Humans do not respond to the pain of all humans equally; physical appearance and associated group identity affect how people respond to the pain of others. Here we ask if a similar differential response occurs when humans evaluate different individuals of another species. Beliefs about pain in pet dogs (Canis familiaris) provide a powerful test, since dogs vary so much in size, shape, and color, and are often associated with behavioral stereotypes. Using an on-line survey, we asked both the general public and veterinarians to rate pain sensitivity in 28 different dog breeds, identified only by their pictures. We found that both the general public and veterinarians rated smaller dogs (i.e. based on height and weight) as being more sensitive to pain; the general public respondents rated breeds associated with breed specific legislation as having lower pain sensitivity. While there is currently no known physiological basis for such breed-level differences, over 90% of respondents from both groups indicated belief in differences in pain sensitivity among dog breeds. We discuss how these results inform theories of human social discrimination and suggest that the perception of breed-level differences in pain sensitivity may affect the recognition and management of painful conditions in dogs.

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With the advent of wide-spread global and continental-scale spatiotemporal datasets, increased attention has been given to covariance functions on spheres over time. This paper provides results for stationary covariance functions of random fields defined over d-dimensional spheres cross time. Specifically, we provide a bridge between the characterization in Berg and Porcu (2017) for covariance functions on spheres cross time and Gneiting's lemma (Gneiting, 2002) that deals with planar surfaces.We then prove that there is a valid class of covariance functions similar in form to the Gneiting class of space-time covariance functions (Gneiting, 2002) that replaces the squared Euclidean distance with the great circle distance. Notably, the provided class is shown to be positive definite on every d-dimensional sphere cross time, while the Gneiting class is positive definite over R d × R for fixed d only.In this context, we illustrate the value of our adapted Gneiting class by comparing examples from this class to currently established nonseparable covariance classes using out-of-sample predictive criteria. These comparisons are carried out on two climate reanalysis datasets from the National Centers for Environmental Prediction and National Center for Atmospheric Research. For these datasets, we show that examples from our covariance class have better predictive performance than competing models.

We propose a continuous spatiotemporal model for Mexico City ozone levels that account for distinct daily seasonality, as well as variation across the city and over the peak ozone season (April and May) of 2017. To account for these patterns, we use covariance models over space, circles, and time. We review relevant existing covariance models and develop new classes of nonseparable covariance models appropriate for seasonal data collected at many locations. We compare the predictive performance of a variety of models that utilize various nonseparable covariance functions. We use the best model to predict hourly ozone levels at unmonitored locations in April and May to infer compliance with Mexican air quality standards and to estimate the respiratory health risk associated with ozone exposure. We find that predicted compliance with air quality standards and estimated respiratory health risk vary greatly over space and time. In some regions, we predict exceedance of national standards for more than a third of the hours in April and May, and on many days, we predict that nearly all of Mexico City exceeds nationally legislated ozone thresholds at least once. In southern Mexico City, we estimate the respiratory risk for ozone to be 55% higher, on average, than the annual average risk and as much at 170% higher on some days.

In this study, we develop a model for Antarctic surface mass balance (SMB), which allows us to assess regional and global uncertainty in SMB estimation and carry out a model‐based design to propose new measurement sites. For this analysis, we use a quality‐controlled aggregate data set of SMB field measurements with significantly more observations than previous analyses; however, many of the measurements in this data set lack quality ratings. In addition, these data demonstrate spatial autocorrelation, heteroscedasticity, and non‐Gaussianity. To account for these data attributes, we pose a Bayesian Gaussian process generalized linear model for SMB. To address missing reliability ratings, we use a mixture model with different variances to add robustness to our model. In addition, we present a novel approach for modeling the variance as a function of the mean to account for the heteroscedasticity in the data. Using this model, we predict Antarctic SMB and compare our estimates with previous estimates. In addition, we create prediction maps with uncertainty to visualize spatial patterns in SMB and to identify regions of high SMB uncertainty. Our model estimates the total SMB to be 2,156 Gton/yr over the range of our data, with 95% credible interval (2,081, 2,234) Gton/yr. Overall, our results suggest lower Antarctic SMB than previously reported. This lower SMB estimate may be indicative of a more dire diagnosis of the long‐term health of the Antarctic ice sheets. Lastly, we use our model to propose 25 new measurement sites for the field study utilizing a sequential design, minimizing the integrated mean squared error.