Evaluating the incremental return on ad spend (iROAS) of a prospective online marketing strategy (i.e., the ratio of the strategy’s causal effect on some response metric of interest relative to its causal effect on the ad spend) has become increasingly more important. Although randomized “geo experiments” are frequently employed for this evaluation, obtaining reliable estimates of iROAS can be challenging, as oftentimes only a small number of highly heterogeneous units are used. Moreover, advertisers frequently impose budget constraints on their ad spends which further complicates causal inference by introducing interference between the experimental units. In this paper we formulate a novel statistical framework for inferring the iROAS of online advertising from randomized paired geo experiment, which further motivates and provides new insights into Rosenbaum’s arguments on instrumental variables, and we propose and develop a robust, distribution-free and interpretable estimator “Trimmed Match” as well as a data-driven choice of the tuning parameter which may be of independent interest. We investigate the sensitivity of Trimmed Match to some violations of its assumptions and show that it can be more efficient than some alternative estimators based on simulated data. We then demonstrate its practical utility with real case studies.

Access and adherence to antiretroviral therapy (ART) has transformed the face of HIV infection from a fatal to a chronic disease. However, ART is also known for its side effects. Studies have reported that ART is associated with depressive symptomatology. Large-scale HIV clinical databases with individuals’ longitudinal depression records, ART medications, and clinical characteristics offer researchers unprecedented opportunities to study the effects of ART drugs on depression over time. We develop BAGEL, a Bayesian graphical model, to investigate longitudinal effects of ART drugs on a range of depressive symptoms while adjusting for participants’ demographic, behavior, and clinical characteristics, and taking into account the heterogeneous population through a Bayesian nonparametric prior. We evaluate BAGEL through simulation studies. Application to a dataset from the Women’s Interagency HIV Study yields interpretable and clinically useful results. BAGEL not only can improve our understanding of ART drugs’ effects on disparate depression symptoms but also has clinical utility in guiding informed and effective treatment selection to facilitate precision medicine in HIV.

When treatment effect heterogeneity exists, identifying the subgroup of patients who would benefit from an active treatment relative to a control is an important question. This article focuses on subgroup identification in the presence of a large dimensional set of covariates, with the number of covariates possibly greater than the sample size. We approach this problem from the perspective of optimal treatment decision rules and propose methods that can simultaneously estimate the treatment decision rule and select prescriptive variables important for treatment decision making and subgroup identification. The proposed methods are built within a robust classification framework based on doubly robust augmented inverse probability weighted estimators (AIPWE), hence sharing the robustness property. An ${\mathit{L}}_1$ (lasso-type) penalty is used within the classification framework to target selection of prescriptive variables. We further propose a backward elimination process for fine-tuning selection. The methods can be conveniently implemented by taking advantage of standard software for logistic regression and lasso. The methods are evaluated by extensive simulation studies which demonstrated the superior and robust performance of the proposed methods relative to existing ones. In addition, the estimated decision rules from the proposed methods are considerably simpler than other methods. We applied various methods to identify the subgroup of patients suitable for each of the two commonly used anticoagulants in terms of bleeding risk for patients with acute myocardial infarction undergoing percutaneous coronary intervention.

Estimation of local average treatment effects in randomized trials typically relies upon the exclusion restriction assumption in cases where we are unwilling to rule out the possibility of unmeasured confounding. Under this assumption, treatment effects are mediated through the post-randomization variable being conditioned upon and directly attributable to neither the randomization itself nor its latent descendants. Recently, there has been interest in mobile health interventions to provide healthcare support. Mobile health interventions (e.g., the Rapid Encouragement/Education and Communications for Health, or REACH, designed to support self management for adults with type 2 diabetes) often involve both one-way and interactive messages. In practice, it is highly likely that any benefit from the intervention is achieved both through receipt of the intervention content and through engagement with/response to it. Application of an instrumental variable analysis in order to understand the role of engagement with REACH (or a similar intervention) requires the traditional exclusion restriction assumption to be relaxed. We propose a conceptually intuitive sensitivity analysis procedure for the REACH randomized trial that places bounds on local average treatment effects. Simulation studies reveal this approach to have desirable finite-sample behavior and to recover local average treatment effects under correct specification of sensitivity parameters.

