51,210 research outputs found
Probability and Statistics for Particle Physicists
Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy
Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics
in probability and statistics is presented. Choice and emphasis are driven by
the author's personal experience, predominantly in the context of physics
analyses using experimental data from high-energy physics detectors.Comment: Updated version of lectures given at the First Asia-Europe-Pacific
School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. Published
as a CERN Yellow Report (CERN-2014-001) and KEK report
(KEK-Proceedings-2013-8), K. Kawagoe and M. Mulders (eds.), 2014, p. 219.
Total 28 pages, 36 figure
Bayesian nonparametric models for spatially indexed data of mixed type
We develop Bayesian nonparametric models for spatially indexed data of mixed
type. Our work is motivated by challenges that occur in environmental
epidemiology, where the usual presence of several confounding variables that
exhibit complex interactions and high correlations makes it difficult to
estimate and understand the effects of risk factors on health outcomes of
interest. The modeling approach we adopt assumes that responses and confounding
variables are manifestations of continuous latent variables, and uses
multivariate Gaussians to jointly model these. Responses and confounding
variables are not treated equally as relevant parameters of the distributions
of the responses only are modeled in terms of explanatory variables or risk
factors. Spatial dependence is introduced by allowing the weights of the
nonparametric process priors to be location specific, obtained as probit
transformations of Gaussian Markov random fields. Confounding variables and
spatial configuration have a similar role in the model, in that they only
influence, along with the responses, the allocation probabilities of the areas
into the mixture components, thereby allowing for flexible adjustment of the
effects of observed confounders, while allowing for the possibility of residual
spatial structure, possibly occurring due to unmeasured or undiscovered
spatially varying factors. Aspects of the model are illustrated in simulation
studies and an application to a real data set
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