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North Atlantic right whales are an endangered species; their entire population numbers approximately 372 individuals, and they are subject to major anthropogenic threats. They feed on zooplankton species whose distribution shifts in a dynamic and warming oceanic environment. Because right whales in turn follow their shifting food resource, it is necessary to jointly study the distribution of whales and their prey. The innovative joint species distribution modeling (JSDM) contribution here is different from anything in the large JDSM literature, reflecting the processes and data we have to work with. Specifically, our JSDM supplies a geostatistical model for expected amount of zooplankton collected at a site. We require a point pattern model for the intensity of right whale abundance. The two process models are joined through a latent conditional-marginal specification. Further, each species has two data sources to inform their respective distributions and these sources require novel data fusion. What emerges is a complex multi-level model. Through simulation we demonstrate the ability of our joint specification to identify model unknowns and learn better about the species distributions than modeling them individually. We then apply our modeling to real data from Cape Cod Bay, Massachusetts in the U.S.

Marine Protected Areas (MPAs) have been established globally to conserve marine resources. Given their maintenance costs and impact on commercial fishing, it is critical to evaluate their effectiveness to support future conservation. In this paper, we use data collected from the Australian coast to estimate the effect of MPAs on biodiversity. Environmental studies such as these are often observational, and processes of interest exhibit spatial dependence, which presents challenges in estimating the causal effects. Spatial data can also be subject to preferential sampling, where the sampling locations are related to the response variable, further complicating inference and prediction. To address these challenges, we propose a spatial causal inference method that simultaneously accounts for unmeasured spatial confounders in both the sampling process and the treatment allocation. We prove the identifiability of key parameters in the model and the consistency of the posterior distributions of those parameters. We show via simulation studies that the causal effect of interest can be reliably estimated under the proposed model. The proposed method is applied to assess the effect of MPAs on fish biomass. We find evidence of preferential sampling and that properly accounting for this source of bias impacts the estimate of the causal effect.

Team and player evaluation in professional sport is extremely important given the financial implications of success/failure. It is especially critical to identify and retain elite shooters in the National Basketball Association (NBA), one of the premier basketball leagues worldwide because the ultimate goal of the game is to score more points than one's opponent. To this end we propose two novel basketball metrics: "expected points" for team-based comparisons and "expected points above average (EPAA)" as a player-evaluation tool. Both metrics leverage posterior samples from Bayesian hierarchical modeling framework to cluster teams and players based on their shooting propensities and abilities. We illustrate the concepts for the top 100 shot takers over the last decade and offer our metric as an additional metric for evaluating players.

Sound is assumed to be the primary modality of communication among marine mammal species. Analyzing acoustic recordings helps to understand the function of the acoustic signals as well as the possible impact of anthropogenic noise on acoustic behavior. Motivated by a dataset from a network of hydrophones in Cape Cod Bay, Massachusetts, utilizing automatically detected calls in recordings, we study the communication process of the endangered North Atlantic right whale. For right whales an "up-call" is known as a contact call, and ensuing counter-calling between individuals is presumed to facilitate group cohesion. We present novel spatiotemporal excitement modeling consisting of a background process and a counter-call process. The background process intensity incorporates the influences of diel patterns and ambient noise on occurrence. The counter-call intensity captures potential excitement, that calling elicits calling behavior. Call incidence is found to be clustered in space and time; a call seems to excite more calls nearer to it in time and space. We find evidence that whales make more calls during twilight hours, respond to other whales nearby, and are likely to remain quiet in the presence of increased ambient noise.

Marine mammals are increasingly vulnerable to human disturbance and climate change. Their diving behavior leads to limited visual access during data collection, making studying the abundance and distribution of marine mammals challenging. In theory, using data from more than one observation modality should lead to better informed predictions of abundance and distribution. With focus on North Atlantic right whales, we consider the fusion of two data sources to inform about their abundance and distribution. The first source is aerial distance sampling which provides the spatial locations of whales detected in the region. The second source is passive acoustic monitoring (PAM), returning calls received at hydrophones placed on the ocean floor. Due to limited time on the surface and detection limitations arising from sampling effort, aerial distance sampling only provides a partial realization of locations. With PAM, we never observe numbers or locations of individuals. To address these challenges, we develop a novel thinned point pattern data fusion. Our approach leads to improved inference regarding abundance and distribution of North Atlantic right whales throughout Cape Cod Bay, Massachusetts in the US. We demonstrate performance gains of our approach compared to that from a single source through both simulation and real data.