The emerging field of precision medicine is transforming statistical analysis from the classical paradigm of population-average treatment effects into that of personal treatment effects. This new scientific mission has called for adequate statistical methods to assess heterogeneous covariate effects in regression analysis. This paper focuses on a subgroup analysis that consists of two primary analytic tasks: identification of treatment effect subgroups and individual group memberships, and statistical inference on treatment effects by subgroup. We propose an approach to synergizing supervised clustering analysis via alternating direction method of multipliers (ADMM) algorithm and statistical inference on subgroup effects via expectation-maximization (EM) algorithm. Our proposed procedure, termed as hybrid operation for subgroup analysis (HOSA), enjoys computational speed and numerical stability with interpretability and reproducibility. We establish key theoretical properties for both proposed clustering and inference procedures. Numerical illustration includes extensive simulation studies and analyses of motivating data from two randomized clinical trials to learn subgroup treatment effects.

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This assumption might be overly restrictive and could have a deleterious impact on forecasting accuracy. As a solution we propose combining VAR with Bayesian additive regression tree (BART) models. The resulting Bayesian additive vector autoregressive tree (BAVART) model is capable of capturing arbitrary nonlinear relations between the endogenous variables and the covariates without much input from the researcher. Since controlling for heteroscedasticity is key for producing precise density forecasts, our model allows for stochastic volatility in the errors. We apply our model to two datasets. The first application shows that the BAVART model yields highly competitive forecasts of the U.S. term structure of interest rates. In a second application we estimate our model using a moderately sized Eurozone dataset to investigate the dynamic effects of uncertainty on the economy.

In order to implement disease-specific interventions in young age groups, policy makers in low- and middle-income countries require timely and accurate estimates of age- and cause-specific child mortality. High-quality data is not available in settings where these interventions are most needed, but there is a push to create sample registration systems that collect detailed mortality information. Current methods that estimate mortality from this data employ multistage frameworks without rigorous statistical justification that separately estimate all-cause and cause-specific mortality and are not sufficiently adaptable to capture important features of the data. We propose a flexible Bayesian modeling framework to estimate age- and cause-specific child mortality from sample registration data. We provide a theoretical justification for the framework, explore its properties via simulation, and use it to estimate mortality trends using data from the Maternal and Child Health Surveillance System in China.

Leveraging multivariate spatial dependence to improve the precision of estimates using American Community Survey data and other sample survey data has been a topic of recent interest among data users and federal statistical agencies. One strategy is to use a multivariate spatial mixed effects model with a Gaussian observation model and latent Gaussian process model. In practice, this works well for a wide range of tabulations. Nevertheless, in situations in which the data exhibit heterogeneity within or across geographies, and/or there is sparsity in the data, the Gaussian assumptions may be problematic and lead to underperformance. To remedy these situations, we propose a multivariate hierarchical Bayesian nonparametric mixed effects spatial mixture model to increase model flexibility. The number of clusters is chosen automatically in a data-driven manner. The effectiveness of our approach is demonstrated through a simulation study and motivating application of special tabulations for American Community Survey data.

Recent technological advancements have led to the rapid generation of high-throughput biological data which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with covariates annotating both its rows and columns. Matrix linear models provide a convenient way for modeling such data. In many situations, sparse estimation of these models is desired. We present fast, general methods for fitting sparse matrix linear models to structured high-throughput data. We induce model sparsity using an ${\mathit{L}}_1$ penalty and consider the case when the response matrix and the covariate matrices are large. Due to data size, standard methods for estimation of these penalized regression models fail if the problem is converted to the corresponding univariate regression scenario. By leveraging matrix properties in the structure of our model, we develop several fast estimation algorithms (coordinate descent, FISTA and ADMM) and discuss their trade-offs. We evaluate our method’s performance on simulated data, E. coli chemical genetic screening data and two Arabidopsis genetic datasets with multivariate responses. Our algorithms have been implemented in the Julia programming language and are available at https://github.com/senresearch/MatrixLMnet.jl.

Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogeneity beyond what was observed in single tumor and single platform studies. However, these studies have been limited by available statistical methodology. We propose a flexible approach to the simultaneous factorization and decomposition of variation across such bidimensionally linked matrices, BIDIFAC+. BIDIFAC+ decomposes variation into a series of low-rank components that may be shared across any number of row sets (e.g., omics platforms) or column sets (e.g., cancer types). This builds on a growing literature for the factorization and decomposition of linked matrices which has primarily focused on multiple matrices that are linked in one dimension (rows or columns) only. Our objective function extends nuclear norm penalization, is motivated by random matrix theory, gives a unique decomposition under relatively mild conditions, and can be shown to give the mode of a Bayesian posterior distribution. We apply BIDIFAC+ to pan-omics pan-cancer data from TCGA, identifying shared and specific modes of variability across $\mathit{four}$ different omics platforms and 29 different cancer types.

The Argo data is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2000 meters of depth of the ocean. We study the Argo data from the perspective of functional data analysis (FDA). We develop spatiotemporal functional kriging methodology for mean and covariance estimation to predict temperature and salinity at a fixed location as a smooth function of depth. By combining tools from FDA and spatial statistics, including smoothing splines, local regression, and multivariate spatial modeling and prediction, our approach provides advantages over current methodology that consider pointwise estimation at fixed depths. Our approach naturally leverages the irregularly-sampled data in space, time, and depth to fit a space-time functional model for temperature and salinity. The developed framework provides new tools to address fundamental scientific problems involving the entire upper water column of the oceans, such as the estimation of ocean heat content, stratification, and thermohaline oscillation. For example, we show that our functional approach yields more accurate ocean heat content estimates than ones based on discrete integral approximations in pressure. Further, using the derivative function estimates, we obtain a new product of a global map of the mixed layer depth, a key component in the study of heat absorption and nutrient circulation in the oceans. The derivative estimates also reveal evidence for density inversions in areas distinguished by mixing of particularly different water masses.

Atmospheric rivers (ARs) are elongated regions of water vapor in the atmosphere that play a key role in global water cycles, particularly in western U.S. precipitation. The primary component of many AR detection schemes is the thresholding of the integrated water vapor transport (IVT) magnitude at a single quantile over time. Utilizing a recently developed family of parametric distributions for quantile regression, this paper develops a flexible dynamic quantile linear model (exDQLM) which enables versatile, structured, and informative estimation of the IVT quantile threshold. A simulation study illustrates our exDQLM to be more robust than the standard Bayesian parametric quantile regression approach for nonstandard distributions, performing better in both quantile estimation and predictive accuracy. In addition to a Markov chain Monte Carlo (MCMC) algorithm, we develop an efficient importance sampling variational Bayes (ISVB) algorithm for fast approximate Bayesian inference which is found to produce comparable results to the MCMC in a fraction of the computation time. Further, we develop a transfer function extension to our exDQLM as a method for quantifying nonlinear relationships between a quantile of a climatological response and an input. The utility of our transfer function exDQLM is demonstrated in capturing both the immediate and lagged effects of El Niño Southern Oscillation Longitude Index on the estimation of the 0.85 quantile IVT.

