a computationally efficient distributed algorithm. The proposed methods and theory are general and relevant for many statistical problems of testing independence structure among the components of high-dimensional random vectors with arbitrary dependence structures. We also illustrate our proposed methods via extensive simulations and analysis of five task fMRI contrast maps in the HCP study.

Out-of-sample prediction is the acid test of predictive models, yet an independent test dataset is often not available for assessment of the prediction error. For this reason, out-of-sample performance is commonly estimated using data splitting algorithms such as cross-validation or the bootstrap. For quantitative outcomes, the ratio of variance explained to total variance can be summarized by the coefficient of determination or in-sample $R^2$, which is easy to interpret and to compare across different outcome variables. As opposed to the in-sample $R^2$, the out-of-sample $R^2$ has not been well defined and the variability on the out-of-sample $\hat{R}^2$ has been largely ignored. Usually only its point estimate is reported, hampering formal comparison of predictability of different outcome variables. Here we explicitly define the out-of-sample $R^2$ as a comparison of two predictive models, provide an unbiased estimator and exploit recent theoretical advances on uncertainty of data splitting estimates to provide a standard error for the $\hat{R}^2$. The performance of the estimators for the $R^2$ and its standard error are investigated in a simulation study. We demonstrate our new method by constructing confidence intervals and comparing models for prediction of quantitative $\text{Brassica napus}$ and $\text{Zea mays}$ phenotypes based on gene expression data.

A new method for clustering functional data is proposed via information maximization. The proposed method learns a probabilistic classifier in an unsupervised manner so that mutual information (or squared loss mutual information) between data points and cluster assignments is maximized. A notable advantage of this proposed method is that it only involves continuous optimization of model parameters, which is simpler than discrete optimization of cluster assignments and avoids the disadvantages of generative models. Unlike some existing methods, the proposed method does not require estimating the probability densities of Karhunen-Lo`eve expansion scores under different clusters and also does not require the common eigenfunction assumption. The empirical performance and the applications of the proposed methods are demonstrated by simulation studies and real data analyses. In addition, the proposed method allows for out-of-sample clustering, and its effect is comparable with that of some supervised classifiers.

In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, here we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and over-dispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters ($\lambda$ and $\nu$). We then fit our model to neural data from neurons in primary visual cortex and "place cells" in the hippocampus. We find that this method out-performs previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience., Comment: 6 figures

Clinical trials disruption has always represented a non negligible part of the ending of interventional studies. While the SARS-CoV-2 (COVID-19) pandemic has led to an impressive and unprecedented initiation of clinical research, it has also led to considerable disruption of clinical trials in other disease areas, with around 80% of non-COVID-19 trials stopped or interrupted during the pandemic. In many cases the disrupted trials will not have the planned statistical power necessary to yield interpretable results. This paper describes methods to compensate for the information loss arising from trial disruptions by incorporating additional information available from auxiliary data sources. The methods described include the use of auxiliary data on baseline and early outcome data available from the trial itself and frequentist and Bayesian approaches for the incorporation of information from external data sources. The methods are illustrated by application to the analysis of artificial data based on the Primary care pediatrics Learning Activity Nutrition (PLAN) study, a clinical trial assessing a diet and exercise intervention for overweight children, that was affected by the COVID-19 pandemic. We show how all of the methods proposed lead to an increase in precision relative to use of complete case data only.

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while still resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output., Comment: code available at https://github.com/katzfuss-group/BaTraMaSpa

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change observations are allowed to be non-stationary with some possible parametric uncertainty in their distribution. In particular, it is assumed that the cumulative Kullback-Leibler divergence between the post-change and the pre-change distributions grows in a certain manner with time after the change-point. For the case where the post-change distributions are known, a universal asymptotic lower bound on the delay is derived, as the false alarm rate goes to zero. Furthermore, a window-limited Cumulative Sum (CuSum) procedure is developed, and shown to achieve the lower bound asymptotically. For the case where the post-change distributions have parametric uncertainty, a window-limited (WL) generalized likelihood-ratio (GLR) CuSum procedure is developed and is shown to achieve the universal lower bound asymptotically. Extensions to the case with dependent observations are discussed. The analysis is validated through numerical results on synthetic data. The use of the WL-GLR-CuSum procedure in monitoring pandemics is also demonstrated.

