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Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional likelihoods. We propose a shift in viewpoint from whole to local data perspectives that is rooted in distributed model building and integrated estimation and inference. The framework’s backbone is a computationally and statistically efficient integration procedure that simultaneously incorporates dependence within and between spatial resolutions in a recursively partitioned spatial domain. Statistical and computational properties of our distributed approach are investigated theoretically and in simulations. The proposed approach is used to extract new insights into autism spectrum disorder from the autism brain imaging data exchange. 

Untreated periodontitis causes inflammation within the supporting tissue of the teeth and can ultimately lead to tooth loss. Modeling periodontal outcomes is beneficial as they are difficult and time‐consuming to measure, but disparities in representation between demographic groups must be considered. There may not be enough participants to build group‐specific models, and it can be ineffective, and even dangerous, to apply a model to participants in an underrepresented group if demographic differences were not considered during training. We propose an extension to the RECaST Bayesian transfer learning framework. Our method jointly models multivariate outcomes, exhibiting significant improvement over the previous univariate RECaST method. Further, we introduce an online approach to model sequential data sets. Negative transfer is mitigated to ensure that the information shared from the other demographic groups does not negatively impact the modeling of the underrepresented participants. The Bayesian framework naturally provides uncertainty quantification on predictions. Especially important in medical applications, our method does not share data between domains. We demonstrate the effectiveness of our method in both predictive performance and uncertainty quantification on simulated data and on a database of dental records from the HealthPartners Institute. 

ABSTRACT Classic Bayesian methods with complex environmental models are frequently infeasible due to an intractable likelihood. Simulation‐based inference methods, such as neural posterior estimation, calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high‐dimensional settings. In this paper, we suggest that imposing strict variational assumptions on the form of the posterior can often combat these computational issues. Posterior distributions of model parameters are efficiently obtained by assuming a parametric form for the posterior, parametrized by the machine learning model, which is trained with the simulated data as inputs and the associated parameters as outputs. We show theoretically that if the parametric family of the variational posterior is correct, our posteriors converge to the true posteriors in Kullback–Leibler divergence. We also provide tools to help us identify if our parametric assumption is close to the true posterior, and modeling options if that is not the case. Comprehensive simulation studies using environmental models highlight our method's robustness and versatility. An analysis of the Zika virus in Brazil provides a thorough case study. 

Abstract Geostationary weather satellites collect high‐resolution data comprising a series of images. The Derived Motion Winds (DMW) Algorithm is commonly used to process these data and estimate atmospheric winds by tracking features in the images. However, the wind estimates from the DMW Algorithm are often missing and do not come with uncertainty measures. Also, the DMW Algorithm estimates can only be half‐integers, since the algorithm requires the original and shifted data to be at the same locations, in order to calculate the displacement vector between them. This motivates us to statistically model wind motions as a spatial process drifting in time. Using a covariance function that depends on spatial and temporal lags and a drift parameter to capture the wind speed and wind direction, we estimate the parameters by local maximum likelihood. Our method allows us to compute standard errors of the local estimates, enabling spatial smoothing of the estimates using a Gaussian kernel weighted by the inverses of the estimated variances. We conduct extensive simulation studies to determine the situations where our method performs well. The proposed method is applied to the GOES‐15 brightness temperature data over Colorado and reduces prediction error of brightness temperature compared to the DMW Algorithm. 

Given the increasing prevalence of wildland fires in the Western US, there is a crit- ical need to develop tools to understand and accurately predict burn severity. We develop a novel machine learning model to predict post-fire burn severity using pre- fire remotely sensed data. Hydrological, ecological, and topographical variables col- lected from four regions of California — the site of the Kincade fire (2019), the CZU Lightning Complex fire (2020), the Windy fire (2021), and the KNP Fire (2021) — are used as predictors of the differenced normalized burn ratio. We hypothesize that a Super Learner (SL) algorithm that accounts for spatial autocorrelation using Vec- chia’s Gaussian approximation will accurately model burn severity. We use a cross- validation study to show that the spatial SL model can predict burn severity with reasonable classification accuracy, including high burn severity events. After fitting and verifying the performance of the SL model, we use interpretable machine learn- ing tools to determine the main drivers of severe burn damage, including greenness, elevation, and fire weather variables. These findings provide actionable insights that enable communities to strategize interventions, such as early fire detection systems, pre-fire season vegetation clearing activities, and resource allocation during emer- gency responses. When implemented, this model has the potential to minimize the loss of human life, property, resources, and ecosystems in California.