The modeling of spatiotemporal trends in temperature extremes can help better understand the structure and frequency of heatwaves in a changing climate and assess the environmental, societal, economic and health-related risks they entail. Here, we study annual temperature maxima over Southern Europe using a century-spanning dataset observed at 44 monitoring stations. Extending the spectral representation of max-stable processes, our modeling framework relies on a novel construction of max-infinitely divisible processes which include covariates to capture spatiotemporal nonstationarities. Our new model keeps a popular max-stable process on the boundary of the parameter space, while flexibly capturing weakening extremal dependence at increasing quantile levels and asymptotic independence. This is achieved by linking the overall magnitude of a spatial event to its spatial correlation range in such a way that more extreme events become less spatially dependent, thus more localized. Our model reveals salient features of the spatiotemporal variability of European temperature extremes, and it clearly outperforms natural alternative models. Results show that the spatial extent of heatwaves is smaller for more severe events at higher elevations and that recent heatwaves are moderately wider. Our probabilistic assessment of the 2019 annual maxima confirms the severity of the 2019 heatwaves both spatially and at individual sites, especially when compared to climatic conditions prevailing in 1950–1975. Our results could be exploited in practice to understand the spatiotemporal dynamics, severity and frequency of extreme heatwaves and to design suitable region-specific mitigation measures.

In this paper we introduce strategies for modeling, monitoring, and forecasting sequential web traffic data using flows from the Fox News website. In our analysis we consider a family of Poisson-gamma state space (PGSS) models that can accurately quantify the uncertainty exhibited by web traffic data, can provide fast sequential monitoring and prediction mechanisms for high frequency time intervals, and are computationally feasible when structural breaks are present. As such, we extend the family of PGSS models to include the state augmented (sa-)PGSS model whose state evolution structure is flexible and responsive to sudden changes. Such adaptability is achieved by augmenting the state vector of the PGSS model with an additional state variable for a time-varying discount factor. We develop an efficient particle-based estimation procedure that is suitable for sequential analysis, allowing us to estimate dynamic state variables and static parameters via closed-form conditional sufficient statistics. We compare the performance of the PGSS family of models against viable alternatives from the literature and argue that, especially in the presence of structural breaks, our proposed approach yields superior sequential model fit and predictive performance while preserving computational feasibility. We provide additional insights by designing a simulation study that mimics potential web traffic data patterns.

Following the introduction of high-resolution player tracking technology, a new range of statistical analysis has emerged in sports, specifically in basketball. However, such high-dimensional data are often challenging for statistical inference and decision making. In this article we employ a state-of-the-art Bayesian mixture model that allows the estimation of heterogeneous intrinsic dimension (ID) within a dataset, and we propose some theoretical enhancements. Informally, the ID can be seen as an indicator of complexity and dependence of the data at hand, and it is usually assumed unique. Our method provides the capacity to reveal valuable insights about the hidden dynamics of sports interactions in space and time which helps to translate complex patterns into more coherent statistics. The application of this technique is illustrated using NBA basketball players’ tracking data, allowing effective classification and clustering. In movement data the analysis identified key stages of offensive actions, such as creating space for passing, preparation/shooting, and following through which are relevant for invasion sports. We found that the ID value spikes, reaching a peak between four and eight seconds in the offensive part of the court, after which it declines. In shot charts we obtained groups of shots that produce substantially higher and lower successes. Overall, game-winners tend to have a larger intrinsic dimension, indicative of greater unpredictability and unique shot placements. Similarly, we found higher ID values in plays when the score margin is smaller rather than larger. The exploitation of these results can bring clear strategic advantages in sports games.

This paper develops new methods for providing instantaneous in-game win probabilities for the National Rugby League. Besides the score differential, betting odds, and real-time features extracted from the match event data are also used as inputs to inform the in-game win probabilities. Rugby matches evolve continuously in time, and the circumstances change over the duration of the match. Therefore, the match data are considered as functional data, and the in-game win probability is a function of the time of the match. We express the in-game win probability using a conditional probability formulation, the components of which are evaluated from the perspective of functional data analysis. Specifically, we model the score differential process and functional feature extracted from the match event data as sums of mean functions and noises. The mean functions are approximated by B-spline basis expansions with functional parameters. Since each match is conditional on a unique kickoff win probability of the home team obtained from the betting odds (i.e., the functional data are not independent and identically distributed), we propose a weighted least squares method to estimate the functional parameters by borrowing the information from matches with similar kickoff win probabilities. The variance and covariance elements are obtained by the maximum likelihood estimation method. The proposed method is applicable to other sports when suitable match event data are available.