Single-arm trials (SATs) may be used to support regulatory submissions in settings where there is a high unmet medical need and highly promising early efficacy data undermine the equipoise needed for randomization. In this context, patient-level real-world data (RWD) may be used to create an external control arm (ECA) to contextualize the SAT results. However, naive comparisons of the SAT with its ECA will yield biased estimates of causal effects if groups are imbalanced with regards to (un)measured prognostic factors. Several methods are available to adjust for measured confounding, but the interpretation of such analyses is challenging unless the causal question of interest is clearly defined, and the estimator is aligned with the estimand. Additional complications arise when patients in the ECA are eligible for the SAT at multiple timepoints. In this paper, we use a case-study of a pivotal SAT of a novel CAR-T therapy for heavily pre-treated patients with follicular lymphoma to illustrate how a combination of the target trial and the ICH E9(R1) estimand frameworks can be used to define the target estimand and avoid common methodological pitfalls related to the design of the ECA and comparisons with the SAT. We also propose an approach to address the challenge of how to define an appropriate time zero for external controls who meet the SAT inclusion/exclusion criteria at several timepoints. Use of the target trial and estimand frameworks facilitates discussions amongst internal and external stakeholders, as well as an early assessment of the adequacy of the available RWD.

Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the estimation of neuronal activity from functional magnetic resonance data without prior knowledge of the stimulus or activation timing, utilizing an approximate knowledge of the hemodynamic response to local neuronal activity. These methods work by generating a parametric family of solutions with different sparsity, among which an ultimate choice is made using an information criteria. We propose a novel approach, that instead of selecting a single option from the family of regularized solutions, utilizes the whole family of such sparse regression solutions. Namely, their ensemble provides a first approximation of probability of activation at each time-point, and together with the conditional neuronal activity distributions estimated with the theory of mixtures with varying concentrations, they serve as the inputs to a Bayes classifier eventually deciding on the verity of activation at each time-point. We show in extensive numerical simulations that this new method performs favourably in comparison with standard approaches in a range of realistic scenarios. This is mainly due to the avoidance of overfitting and underfitting that commonly plague the solutions based on sparse regression combined with model selection methods, including the corrected Akaike Information Criterion. This advantage is finally documented in selected fMRI task datasets.

The seminal Bradley-Terry model exhibits transitivity, i.e., the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each player. Such transitive models do not account for different strategies of play between each pair of players, which gives rise to {\it intransitivity}. Various intransitive parametric models have been proposed but they lack the flexibility to cover the different strategies across $n$ players, with the $O(n^2)$ values of intransitivity modelled using $O(n)$ parameters, whilst they are not parsimonious when the intransitivity is simple. We overcome their lack of adaptability by allocating each pair of players to one of a random number of $K$ intransitivity levels, each level representing a different strategy. Our novel approach for the skill parameters involves having the $n$ players allocated to a random number of $A, Comment: 24 pages, 2 figures, 1 tables in the main text

By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular biology, theory building in particle physics, and resource allocation in epidemiology, for example. We introduce the probabilistic and computational concepts underlying modern generative models and then analyze how they can be used to inform experimental design, iterative model refinement, goodness-of-fit evaluation, and agent based simulation. We emphasize a modular view of generative mechanisms and discuss how they can be flexibly recombined in new problem contexts. We provide practical illustrations throughout, and code for reproducing all examples is available at https://github.com/krisrs1128/generative_review . Finally, we observe how research in generative models is currently split across several islands of activity, and we highlight opportunities lying at disciplinary intersections.

A common approach to modelling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to datasets from economics and neuroscience.

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. Here we show that in the context of inverse problems involving integral operators, one faces additional difficulties that hinder inversion on large grids. Furthermore, in that context, covariance matrices can become too large to be stored. By leveraging recent results about sequential disintegrations of Gaussian measures, we are able to introduce an implicit representation of posterior covariance matrices that reduces the memory footprint by only storing low rank intermediate matrices, while allowing individual elements to be accessed on-the-fly without needing to build full posterior covariance matrices. Moreover, it allows for fast sequential inclusion of new observations. These features are crucial when considering sequential experimental design tasks. We demonstrate our approach by computing sequential data collection plans for excursion set recovery for a gravimetric inverse problem, where the goal is to provide fine resolution estimates of high density regions inside the Stromboli volcano, Italy. Sequential data collection plans are computed by extending the weighted integrated variance reduction (wIVR) criterion to inverse problems. Our results show that this criterion is able to significantly reduce the uncertainty on the excursion volume, reaching close to minimal levels of residual uncertainty. Overall, our techniques allow the advantages of probabilistic models to be brought to bear on large-scale inverse problems arising in the natural sciences. Particularly, applying the latest developments in Bayesian sequential experimental design on realistic large-scale problems opens new venues of research at a crossroads between mathematical modelling of natural phenomena, statistical data science, and active learning.

