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<p>We address predictive modeling for spatial and spatiotemporal modeling in a variety
of settings. First, we discuss spatial and spatiotemporal data and corresponding model
types used in later chapters. Specifically, we discuss Markov random fields, Gaussian
processes, and Bayesian inference. Then, we outline the dissertation.</p><p>In Chapter
2, we consider the setting where areal unit data are only partially observed. First,
we consider setting where a portion of the areal units have been observed, and we
seek prediction of the remainder. Second, we leverage these ideas for model comparison
where we fit models of interest to a portion of the data and hold out the rest for
model comparison.</p><p>In Chapters 3 and 4, we consider pollution data from Mexico
City in 2017. In Chapter 3 we forecast pollution emergencies. Mexico City defines
pollution emergencies using thresholds that rely on regional maxima for ozone and
for particulate matter with diameter less than 10 micrometers (PM10). To predict local
pollution emergencies and to assess compliance with Mexican ambient air quality standards,
we analyze hourly ozone and PM10 measurements from 24 stations across Mexico City
from 2017 using a bivariate spatiotemporal model. With this model, we predict future
pollutant levels using current weather conditions and recent pollutant concentrations.
Employing hourly pollutant projections, we predict regional maxima needed to estimate
the probability of future pollution emergencies. We discuss how predicted compliance
with legislated pollution limits varies across regions within Mexico City in 2017.</p><p>In
Chapter 4, we propose a continuous spatiotemporal model for Mexico City ozone levels
that accounts 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 respiratory
health risk associated with ozone exposure.</p>
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