Networks arise in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks representing text documents in corpus linguistics. We identify networks with their graph Laplacian matrices for which we define metrics, embeddings, tangent spaces and a projection from Euclidean space to the space of graph Laplacians. This framework provides a way of computing means, performing principal component analysis, regression, and carrying out hypothesis tests, such as for testing for equality of means between two samples of networks. We apply the methodology to the set of novels by Jane Austen and Charles Dickens.

Characterizing the shared memberships of individuals in a classification scheme poses severe interpretability issues, even when using a moderate number of classes (say four). Mixed membership models quantify this phenomenon, but they typically focus on goodness-of-fit more than on interpretable inference. To achieve a good numerical fit, these models may, in fact, require many extreme profiles, making the results difficult to interpret. We introduce a new class of multivariate mixed membership models that, when variables can be partitioned into subject-matter based domains, can provide a good fit to the data using fewer profiles than standard formulations. The proposed model explicitly accounts for the blocks of variables corresponding to the distinct domains along with a cross-domain correlation structure which provides new information about shared membership of individuals in a complex classification scheme. We specify a multivariate logistic normal distribution for the membership vectors which allows easy introduction of auxiliary information leveraging a latent multivariate logistic regression. A Bayesian approach to inference, relying on Pólya gamma data augmentation, facilitates efficient posterior computation via Markov chain Monte Carlo. We apply this methodology to a spatially explicit study of malaria risk over time on the Brazilian Amazon frontier.

The Florence branch of an Italian supermarket chain recently implemented a strategy that permanently lowered the price of numerous store brands in several product categories. To quantify the impact of such a policy change, researchers often use synthetic control methods for estimating causal effects when a subset of units receive a single persistent treatment and the rest are unaffected by the change. In our applications, however, competitor brands not assigned to treatment are likely impacted by the intervention because of substitution effects; more broadly, this type of interference occurs whenever the treatment assignment of one unit affects the outcome of another. This paper extends the synthetic control methods to accommodate partial interference, allowing interference within predefined groups but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention, enabling us to estimate our novel effects. In a simulation study we explore our Bayesian procedures’ empirical properties and show that it achieves good frequentists coverage, even when the model is misspecified. We use our new methodology to make causal statements about the impact on sales of the affected store brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.

A key challenge in estimating the infection fatality rate (IFR), along with its relation with various factors of interest, is determining the total number of cases. The total number of cases is not known not only because not everyone is tested but also, more importantly, because tested individuals are not representative of the population at large. We refer to the phenomenon whereby infected individuals are more likely to be tested than noninfected individuals as “preferential testing.” An open question is whether or not it is possible to reliably estimate the IFR without any specific knowledge about the degree to which the data are biased by preferential testing. In this paper we take a partial identifiability approach, formulating clearly where deliberate prior assumptions can be made and presenting a Bayesian model which pools information from different samples. When the model is fit to European data obtained from seroprevalence studies and national official COVID-19 statistics, we estimate the overall COVID-19 IFR for Europe to be 0.53%, 95% $\mathrm{C}.\mathrm{I}.=[0.38\mathrm{\%},0.70\mathrm{\%}]$.

It is widely known that preelectoral polls often suffer from nonsampling errors that pollsters try to compensate for in final estimates by means of diverse ad hoc adjustments, thus leading to well-known house effects. We propose a Bayesian hierarchical model to investigate the role of house effects on the total variability of predictions. To illustrate the model, data from preelectoral polls in Italy in 2006, 2008 and 2013 are considered. Unlike alternative techniques or models, our proposal leads: (i) to correctly decompose the different sources of variability; (ii) to recognize the role of house effects; (iii) to evaluate its dynamics, showing that variability of house effects across pollsters diminishes as the date of election approaches; (iv) to investigate the relationship between house effects and overall prediction errors.