Understanding how microbes interact with each other is key to revealing the underlying role that microorganisms play in the host or environment and to identifying microorganisms as an agent that can potentially alter the host or environment. For example, understanding how the microbial interactions associate with parasitic infection can help resolve potential drug or diagnostic test for parasitic infection. To unravel the microbial interactions, existing tools often rely on graphical models to infer the conditional dependence of microbial abundances to represent their interactions. However, current methods do not simultaneously account for the discreteness, compositionality, and heterogeneity inherent to microbiome data. Thus, we build a new approach called "compositional graphical lasso" upon existing tools by incorporating the above characteristics into the graphical model explicitly. We illustrate the advantage of compositional graphical lasso over current methods under a variety of simulation scenarios and on a benchmark study, the Tara Oceans Project. Moreover, we present our results from the analysis of a dataset from the Zebrafish Parasite Infection Study. Our approach identifies changes in interaction degree between infected and uninfected individuals for three taxa, Photobacterium, Gemmobacter, and Paucibacter, which are inversely predicted by other methods. Further investigation of these method-specific taxa interaction changes reveals their biological plausibility. In particular, we speculate on the potential pathobiotic roles of Photobacterium and Gemmobacter in the zebrafish gut, and the potential probiotic role of Paucibacter. Collectively, our analyses demonstrate that compositional graphical lasso provides a powerful means of accurately resolving interactions between microbiota and can thus drive novel biological discovery.

Researchers faced with a sequence of candidate model specifications must often choose the best specification that does not violate a testable identification assumption. One option in this scenario is sequential specification tests: hypothesis tests of the identification assumption over the sequence. Borrowing an idea from the change-point literature, this paper shows how to use the distribution of p-values from sequential specification tests to estimate the point in the sequence where the identification assumption ceases to hold. Unlike current approaches, this method is robust to individual errant p-values and does not require choosing a test level or tuning parameter. This paper demonstrates the method's properties with a simulation study, and illustrates it by application to the problems of choosing a bandwidth in a regression discontinuity design while maintaining covariate balance and of choosing a lag order for a time series model., Forthcoming in Communications in Statistics -- Theory and Methods

Pediatric patients should have access to medicines that have been appropriately evaluated for safety and efficacy. Given this goal of revised labelling, the adequacy of the pediatric clinical development plan and resulting safety database must inform a favorable benefit-risk assessment for the intended use of the medicinal product. While extrapolation from adults can be used to support efficacy of drugs in children, there may be a reluctance to use the same approach in safety assessments, wiping out potential gains in trial efficiency through a reduction of sample size. To address this reluctance, we explore safety review in pediatric trials, including factors affecting these data, specific types of safety assessments, and precision on the estimation of event rates for specific adverse events (AEs) that can be achieved. In addition, we discuss the assessments which can provide a benchmark for the use of extrapolation of safety that focuses on on-target effects. Finally, we explore a unified approach for understanding precision using Bayesian approaches as the most appropriate methodology to describe/ascertain risk in probabilistic terms for the estimate of the event rate of specific AEs.

This paper proposes a data-driven machine learning framework for parameter estimation and uncertainty quantification in epidemic models based on two key ingredients: (i) prior parameters learning via the cross-entropy method and (ii) update of the model calibration and uncertainty propagation through approximate Bayesian computation. The effectiveness of the new methodology is illustrated with the aid of actual data from COVID-19 epidemic at Rio de Janeiro city in Brazil, employing an ordinary differential equation based model with a generalized SEIR-type mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, which makes the proposed methodology very appealing for use in the context of real-time epidemic modeling.

In network meta-analysis (NMA), we synthesize all relevant evidence about health outcomes with competing treatments. The evidence may come from randomized clinical trials (RCT) or non-randomized studies (NRS) as individual participant data (IPD) or as aggregate data (AD). We present a suite of Bayesian NMA and network meta-regression (NMR) models allowing for cross-design and cross-format synthesis. The models integrate a three-level hierarchical model for synthesizing IPD and AD into four approaches. The four approaches account for differences in the design and risk of bias (RoB) in the RCT and NRS evidence. These four approaches variously ignoring differences in RoB, using NRS to construct penalized treatment effect priors and bias-adjustment models that control the contribution of information from high RoB studies in two different ways. We illustrate the methods in a network of three pharmacological interventions and placebo for patients with relapsing-remitting multiple sclerosis. The estimated relative treatment effects do not change much when we accounted for differences in design and RoB. Conducting network meta-regression showed that intervention efficacy decreases with increasing participant age. We also re-analysed a network of 431 RCT comparing 21 antidepressants, and we did not observe material changes in intervention efficacy when adjusting for studies' high RoB. We re-analysed both case studies accounting for different study RoB. In summary, the described suite of NMA/NMR models enables inclusion of all relevant evidence while incorporating information on the within-study bias in both observational and experimental data and enabling estimation of individualized treatment effects through the inclusion of participant characteristics. This article is protected by copyright. All rights reserved.

