46,231 research outputs found
Combining spatial information sources while accounting for systematic errors in proxies
Environmental research increasingly uses high-dimensional remote sensing and
numerical model output to help fill space-time gaps between traditional
observations. Such output is often a noisy proxy for the process of interest.
Thus one needs to separate and assess the signal and noise (often called
discrepancy) in the proxy given complicated spatio-temporal dependencies. Here
I extend a popular two-likelihood hierarchical model using a more flexible
representation for the discrepancy. I employ the little-used Markov random
field approximation to a thin plate spline, which can capture small-scale
discrepancy in a computationally efficient manner while better modeling smooth
processes than standard conditional auto-regressive models. The increased
flexibility reduces identifiability, but the lack of identifiability is
inherent in the scientific context. I model particulate matter air pollution
using satellite aerosol and atmospheric model output proxies. The estimated
discrepancies occur at a variety of spatial scales, with small-scale
discrepancy particularly important. The examples indicate little predictive
improvement over modeling the observations alone. Similarly, in simulations
with an informative proxy, the presence of discrepancy and resulting
identifiability issues prevent improvement in prediction. The results highlight
but do not resolve the critical question of how best to use proxy information
while minimizing the potential for proxy-induced error.Comment: 5 figures, 2 table
The mortality of the Italian population: Smoothing techniques on the Lee--Carter model
Several approaches have been developed for forecasting mortality using the
stochastic model. In particular, the Lee-Carter model has become widely used
and there have been various extensions and modifications proposed to attain a
broader interpretation and to capture the main features of the dynamics of the
mortality intensity. Hyndman-Ullah show a particular version of the Lee-Carter
methodology, the so-called Functional Demographic Model, which is one of the
most accurate approaches as regards some mortality data, particularly for
longer forecast horizons where the benefit of a damped trend forecast is
greater. The paper objective is properly to single out the most suitable model
between the basic Lee-Carter and the Functional Demographic Model to the
Italian mortality data. A comparative assessment is made and the empirical
results are presented using a range of graphical analyses.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS394 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression provides a general framework for complex
Gaussian and non-Gaussian regression models, with predictors comprising
arbitrary combinations of nonlinear functions and surfaces, spatial effects,
varying coefficients, random effects and further regression terms. The large
flexibility of structured additive regression makes function selection a
challenging and important task, aiming at (1) selecting the relevant
covariates, (2) choosing an appropriate and parsimonious representation of the
impact of covariates on the predictor and (3) determining the required
interactions. We propose a spike-and-slab prior structure for function
selection that allows to include or exclude single coefficients as well as
blocks of coefficients representing specific model terms. A novel
multiplicative parameter expansion is required to obtain good mixing and
convergence properties in a Markov chain Monte Carlo simulation approach and is
shown to induce desirable shrinkage properties. In simulation studies and with
(real) benchmark classification data, we investigate sensitivity to
hyperparameter settings and compare performance to competitors. The flexibility
and applicability of our approach are demonstrated in an additive piecewise
exponential model with time-varying effects for right-censored survival times
of intensive care patients with sepsis. Geoadditive and additive mixed logit
model applications are discussed in an extensive appendix
Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models
In regression models with many potential predictors, choosing an appropriate subset of covariates and their interactions at the same time as determining whether linear or more flexible functional forms are required is a challenging and important task. We propose a spike-and-slab prior structure in order to include or exclude single coefficients as well as blocks of coefficients associated
with factor variables, random effects or basis expansions
of smooth functions. Structured additive models with this prior structure are estimated with Markov Chain Monte Carlo using a redundant multiplicative parameter expansion. We discuss shrinkage properties of the novel prior induced by the redundant parameterization, investigate its sensitivity to hyperparameter settings and compare performance of the proposed method in terms of model selection, sparsity recovery, and estimation error for Gaussian, binomial and Poisson responses on real and simulated data sets with that of component-wise boosting and other approaches
Structured penalties for functional linear models---partially empirical eigenvectors for regression
One of the challenges with functional data is incorporating spatial
structure, or local correlation, into the analysis. This structure is inherent
in the output from an increasing number of biomedical technologies, and a
functional linear model is often used to estimate the relationship between the
predictor functions and scalar responses. Common approaches to the ill-posed
problem of estimating a coefficient function typically involve two stages:
regularization and estimation. Regularization is usually done via dimension
reduction, projecting onto a predefined span of basis functions or a reduced
set of eigenvectors (principal components). In contrast, we present a unified
approach that directly incorporates spatial structure into the estimation
process by exploiting the joint eigenproperties of the predictors and a linear
penalty operator. In this sense, the components in the regression are
`partially empirical' and the framework is provided by the generalized singular
value decomposition (GSVD). The GSVD clarifies the penalized estimation process
and informs the choice of penalty by making explicit the joint influence of the
penalty and predictors on the bias, variance, and performance of the estimated
coefficient function. Laboratory spectroscopy data and simulations are used to
illustrate the concepts.Comment: 29 pages, 3 figures, 5 tables; typo/notational errors edited and
intro revised per journal review proces
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