Approximate reference priors for Gaussian random fields

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles that make their application in practice challenging. In this work, we derive a new class of default priors that approximate reference priors for the parameters of some Gaussian random fields. It is based on an approximation to the integrated likelihood of the covariance parameters derived from the spectral approximation of stationary random fields. This prior depends on the structure of the mean function and the spectral density of the model evaluated at a set of spectral points associated with an auxiliary regular grid. In addition to preserving the desirable Bayesian and frequentist properties, these approximate reference priors are more stable, and their computations are much less onerous than those of exact reference priors. Unlike exact reference priors, the marginal approximate reference prior of correlation parameter is always proper, regardless of the mean function or the smoothness of the correlation function. This property has important consequences for covariance model selection. An illustration comparing default Bayesian analyses is provided with a dataset of lead pollution in Galicia, Spain.     

Average and Quantile Effects in Nonseparable Panel Models

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time‐homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial‐identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed‐effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial‐identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete‐choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.     

Local Identification of Nonparametric and Semiparametric Models

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification. Importantly, we show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models and semiparametric consumption‐based asset pricing models.     

Risk heatmaps as visual displays: Opening movie studios after the COVID-19 shutdown

Upon shutting down operations in early 2020 due to the COVID-19 pandemic, the movie industry assembled teams of experts to help develop guidelines for returning to operation. It resulted in a joint report, The Safe Way Forward, which was created in consultation with union members and provided the basis for negotiations with the studios. A centerpiece of the report was a set of heatmaps displaying SARS-CoV-2 risks for a shoot, as a function of testing rate, community infection prevalence, community transmission rate (R0), and risk measure (either expected number of cases or probability of at least one case). We develop and demonstrate a methodology for evaluating such complex displays, in terms of how well they inform potential users, in this case, workers deciding whether the risks of a shoot are acceptable. We ask whether individuals making hypothetical return-to-work decisions can (a) read display entries, (b) compare display entries, and (c) make inferences based on display entries. Generally speaking, respondents recruited through the Amazon MTurk platform could interpret the display information accurately and make coherent decisions, suggesting that heatmaps can communicate complex risks to lay audiences. Although these heatmaps were created for practical, rather than theoretical, purposes, these results provide partial support for theoretical accounts of visual information processing and identify challenges in applying them to complex settings.