Inter-rater reliability (IRR), which is a prerequisite of high-quality ratings and assessments, may be affected by contextual variables, such as the rater’s or ratee’s gender, major, or experience. Identification of such heterogeneity sources in IRR is important for the implementation of policies with the potential to decrease measurement error and to increase IRR by focusing on the most relevant subgroups. In this study, we propose a flexible approach for assessing IRR in cases of heterogeneity due to covariates by directly modeling differences in variance components. We use Bayes factors (BFs) to select the best performing model, and we suggest using Bayesian model averaging as an alternative approach for obtaining IRR and variance component estimates, allowing us to account for model uncertainty. We use inclusion BFs considering the whole model space to provide evidence for or against differences in variance components due to covariates. The proposed method is compared with other Bayesian and frequentist approaches in a simulation study, and we demonstrate its superiority in some situations. Finally, we provide real data examples from grant proposal peer review, demonstrating the usefulness of this method and its flexibility in the generalization of more complex designs.

Stroke is known as a major global health problem, and for stroke survivors it is key to monitor the recovery levels. However, traditional stroke rehabilitation assessment methods (such as the popular clinical assessment) can be subjective and expensive, and it is also less convenient for patients to visit clinics in a high frequency. To address this issue, in this work based on wearable sensing and machine learning techniques, we develop an automated system that can predict the assessment score in an objective manner. With wrist-worn sensors, accelerometer data is collected from 59 stroke survivors in free-living environments for a duration of 8 weeks, and we map the week-wise accelerometer data(3 days per week) to the assessment score by developing signal processing and predictive model pipeline. To achieve this, we propose two types of new features, which can encode the rehabilitation information from both paralysed and non-paralysed sides while suppressing the high level noises such as irrelevant daily activities. Based on the proposed features, we further develop the longitudinal mixed-effects model with Gaussian process prior (LMGP), which can model the random effects caused by different subjects and time slots (during the 8 weeks). Comprehensive experiments are conducted to evaluate our system on both acute and chronic patients, and the promising results suggest its effectiveness., Comment: 32 pages, accepted for publication in CCF Transactions on Pervasive Computing and Interaction

Upright stance tested with a superposition of support surface tilt and translation. Steady state response is characterized by frequency response function. Interaction between two stimuli absent in most of the cases. Larger stimuli may create interaction. Simulations suggest that the observed effects can be due to joint stiffness modulation., Comment: 10 pages, 7 figures

Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modelling to the relative survival framework. In order to facilitate the inference on the parameters of the proposed model, we select frailty distributions which produce closed-form expressions of the marginal hazard and survival functions. The resulting model allows for an intuitive interpretation, in which the frailties induce a selection of the healthier individuals among survivors. We model the excess hazard using a flexible parametric model with a general hazard structure which facilitates the inclusion of time-dependent effects. We illustrate the performance of the proposed methodology through a simulation study. We present a real-data example using data from lung cancer patients diagnosed in England, and discuss the impact of not accounting for unobserved heterogeneity on the estimation of net survival. The methodology is implemented in the R package IFNS., Accepted for publication in Statistics in Medicine. Codes and Examples can be found at: https://github.com/FJRubio67/IFNS

Aims Multinomial logistic regression models allow one to predict the risk of a categorical outcome with > 2 categories. When developing such a model, researchers should ensure the number of participants ([Formula: see text]) is appropriate relative to the number of events ([Formula: see text]) and the number of predictor parameters ([Formula: see text]) for each category k. We propose three criteria to determine the minimum n required in light of existing criteria developed for binary outcomes. Proposed criteria The first criterion aims to minimise the model overfitting. The second aims to minimise the difference between the observed and adjusted [Formula: see text] Nagelkerke. The third criterion aims to ensure the overall risk is estimated precisely. For criterion (i), we show the sample size must be based on the anticipated Cox-snell [Formula: see text] of distinct ‘one-to-one’ logistic regression models corresponding to the sub-models of the multinomial logistic regression, rather than on the overall Cox-snell [Formula: see text] of the multinomial logistic regression. Evaluation of criteria We tested the performance of the proposed criteria (i) through a simulation study and found that it resulted in the desired level of overfitting. Criterion (ii) and (iii) were natural extensions from previously proposed criteria for binary outcomes and did not require evaluation through simulation. Summary We illustrated how to implement the sample size criteria through a worked example considering the development of a multinomial risk prediction model for tumour type when presented with an ovarian mass. Code is provided for the simulation and worked example. We will embed our proposed criteria within the pmsampsize R library and Stata modules.

Covariate balance is crucial in obtaining unbiased estimates of treatment effects in observational studies. Methods based on inverse probability weights have been widely used to estimate treatment effects with observational data. Machine learning techniques have been proposed to estimate propensity scores. These techniques however target accuracy instead of covariate balance. Methods that target covariate balance have been successfully proposed and largely applied to estimate treatment effects on continuous outcomes. However, in many medical and epidemiological applications, the interest lies in estimating treatment effects on time-to-event outcomes. With this type of data, one of the most common estimands of interest is the marginal hazard ratio of the Cox proportional hazard model. In this paper, we start by presenting robust orthogonality weights (ROW), a set of weights obtained by solving a quadratic constrained optimization problem that maximizes precision while constraining covariate balance defined as the sample correlation between confounders and treatment. By doing so, ROW optimally deal with both binary and continuous treatments. We then evaluate the performance of the proposed weights in estimating marginal hazard ratios of binary and continuous treatments with time-to-event outcomes in a simulation study. We finally apply ROW on the evaluation of the effect of hormone therapy on time to coronary heart disease and on the effect of red meat consumption on time to colon cancer among 24,069 postmenopausal women enrolled in the Women's Health Initiative observational study.

