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Wildlife telemetry data may be used to answer a diverse range of questions relevant to wildlife ecology and management. One challenge to modeling telemetry data is that animal movement often varies greatly in pattern over time, and current continuous‐time modeling approaches to handle such nonstationarity require bespoke and often complex models that may pose barriers to practitioner implementation. We demonstrate a novel application of treed Gaussian process (TGP) modeling, a Bayesian machine learning approach that automatically captures the nonstationarity and abrupt transitions present in animal movement. The machine learning formulation of TGPs enables modeling to be nearly automated, while their Bayesian formulation allows for the derivation of movement descriptors with associated uncertainty measures. We demonstrate the use of an existing R package to implement TGPs using the familiar Markov chain Monte Carlo algorithm. We then use estimated movement trajectories to derive movement descriptors that can be compared across individuals and populations. We applied the TGP model to a case study of lesser prairie‐chickens (Tympanuchus pallidicinctus) to demonstrate the benefits of TGP modeling and compared distance traveled and residence times across lesser prairie‐chicken individuals and populations. For broad usability, we outline all steps necessary for practitioners to specify relevant movement descriptors (e.g., turn angles, speed, contact points) and apply TGP modeling and trajectory comparison to their own telemetry datasets. Combining the predictive power of machine learning and the statistical inference of Bayesian methods to model movement trajectories allows for the estimation of statistically comparable movement descriptors from telemetry studies. Our use of an accessible R package allows practitioners to model trajectories and estimate movement descriptors, facilitating the use of telemetry data to answer applied management questions. We apply a recently developed Bayesian machine learning model to both increase the accessibility of complex animal movement models and simultaneously achieve advanced modeling of highly varied telemetry data. By nesting this model within a widely applicable inferential framework and utilizing an accessible R package for modeling, we facilitate application by practitioners to model trajectories, estimate movement descriptors, and answer applied management questions.

Gaussian process models have been widely used in spatial statistics but face tremendous modeling and computational challenges for very large nonstationary spatial datasets. To address these challenges, we develop a Bayesian modeling approach using a nonstationary covariance function constructed based on adaptively selected partitions. The partitioned nonstationary class allows one to knit together local covariance parameters into a valid global nonstationary covariance for prediction, where the local covariance parameters are allowed to be estimated within each partition to reduce computational cost. To further facilitate the computations in local covariance estimation and global prediction, we use the full-scale covariance approximation (FSA) approach for the Bayesian inference of our model. One of our contributions is to model the partitions stochastically by embedding a modified treed partitioning process into the hierarchical models that leads to automated partitioning and substantial computational benefits. We illustrate the utility of our method with simulation studies and the global Total Ozone Matrix Spectrometer (TOMS) data. Supplementary materials for this article are available online.

Optimization for complex systems in engineering often involves the use of expensive computer simulation. By combining statistical emulation using treed Gaussian processes with pattern search optimization, we are able to perform robust local optimization more efficiently and effectively than when using either method alone. Our approach is based on the augmentation of local search patterns with location sets generated through improvement prediction over the input space. We further develop a computational framework for asynchronous parallel implementation of the optimization algorithm. We demonstrate our methods on two standard test problems and our motivating example of calibrating a circuit device simulator.

Computer experiments are widely used in scientific research to study and predict the behavior of complex systems, which often have responses consisting of a set of nonstationary outputs. The computational cost of simulations at high resolution often is expensive and impractical for parametric studies at different input values. In this article, we develop a Bayesian treed multivariate Gaussian process (BTMGP) as an extension of the Bayesian treed Gaussian process (BTGP) to model the cross-covariance function and the nonstationarity of the multivariate output. We facilitate the computational complexity of the Markov chain Monte Carlo sampler by choosing appropriately the covariance function and prior distributions. Based on the BTMGP, we develop a sequential design of experiment for the input space and construct an emulator. We demonstrate the use of the proposed method in test cases and compare it with alternative approaches. We also apply the sequential sampling technique and BTMGP to model the multiphase flow in a full scale regenerator of a carbon capture unit.

To improve short-horizon exchange rate forecasts, we employ foreign exchange market risk factors as fundamentals, and Bayesian treed Gaussian process (BTGP) models to handle non-linear, time-varying relationships between these fundamentals and exchange rates. Forecasts from the BTGP model conditional on the carry and dollar factors dominate random walk forecasts on accuracy and economic criteria in the Meese-Rogoff setting. Superior market timing ability for large moves, more than directional accuracy, drives the BTGP's success. We explain how, through amodel averaging Monte Carlo scheme, the BTGP is able to simultaneously exploit smoothness and rough breaks in between-variable dynamics. Either feature in isolation is unable to consistently outperform benchmarks throughout the full span of time in our forecasting exercises. Trading strategies based on ex ante BTGP forecasts deliver the highest out-of-sample risk-adjusted returns for the median currency, as well as for both predictable, traded risk factors.

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have, separately, enjoyed great success in application to classification problems. An example of the former is Bayesian CART. In the latter, real-valued GP output may be utilized for classification via latent variables, which provide classification rules by means of a softmax function. We formulate a Bayesian model averaging scheme to combine these two models and describe a Monte Carlo method for sampling from the full posterior distribution with joint proposals for the tree topology and the GP parameters corresponding to latent variables at the leaves. We concentrate on efficient sampling of the latent variables, which is important to obtain good mixing in the expanded parameter space. The tree structure is particularly helpful for this task and also for developing an efficient scheme for handling categorical predictors, which commonly arise in classification problems. Our proposed classification TGP (CTGP) methodology is illustrated on a collection of synthetic and real data sets. We assess performance relative to existing methods and thereby show how CTGP is highly flexible, offers tractable inference, produces rules that are easy to interpret, and performs well out of sample.