The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online. Electronic Supplementary Material Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the compressed data is available analytically, speeding up computation by many orders of magnitude while also bypassing robustness issues due to convergence and mixing problems with MCMC. Model averaging is used to reduce sensitivity to the random projection matrix, while accommodating uncertainty in the subspace dimension. Strong theoretical support is provided for the approach by showing near parametric convergence rates for the predictive density in the large p small n asymptotic paradigm. Practical performance relative to competitors is illustrated in simulations and real data applications.

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations becomes large. There is a burgeoning literature on approaches for analyzing large spatial datasets. In this article, we propose a divide-and-conquer strategy within the Bayesian paradigm. We partition the data into subsets, analyze each subset using a Bayesian spatial process model and then obtain approximate posterior inference for the entire dataset by combining the individual posterior distributions from each subset. Importantly, as often desired in spatial analysis, we offer full posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. We call this approach “Spatial Meta-Kriging” (SMK). We do not need to store the entire data in one processor, and this leads to superior scalability. We demonstrate SMK with various spatial regression models including Gaussian processes and tapered Gaussian processes. The approach is intuitive, easy to implement, and is supported by theoretical results presented in the supplementary material available online. Empirical illustrations are provided using different simulation experiments and a geostatistical analysis of Pacific Ocean sea surface temperature data.

Large point referenced datasets occur frequently in the environmental and natural sciences. Use of Bayesian hierarchical spatial models for analyzing these datasets is undermined by onerous computational burdens associated with parameter estimation. Low-rank spatial process models attempt to resolve this problem by projecting spatial effects to a lower-dimensional subspace. This subspace is determined by a judicious choice of “knots” or locations that are fixed a priori. One such representation yields a class of predictive process models (e.g., Banerjee et al., 2008) for spatial and spatial-temporal data. Our contribution here expands upon predictive process models with fixed knots to models that accommodate stochastic modeling of the knots. We view the knots as emerging from a point pattern and investigate how such adaptive specifications can yield more flexible hierarchical frameworks that lead to automated knot selection and substantial computational benefits.

Background Human papillomavirus (HPV) is the most common sexually transmitted infection in the world. It can lead to anogenital, cervical, and head and neck cancer, with higher risk of malignant disease in patients with human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) patients. In India, 73,000 of the 130,000 women diagnosed with cervical cancer die annually. Gardasil®, a vaccine available against HPV types 6, 11, 16, and 18, is approved for use in women in India but not men. A backlash to post-licensure trials has created a negative public opinion of the vaccine for women. Vaccinating boys and men is an alternate approach to prevent cervical cancer in women. This study gauges facilitators and barriers to vaccination acceptance among men in Bangalore, India. Materials and methods Young men presenting to a dermatology clinic or an ART center in Bangalore, India, answered a seven-point survey assessing acceptance of the HPV vaccine, perceived barriers to vaccination, and acceptance of vaccination for their children. Ninety-three general dermatology patients and 85 patients with HIV/AIDS participated. Results There was a high degree of vaccine acceptance for both groups, 83 and 98%, respectively. Vaccine side effects and cost were cited as key barriers to vaccination, and doctor recommendation and government approval were the main facilitators. Conclusion There is potential for high acceptability of the HPV vaccine among men in India. These results can facilitate further study of vaccine acceptance among males and physician opinion and knowledge about HPV vaccine use. Vaccination of males is a hopeful strategy to protect men and women from HPV-related malignancies.