One of the essential elements in implementing a closed-loop irrigation system is soil moisture estimation based on a limited number of available sensors. One associated problem is the determination of the optimal locations to install the sensors such that good soil moisture estimation can be obtained. In our previous work, the modal degree of observability was employed to address the problem of optimal sensor placement for soil moisture estimation of agro-hydrological systems. It was demonstrated that the optimally placed sensors can improve the soil moisture estimation performance. However, it is unclear whether the optimal sensor placement can significantly improve the soil moisture estimation performance in actual applications. In this work, we investigate the impact of sensor placement in soil moisture estimation for an actual agricultural field in Lethbridge, Alberta, Canada. In an experiment on the studied field, 42 soil moisture sensors were installed at different depths to collect the soil moisture measurements for one growing season. A three-dimensional agro-hydrological model with heterogeneous soil parameters of the studied field is developed. The modal degree of observability is applied to the three-dimensional system to determine the optimal sensor locations. The extended Kalman filter (EKF) is chosen as the data assimilation tool to estimate the soil moisture content of the studied field. Soil moisture estimation results for different scenarios are obtained and analyzed to investigate the effects of sensor placement on the performance of soil moisture estimation in the actual applications.

The generalized g-formula can be used to estimate the probability of survival under a sustained treatment strategy. When treatment strategies are deterministic, estimators derived from the so-called efficient influence function (EIF) for the g-formula will be doubly robust to model misspecification. In recent years, several practical applications have motivated estimation of the g-formula under non-deterministic treatment strategies where treatment assignment at each time point depends on the observed treatment process. In this case, EIF-based estimators may or may not be doubly robust. In this paper, we provide sufficient conditions to ensure existence of doubly robust estimators for intervention treatment distributions that depend on the observed treatment process for point treatment interventions, and give a class of intervention treatment distributions dependent on the observed treatment process that guarantee model doubly and multiply robust estimators in longitudinal settings. Motivated by an application to pre-exposure prophylaxis (PrEP) initiation studies, we propose a new treatment intervention dependent on the observed treatment process. We show there exist 1) estimators that are doubly and multiply robust to model misspecification, and 2) estimators that when used with machine learning algorithms can attain fast convergence rates for our proposed intervention. Theoretical results are confirmed via simulation studies., 19 pages, 1 figure

Precise segmentation is a vital first step to analyze semantic information of cardiac cycle and capture anomaly with cardiovascular signals. However, in the field of deep semantic segmentation, inference is often unilaterally confounded by the individual attribute of data. Towards cardiovascular signals, quasi-periodicity is the essential characteristic to be learned, regarded as the synthesize of the attributes of morphology (Am) and rhythm (Ar). Our key insight is to suppress the over-dependence on Am or Ar while the generation process of deep representations. To address this issue, we establish a structural causal model as the foundation to customize the intervention approaches on Am and Ar, respectively. In this paper, we propose contrastive causal intervention (CCI) to form a novel training paradigm under a frame-level contrastive framework. The intervention can eliminate the implicit statistical bias brought by the single attribute and lead to more objective representations. We conduct comprehensive experiments with the controlled condition for QRS location and heart sound segmentation. The final results indicate that our approach can evidently improve the performance by up to 0.41% for QRS location and 2.73% for heart sound segmentation. The efficiency of the proposed method is generalized to multiple databases and noisy signals., Comment: submitted to IEEE Journal of Biomedical and Health Informatics (J-BHI)

Predicting the future performance of young runners is an important research issue in experimental sports science and performance analysis. We analyse a dataset with annual seasonal best performances of male middle distance runners for a period of 14 years and provide a modelling framework that accounts for both the fact that each runner has typically run in 3 distance events (800, 1,500, and 5,000 m) and the presence of periods of no running activities. We propose a latent class matrix-variate state space model and we empirically demonstrate that accounting for missing data patterns in runners’ careers improves the out of sample prediction of their performances over time. In particular, we demonstrate that for this analysis, the missing data patterns provide valuable information for the prediction of runner’s performance.

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations., major revision - fixed a mistake in the proof

We demonstrate how Hahn et al.'s Bayesian Causal Forests model (BCF) can be used to estimate conditional average treatment effects for the longitudinal dataset in the 2022 American Causal Inference Conference Data Challenge. Unfortunately, existing implementations of BCF do not scale to the size of the challenge data. Therefore, we developed flexBCF -- a more scalable and flexible implementation of BCF -- and used it in our challenge submission. We investigate the sensitivity of our results to the choice of propensity score estimation method and the use of sparsity-inducing regression tree priors. While we found that our overall point predictions were not especially sensitive to these modeling choices, we did observe that running BCF with flexibly estimated propensity scores often yielded better-calibrated uncertainty intervals.