We propose a framework to detect and model shifts in a time series of continuous proportions, that is, a vector of proportions measuring the parts of a whole. By reparameterizing the shape of a Dirichlet distribution, we can model the location and scale separately through generalized linear models. A hidden Markov model allows the coefficients of the generalized linear models to change, thus allowing for the time series to undergo multiple regimes. This framework allows a practitioner to adequately model seasonality, trends, or include covariate information as well as detect change points. The model’s behavior is studied via simulation and through the analysis of lake phytoplankton data from 1992 through 2012. Our analyses demonstrate that the model can be effective in detecting and modeling changes in a time series of proportions. Pertaining to the phytoplankton data, the overall biomass has grown with some changes to the community level dynamics occurring circa 2000. Specifically, the proportion of cyanobacteria appears to have increased to the detriment of diatoms.

Family history is a major risk factor for many types of cancer. Mendelian risk prediction models translate family histories into cancer risk predictions, based on knowledge of cancer susceptibility genes. These models are widely used in clinical practice to help identify high-risk individuals. Mendelian models leverage the entire family history, but they rely on many assumptions about cancer susceptibility genes that are either unrealistic or challenging to validate, due to low mutation prevalence. Training more flexible models, such as neural networks, on large databases of pedigrees can potentially lead to accuracy gains. In this paper we develop a framework to apply neural networks to family history data and investigate their ability to learn inherited susceptibility to cancer. While there is an extensive literature on neural networks and their state-of-the-art performance in many tasks, there is little work applying them to family history data. We propose adaptations of fully-connected neural networks and convolutional neural networks to pedigrees. In data simulated under Mendelian inheritance, we demonstrate that our proposed neural network models are able to achieve nearly optimal prediction performance. Moreover, when the observed family history includes misreported cancer diagnoses, neural networks are able to outperform the Mendelian BRCAPRO model embedding the correct inheritance laws. Using a large dataset of over 200,000 family histories, the Risk Service cohort, we train prediction models for future risk of breast cancer. We validate the models using data from the Cancer Genetics Network.

DNA methylation can be transmitted through generations. This paper proposes a clustering method to identify the intergenerational patterns from parents to their offspring. Motivated by the potential of correlation between DNA methylation sites, we use the multivariate generalized beta distribution to model the blockwise correlation structure among the sites. A stochastic EM algorithm is implemented to estimate the parameters, and BIC is applied to determine the optimal number of clusters. Simulations demonstrate the feasibility of the proposed method. We further applied the approach to cluster DNA methylation data generated from a cohort study on asthma and allergic conditions.

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, but exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (Macaca mulatta), we introduce the ordinal probit functional outcome regression model (OPFOR). OPFOR models can be fit using one of several basis functions including penalized B-splines, wavelets, and O’Sullivan splines—the last of which typically performs best. Simulation using a variety of underlying covariance patterns shows that the model performs reasonably well in estimation under multiple basis functions with near nominal coverage for joint credible intervals. Finally, in application we use Bayesian model selection criteria adapted to functional outcome regression to best characterize the relation between several demographic factors of interest and the monkeys’ computer use over the course of a year. In comparison with a standard ordinal longitudinal analysis, OPFOR outperforms a cumulative-link mixed-effects model in simulation and provides additional and more nuanced information on the nature of the monkeys’ computer-use behavior.

