536 research outputs found
Comment on Article by Ferreira and Gamerman
A utility-function approach to optimal spatial sampling design is a powerful
way to quantify what "optimality" means. The emphasis then should be to capture
all possible contributions to utility, including scientific impact and the cost
of sampling. The resulting sampling plan should contain a component of designed
randomness that would allow for a non-parametric design-based analysis if
model-based assumptions were in doubt. [arXiv:1509.03410]Comment: Published at http://dx.doi.org/10.1214/15-BA944B in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
A spatial analysis of multivariate output from regional climate models
Climate models have become an important tool in the study of climate and
climate change, and ensemble experiments consisting of multiple climate-model
runs are used in studying and quantifying the uncertainty in climate-model
output. However, there are often only a limited number of model runs available
for a particular experiment, and one of the statistical challenges is to
characterize the distribution of the model output. To that end, we have
developed a multivariate hierarchical approach, at the heart of which is a new
representation of a multivariate Markov random field. This approach allows for
flexible modeling of the multivariate spatial dependencies, including the
cross-dependencies between variables. We demonstrate this statistical model on
an ensemble arising from a regional-climate-model experiment over the western
United States, and we focus on the projected change in seasonal temperature and
precipitation over the next 50 years.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS369 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On statistical approaches to generate Level 3 products from satellite remote sensing retrievals
Satellite remote sensing of trace gases such as carbon dioxide (CO) has
increased our ability to observe and understand Earth's climate. However, these
remote sensing data, specifically~Level 2 retrievals, tend to be irregular in
space and time, and hence, spatio-temporal prediction is required to infer
values at any location and time point. Such inferences are not only required to
answer important questions about our climate, but they are also needed for
validating the satellite instrument, since Level 2 retrievals are generally not
co-located with ground-based remote sensing instruments. Here, we discuss
statistical approaches to construct Level 3 products from Level 2 retrievals,
placing particular emphasis on the strengths and potential pitfalls when using
statistical prediction in this context. Following this discussion, we use a
spatio-temporal statistical modelling framework known as fixed rank kriging
(FRK) to obtain global predictions and prediction standard errors of
column-averaged carbon dioxide based on Version 7r and Version 8r retrievals
from the Orbiting Carbon Observatory-2 (OCO-2) satellite. The FRK predictions
allow us to validate statistically the Level 2 retrievals globally even though
the data are at locations and at time points that do not coincide with
validation data. Importantly, the validation takes into account the prediction
uncertainty, which is dependent both on the temporally-varying density of
observations around the ground-based measurement sites and on the
spatio-temporal high-frequency components of the trace gas field that are not
explicitly modelled. Here, for validation of remotely-sensed CO data, we
use observations from the Total Carbon Column Observing Network. We demonstrate
that the resulting FRK product based on Version 8r compares better with TCCON
data than that based on Version 7r.Comment: 28 pages, 10 figures, 4 table
Non-Gaussian bivariate modelling with application to atmospheric trace-gas inversion
Atmospheric trace-gas inversion is the procedure by which the sources and
sinks of a trace gas are identified from observations of its mole fraction at
isolated locations in space and time. This is inherently a spatio-temporal
bivariate inversion problem, since the mole-fraction field evolves in space and
time and the flux is also spatio-temporally distributed. Further, the bivariate
model is likely to be non-Gaussian since the flux field is rarely Gaussian.
Here, we use conditioning to construct a non-Gaussian bivariate model, and we
describe some of its properties through auto- and cross-cumulant functions. A
bivariate non-Gaussian, specifically trans-Gaussian, model is then achieved
through the use of Box--Cox transformations, and we facilitate Bayesian
inference by approximating the likelihood in a hierarchical framework.
Trace-gas inversion, especially at high spatial resolution, is frequently
highly sensitive to prior specification. Therefore, unlike conventional
approaches, we assimilate trace-gas inventory information with the
observational data at the parameter layer, thus shifting prior sensitivity from
the inventory itself to its spatial characteristics (e.g., its spatial length
scale). We demonstrate the approach in controlled-experiment studies of methane
inversion, using fluxes extracted from inventories of the UK and Ireland and of
Northern Australia.Comment: 45 pages, 7 figure
Bayesian hierarchical statistical SIRS models
The classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are “mass balanced.” Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynam- ical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS (CSIRS) model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic
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