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

Understanding electrical energy demand at the consumer level plays an important role in planning the distribution of electrical networks and offering of off-peak tariffs, but observing individual consumption patterns is still expensive. On the other hand, aggregated load curves are normally available at the substation level. The proposed methodology separates substation aggregated loads into estimated mean consumption curves, called typical curves, including information given by explanatory variables. In addition, a model-based clustering approach for substations is proposed based on the similarity of their consumers typical curves and covariance structures. The methodology is applied to a real substation load monitoring dataset from the United Kingdom and tested in eight simulated scenarios., 46 pages, 11 figures

In a paper recently published in this journal, van Marle et al. (van Marle et al., 2022) introduce an interesting new data set for land use and land cover change CO2 emissions (LULCC) that they use to study whether a trend is present in the airborne fraction (AF), defined as the fraction of CO2 emissions remaining in the atmosphere. Testing the hypothesis of a trend in the AF has attracted much attention, with the overall consensus that no statistical evidence is found for a trend in the data (Knorr, 2009; Gloor et al., 2010; Raupach et al., 2014; Bennedsen et al., 2019). In their paper, van Marle et al. analyze the AF as implied by three different LULCC emissions time series (GCP, H&N, and their new data series). In a Monte Carlo simulation study based on their new LULCC emissions data, van Marle et al. find evidence of a declining trend in the AF. In this note, we argue that the statistical analysis presented in van Marle et al. can be improved in several respects. Specifically, the Monte Carlo study presented in van Marle et al. is not conducive to determine whether there is a trend in the AF. Further, we re-examine the evidence for a trend in the AF by using a variety of different statistical tests. The statistical evidence for an uninterrupted (positive or negative) trend in the airborne fraction remains mixed at best. When allowing for a break in the trend, there is some evidence for upward trends in both subsamples.

The distribution of the incubation period of the novel coronavirus disease that emerged in 2019 (COVID-19) has crucial clinical implications for understanding this disease and devising effective disease-control measures. Qin et al. (2020) designed a cross-sectional and forward follow-up study to collect the duration times between a specific observation time and the onset of COVID-19 symptoms for a number of individuals. They further proposed a mixture forward-incubation-time epidemic model, which is a mixture of an incubation-period distribution and a forward time distribution, to model the collected duration times and to estimate the incubation-period distribution of COVID-19. In this paper, we provide sufficient conditions for the identifiability of the unknown parameters in the mixture forward-incubation-time epidemic model when the incubation period follows a two-parameter distribution. Under the same setup, we propose a likelihood ratio test (LRT) for testing the null hypothesis that the mixture forward-incubation-time epidemic model is a homogeneous exponential distribution. The testing problem is non-regular because a nuisance parameter is present only under the alternative. We establish the limiting distribution of the LRT and identify an explicit representation for it. The limiting distribution of the LRT under a sequence of local alternatives is also obtained. Our simulation results indicate that the LRT has desirable type I errors and powers, and we analyze a COVID-19 outbreak dataset from China to illustrate the usefulness of the LRT., 34 pages, 2 figures, 2 tables

High angular resolution diffusion imaging (HARDI) is a type of diffusion magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere in q-space. It has been widely used in data acquisition for human brain structural connectome analysis. To more accurately estimate the structural connectome, dense samples in q-space are often acquired, potentially resulting in long scanning times and logistical challenges. This paper proposes a statistical method to select q-space directions optimally and estimate the local diffusion function from sparse observations. The proposed approach leverages relevant historical dMRI data to calculate a prior distribution to characterize local diffusion variability in each voxel in a template space. For a new subject to be scanned, the priors are mapped into the subject-specific coordinate and used to help select the best q-space samples. Simulation studies demonstrate big advantages over the existing HARDI sampling and analysis framework. We also applied the proposed method to the Human Connectome Project data and a dataset of aging adults with mild cognitive impairment. The results indicate that with very few q-space samples (e.g., 15 or 20), we can recover structural brain networks comparable to the ones estimated from 60 or more diffusion directions with the existing methods. n Connectome Project data demonstrate that our proposed method provides substantial advantages over its competitors.

The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models. These model ensembles commonly assume stable coexistence of species in the absence of available data. However, existing ensemble-generation methods become computationally inefficient as the size of the ecosystem network increases, preventing larger networks from being studied. We present a novel sequential Monte Carlo sampling approach for ensemble generation that is orders of magnitude faster than existing approaches. We demonstrate that the methods produce equivalent parameter inferences, model predictions, and tightly constrained parameter combinations using a novel sensitivity analysis method. For one case study, we demonstrate a speed-up from 108 days to 6 hours, while maintaining equivalent ensembles. Now, for the first time, larger and more realistic networks can be practically simulated.