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations driving these complex nonlinear dynamic system using data-driven approaches. In this paper we review the current literature on data-driven discovery for dynamic systems. We provide a categorization to the different approaches for data-driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data-driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework, and provide avenues for future work., Comment: 38 pages, 1 figure, 1 table

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent real-world dynamics well. Since the true dynamics of these complex systems are generally unknown, learning the governing equations can improve our understanding of the mechanisms driving the systems. Here, we develop a Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations. Our approach can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty. The proposed framework is illustrated using three simulated systems with varying amounts of observational uncertainty and missing data and applied to a real-world system to infer the temporal evolution of the vorticity of the streamfunction., Comment: 41 pages, 10 Tables, 5 Figures

Environmental time series data observed at high frequencies can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM). HSMMs extend the HMM by explicitly modeling the time spent in each state. In a discrete-time HSMM, the duration in each state can be modeled with a zero-truncated Poisson distribution, where the duration parameter may be state-specific but constant in time. We extend the HSMM by allowing the state-specific duration parameters to vary in time and model them as a function of known covariates observed over a period of time leading up to a state transition. In addition, we propose a data subsampling approach given that high-frequency data can violate the conditional independence assumption of the HSMM. We apply the model to high-frequency data collected by an instrumented buoy in Lake Mendota. We model the phycocyanin concentration, which is used in aquatic systems to estimate the relative abundance of blue-green algae, and identify important time-varying effects associated with the duration in each state., Comment: arXiv admin note: substantial text overlap with arXiv:2010.10739

Informative sampling designs can impact spatial prediction, or kriging, in two important ways. First, the sampling design can bias spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Second, even with unbiased estimates of the spatial covariance parameters, since the kriging variance is a function of the observation locations, these estimates will vary based on the sample and overestimate the population-based estimates. In this work, we develop a weighted composite likelihood approach to improve spatial covariance parameter estimation under informative sampling designs. Then, given these parameter estimates, we propose three approaches to quantify the effects of the sampling design on the variance estimates in spatial prediction. These results can be used to make informed decisions for population-based inference. We illustrate our approaches using a comprehensive simulation study. Then, we apply our methods to perform spatial prediction on nitrate concentration in wells located throughout central California., Comment: 21 pages, 7 figures

Data collected by wearable devices in sports provide valuable information about an athlete's behavior such as their activity, performance, and ability. These time series data can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM) for varied purposes including activity recognition and event detection. HSMMs extend the HMM by explicitly modeling the time spent in each state. In a discrete-time HSMM, the duration in each state can be modeled with a zero-truncated Poisson distribution, where the duration parameter may be state-specific but constant in time. We extend the HSMM by allowing the state-specific duration parameters to vary in time and model them as a function of known covariates derived from the wearable device and observed over a period of time leading up to a state transition. In addition, we propose a data subsampling approach given that high-frequency data from wearable devices can violate the conditional independence assumption of the HSMM. We apply the model to wearable device data collected on a soccer referee in a Major League Soccer game. We model the referee's physiological response to the game demands and identify important time-varying effects of these demands associated with the duration in each state.

Subjective wellness data can provide important information on the well-being of athletes and be used to maximize player performance and detect and prevent against injury. Wellness data, which are often ordinal and multivariate, include metrics relating to the physical, mental, and emotional status of the athlete. Training and recovery can have significant short- and long-term effects on athlete wellness, and these effects can vary across individual. We develop a joint multivariate latent factor model for ordinal response data to investigate the effects of training and recovery on athlete wellness. We use a latent factor distributed lag model to capture the cumulative effects of training and recovery through time. Current efforts using subjective wellness data have averaged over these metrics to create a univariate summary of wellness, however this approach can mask important information in the data. Our multivariate model leverages each ordinal variable and can be used to identify the relative importance of each in monitoring athlete wellness. The model is applied to athlete daily wellness, training, and recovery data collected across two Major League Soccer seasons.

Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi-annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi-annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatio-temporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi-annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally-varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979 to 2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics., Comment: 25 pages, 11 color figures

There is increasing evidence that global warming manifests itself in more frequent warm days and that heat waves will become more frequent. Presently, a formal definition of a heat wave is not agreed upon in the literature. To avoid this debate, we consider extreme heat events, which, at a given location, are well-defined as a run of consecutive days above an associated local threshold. Characteristics of EHEs are of primary interest, such as incidence and duration, as well as the magnitude of the average exceedance and maximum exceedance above the threshold during the EHE. Using approximately 60-year time series of daily maximum temperature data collected at 18 locations in a given region, we propose a spatio-temporal model to study the characteristics of EHEs over time. The model enables prediction of the behavior of EHE characteristics at unobserved locations within the region. Specifically, our approach employs a two-state space-time model for EHEs with local thresholds where one state defines above threshold daily maximum temperatures and the other below threshold temperatures. We show that our model is able to recover the EHE characteristics of interest and outperforms a corresponding autoregressive model that ignores thresholds based on out-of-sample prediction.

Extrapolation is defined as making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are more and more common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we illustrate novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees., Comment: 28 pages, 2 supplementary files, 6 main figures, 2 supplementary figures, 2 supplementary tables

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are observed in an effort to quantify an unobservable continuous measurement. In our example, the latent, or unobservable measurement is wetland condition. While predicted values of the latent wetland condition variable produced by the model at each location do not hold any intrinsic value, the relative magnitudes of the wetland condition values are of interest. In addition, by including point-referenced covariates in the model, we are able to make predictions at new locations for both the latent random variable and the multivariate response. Lastly, the model produces ranks of the multivariate responses in relation to the unobserved latent random field. This is an important result as it allows us to determine which response variables are most closely correlated with the latent variable. Our approach offers an alternative to traditional indices based on best professional judgment that are frequently used in ecology. We apply our model to assess wetland condition in the North Platte and Rio Grande River Basins in Colorado. The model facilitates a comparison of wetland condition at multiple locations and ranks the importance of in-field measurements., Comment: 25 pages, 7 figures