Community water fluoridation is an important component of oral health promotion, as fluoride exposure is a well-documented dental caries-preventive agent. Direct measurements of domestic water fluoride content provide valuable information regarding individuals’ fluoride exposure and thus caries risk; however, they are logistically challenging to carry out at a large scale in oral health research. This article describes the development and evaluation of a novel method for the imputation of missing domestic water fluoride concentration data informed by spatial autocorrelation. The context is a state-wide epidemiologic study of pediatric oral health in North Carolina, where domestic water fluoride concentration information was missing for approximately 75% of study participants with clinical data on dental caries. A new machine-learning-based imputation method that combines partitioning around medoids clustering and random forest classification (PAMRF) is developed and implemented. Imputed values are filtered according to allowable error rates or target sample size, depending on the requirements of each application. In leave-one-out cross-validation and simulation studies, PAMRF outperforms four existing imputation approaches—two conventional spatial interpolation methods (i.e., inverse-distance weighting, IDW and universal kriging, UK) and two supervised learning methods (k-nearest neighbors, KNN, and classification and regression trees, CART). The inclusion of multiply imputed values in the estimation of the association between fluoride concentration and dental caries prevalence resulted in essentially no change in PAMRF estimates but substantial gains in precision due to larger effective sample size. PAMRF is a powerful new method for the imputation of missing fluoride values where geographical information exists.

Self-exciting spatiotemporal Hawkes processes have found increasing use in the study of large-scale public health threats, ranging from gun violence and earthquakes to wildfires and viral contagion. Whereas many such applications feature locational uncertainty, that is, the exact spatial positions of individual events are unknown, most Hawkes model analyses to date have ignored spatial coarsening present in the data. Three particular 21st century public health crises—urban gun violence, rural wildfires and global viral spread—present qualitatively and quantitatively varying uncertainty regimes that exhibit: (a) different collective magnitudes of spatial coarsening, (b) uniform and mixed magnitude coarsening, (c) differently shaped uncertainty regions and—less orthodox—(d) locational data distributed within the “wrong” effective space. We explicitly model such uncertainties in a Bayesian manner and jointly infer unknown locations together with all parameters of a reasonably flexible Hawkes model, obtaining results that are practically and statistically distinct from those obtained while ignoring spatial coarsening. This work also features two different secondary contributions: first, to facilitate Bayesian inference of locations and background rate parameters, we make a subtle yet crucial change to an established kernel-based rate model, and second, to facilitate the same Bayesian inference at scale, we develop a massively parallel implementation of the model’s log-likelihood gradient with respect to locations and thus avoid its quadratic computational cost in the context of Hamiltonian Monte Carlo. Our examples involve thousands of observations and allow us to demonstrate practicality at moderate scales.

Periodontal disease is a serious gum infection impacting half of the U.S. adult population that may lead to loss of teeth. Using standard marginal models to study the association between patient-level predictors and tooth-level outcomes can lead to biased estimates because the independence assumption between the outcome (periodontal disease) and cluster size (number of teeth per patient) is violated. Specifically, the baseline number of teeth of a patient is informative. In this setting a cluster-weighted generalized estimating equations (CWGEE) approach can be used to obtain unbiased marginal inference from data with informative cluster size (ICS). However, in many longitudinal studies of dental health, including the Veterans Affairs Dental Longitudinal Study, the rate of tooth-loss or tooth drop-out over time is also informative, creating a missing at random data mechanism. Here, we propose a novel modeling approach that incorporates the technique of inverse probability censoring weights into CWGEE with binary outcomes to account for ICS and informative drop-out over time. In an extensive simulation study we demonstrate that results obtained from our proposed method yield lower bias and excellent coverage probability, compared to those obtained from traditional methods which do not account for ICS or drop-out.

Mass spectrometry is a potential diagnostic tool for rapid bacterial detection. However, in order to use this technology in clinical settings, it is important to develop sound statistical algorithms that can accurately analyze polymicrobial mass spectrometry data. Here, we propose a likelihood-based bacterial identification algorithm for bimicrobial mass spectrometry data. Specifically, we introduce a two-component mixture model with partially known labels. This method can model peaks with unknown origins. It also considers errors in mass-to-charge ratios and intensities of peaks between observed and reference mass spectra. Coupled with a decoy strategy, the likelihood is used to identify bacterial species and to measure uncertainty of such identifications. Using two real mass spectrometry datasets, we demonstrate the superior performance of our approach in accurate bacterial identifications, compared to model-free approaches. Example datasets and R codes for the proposed method are freely available under MIT license at https://github.com/soyoungryu/BacID.