Modern cell-perturbation experiments expose cells to panels of hundreds of stimuli, such as cytokines or CRISPR guides that perform gene knockouts. These experiments are designed to investigate whether a particular gene is upregulated or downregulated by exposure to each treatment. However, due to high levels of experimental noise, typical estimators of whether a gene is up- or down-regulated make many errors. In this paper, we make two contributions. Our first contribution is a new estimator of regulatory effect that makes use of Gaussian processes and factor analysis to leverage auxiliary information about similarities among treatments, such as the chemical similarity among the drugs used to perturb cells. The new estimator typically has lower variance than unregularized estimators, which do not use auxiliary information, but higher bias. To assess whether this new estimator improves accuracy (i.e., achieves a favorable trade-off between bias and variance), we cannot simply compute its error on heldout data as ``ground truth'' about the effects of treatments is unavailable. Our second contribution is a novel data-splitting method to evaluate error rates. This data-splitting method produces valid error bounds using ``sign-valid'' estimators, which by definition have the correct sign more often than not. Using this data-splitting method, through a series of case studies we find that our new estimator, which leverages auxiliary information, can yield a three-fold reduction in type S error rate.

The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then we turn to the Petersen model for estimating the population size $N$ in a two-way capture recapture experiment. We construct a Bayesian model for $N$ by combining a Waring prior with the hypergeometric distribution for the number of units caught twice in the experiment. Confidence intervals for $N$ are obtained using quantiles of the posterior, a generalized Waring distribution. The standard confidence interval for the population size constructed using the asymptotic variance of Petersen estimator and .5 logit transformed interval are shown to be special cases of the generalized Waring confidence interval. The true coverage of this interval is shown to be bigger than or equal to its nominal converage in small populations, regardless of the capture probabilities. In addition, its length is substantially smaller than that of the .5 logit transformed interval. Thus a generalized Waring confidence interval appears to be the best way to quantify the uncertainty of the Petersen estimator for populations size.

Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly limited to undirected relations. However, direct relations are more common and may introduce extra information. In this paper, we study the community detection (or clustering) in multi-layer directed networks. To take into account the asymmetry, we develop a novel spectral-co-clustering-based algorithm to detect co-clusters, which capture the sending patterns and receiving patterns of nodes, respectively. Specifically, we compute the eigen-decomposition of the debiased sum of Gram matrices over the layer-wise adjacency matrices, followed by the k-means, where the sum of Gram matrices is used to avoid possible cancellation of clusters caused by direct summation. We provide theoretical analysis of the algorithm under the multi-layer stochastic co-block model, where we relax the common assumption that the cluster number is coupled with the rank of the model. After a systematic analysis of the eigen-vectors of population version algorithm, we derive the misclassification rates which show that multi-layers would bring benefit to the clustering performance. The experimental results of simulated data corroborate the theoretical predictions, and the analysis of a real-world trade network dataset provides interpretable results.

An election audit is risk-limiting if the audit limits (to a pre-specified threshold) the chance that an erroneous electoral outcome will be certified. Extant methods for auditing instant-runoff voting (IRV) elections are either not risk-limiting or require cast vote records (CVRs), the voting system's electronic record of the votes on each ballot. CVRs are not always available, for instance, in jurisdictions that tabulate IRV contests manually. We develop an RLA method (AWAIRE) that uses adaptively weighted averages of test supermartingales to efficiently audit IRV elections when CVRs are not available. The adaptive weighting 'learns' an efficient set of hypotheses to test to confirm the election outcome. When accurate CVRs are available, AWAIRE can use them to increase the efficiency to match the performance of existing methods that require CVRs. We provide an open-source prototype implementation that can handle elections with up to six candidates. Simulations using data from real elections show that AWAIRE is likely to be efficient in practice. We discuss how to extend the computational approach to handle elections with more candidates. Adaptively weighted averages of test supermartingales are a general tool, useful beyond election audits to test collections of hypotheses sequentially while rigorously controlling the familywise error rate., 16 pages, 3 figures, accepted for E-Vote-ID 2023

We consider models for network indexed multivariate data involving a dependence between variables as well as across graph nodes. In the framework of these models, we focus on outliers detection and introduce the concept of edgewise outliers. For this purpose, we first derive the distribution of some sums of squares, in particular squared Mahalanobis distances that can be used to fix detection rules and thresholds for outlier detection. We then propose a robust version of the deterministic MCD algorithm that we call edgewise MCD. An application on simulated data shows the interest of taking the dependence structure into account. We also illustrate the utility of the proposed method with a real data set.

In recent years, autonomous vehicles have become increasingly popular, leading to extensive research on their safe and efficient operation. Understanding road yielding behavior is crucial for incorporating the appropriate driving behavior into algorithms. This paper focuses on investigating drivers' yielding behavior at unsignalized intersections. We quantified and modelled the speed reduction time for vulnerable road users at a zebra crossing using parametric survival analysis. We then evaluated the impact of speed reduction time in two different interaction scenarios, compared to the baseline condition of no interaction through an accelerated failure time regression model with the log-logistic distribution. The results demonstrate the unique characteristics of each yielding behavior scenario, emphasizing the need to account for these variations in the modelling process of autonomous vehicles.

A very popular model-agnostic technique for explaining predictive models is the SHapley Additive exPlanation (SHAP). The two most popular versions of SHAP are a conditional expectation version and an unconditional expectation version (the latter is also known as interventional SHAP). Except for tree-based methods, usually the unconditional version is used (for computational reasons). We provide a (surrogate) neural network approach which allows us to efficiently calculate the conditional version for both neural networks and other regression models, and which properly considers the dependence structure in the feature components. This proposal is also useful to provide drop1 and anova analyses in complex regression models which are similar to their generalized linear model (GLM) counterparts, and we provide a partial dependence plot (PDP) counterpart that considers the right dependence structure in the feature components., 24 pages, 9 figures

Malnutrition and dehydration are strongly associated with increased cognitive and functional decline in people living with dementia (PLWD), as well as an increased rate of hospitalisations in comparison to their healthy counterparts. Extreme changes in eating and drinking behaviours can often lead to malnutrition and dehydration, accelerating the progression of cognitive and functional decline and resulting in a marked reduction in quality of life. Unfortunately, there are currently no established methods by which to objectively detect such changes. Here, we present the findings of an extensive quantitative analysis conducted on in-home monitoring data collected from 73 households of PLWD using Internet of Things technologies. The Coronavirus 2019 (COVID-19) pandemic has previously been shown to have dramatically altered the behavioural habits, particularly the eating and drinking habits, of PLWD. Using the COVID-19 pandemic as a natural experiment, we conducted linear mixed-effects modelling to examine changes in mean kitchen activity within a subset of 21 households of PLWD that were continuously monitored for 499 days. We report an observable increase in day-time kitchen activity and a significant decrease in night-time kitchen activity (t(147) = -2.90, p < 0.001). We further propose a novel analytical approach to detecting changes in behaviours of PLWD using Markov modelling applied to remote monitoring data as a proxy for behaviours that cannot be directly measured. Together, these results pave the way to introduce improvements into the monitoring of PLWD in naturalistic settings and for shifting from reactive to proactive care., 12 pages, 7 figures, journal

Text analysis is the process of constructing structured data from unstructured textual content, usually implemented in Python. In terms of the principles of text analysis, a computer program with the ability to read a file and match it with a regular expression is all that is needed for basic text analysis. However, few researchers have used Stata as their main text analysis tool. In this paper, I will take a step-by-step approach to the practical process, giving examples of how text analysis can be performed with Stata, and comparing the code and running time with Python., Declaration: I am Xiangtai Zuo and I have an English name Shutter Zor. This can be found from my Google Scholar or ORCID information. Thanks for The arXiv Content Management & User Support Team

When the COVID-19 pandemic first emerged in early 2020, healthcare and bureaucratic systems worldwide were caught off guard and largely unprepared to deal with the scale and severity of the outbreak. In Italy, this led to a severe underreporting of infections during the first wave of the spread. The lack of accurate data is critical as it hampers the retrospective assessment of nonpharmacological interventions, the comparison with the following waves, and the estimation and validation of epidemiological models. In particular, during the first wave, reported cases of new infections were strikingly low if compared with their effects in terms of deaths, hospitalizations and intensive care admissions. In this paper, we observe that the hospital admissions during the second wave were very well explained by the convolution of the reported daily infections with an exponential kernel. By formulating the estimation of the actual infections during the first wave as an inverse problem, its solution by a regularization approach is proposed and validated. In this way, it was possible to computed corrected time series of daily infections for each age class. The new estimates are consistent with the serological survey published in June 2020 by the National Institute of Statistics (ISTAT) and can be used to speculate on the total number of infections occurring in Italy during 2020, which appears to be about double the number officially recorded., 19 pages, 4 main figures, 2 supplementary figures, 2 tables

A load sharing system has several components and the failure of one component can affect the lifetime of the surviving components. Since component failure does not equate to system failure for different system designs, the analysis of the dependency structure between components becomes a meaningful exercise. The Extended Sequential Order Statistics model allows us to model a dependence structure between heterogeneous components in load sharing systems. However, the results may suggest that the risk of failure decreases as components fail sequentially, which can be counterintuitive, especially when data is scarce. We propose to address this issue by imposing an order restriction on the model parameters that represent increasing failure risks. This assumption corresponds more realistically to the physical properties of the system in many applications. We discuss the advantages of the newly proposed estimates and describe situations where they should be used with caution.