28 research outputs found
Using The Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default
Regression models for limited continuous dependent variables having a
non-negligible probability of attaining exactly their limits are presented. The
models differ in the number of parameters and in their flexibility. Fractional
data being a special case of limited dependent data, the models also apply to
variables that are a fraction or a proportion. It is shown how to fit these
models and they are applied to a Loss Given Default dataset from insurance to
which they provide a good fit
Gaussian Process Boosting
We introduce a novel way to combine boosting with Gaussian process and mixed
effects models. This allows for relaxing, first, the linearity assumption for
the mean function in Gaussian process and grouped random effects models in a
flexible non-parametric way and, second, the independence assumption made in
most boosting algorithms. The former is advantageous for predictive accuracy
and for avoiding model misspecifications. The latter is important for more
efficient learning of the mean function and for obtaining probabilistic
predictions. In addition, we present an extension that scales to large data
using a Vecchia approximation for the Gaussian process model relying on novel
results for covariance parameter inference. We obtain increased predictive
accuracy compared to existing approaches on several simulated and real-world
data sets
A dynamic nonstationary spatio-temporal model for short term prediction of precipitation
Precipitation is a complex physical process that varies in space and time.
Predictions and interpolations at unobserved times and/or locations help to
solve important problems in many areas. In this paper, we present a
hierarchical Bayesian model for spatio-temporal data and apply it to obtain
short term predictions of rainfall. The model incorporates physical knowledge
about the underlying processes that determine rainfall, such as advection,
diffusion and convection. It is based on a temporal autoregressive convolution
with spatially colored and temporally white innovations. By linking the
advection parameter of the convolution kernel to an external wind vector, the
model is temporally nonstationary. Further, it allows for nonseparable and
anisotropic covariance structures. With the help of the Voronoi tessellation,
we construct a natural parametrization, that is, space as well as time
resolution consistent, for data lying on irregular grid points. In the
application, the statistical model combines forecasts of three other
meteorological variables obtained from a numerical weather prediction model
with past precipitation observations. The model is then used to predict
three-hourly precipitation over 24 hours. It performs better than a separable,
stationary and isotropic version, and it performs comparably to a deterministic
numerical weather prediction model for precipitation and has the advantage that
it quantifies prediction uncertainty.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS564 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models
Latent Gaussian process (GP) models are flexible probabilistic non-parametric
function models. Vecchia approximations are accurate approximations for GPs to
overcome computational bottlenecks for large data, and the Laplace
approximation is a fast method with asymptotic convergence guarantees to
approximate marginal likelihoods and posterior predictive distributions for
non-Gaussian likelihoods. Unfortunately, the computational complexity of
combined Vecchia-Laplace approximations grows faster than linearly in the
sample size when used in combination with direct solver methods such as the
Cholesky decomposition. Computations with Vecchia-Laplace approximations thus
become prohibitively slow precisely when the approximations are usually the
most accurate, i.e., on large data sets. In this article, we present several
iterative methods for inference with Vecchia-Laplace approximations which make
computations considerably faster compared to Cholesky-based calculations. We
analyze our proposed methods theoretically and in experiments with simulated
and real-world data. In particular, we obtain a speed-up of an order of
magnitude compared to Cholesky-based inference and a threefold increase in
prediction accuracy in terms of the continuous ranked probability score
compared to a state-of-the-art method on a large satellite data set. All
methods are implemented in a free C++ software library with high-level Python
and R packages
Using the Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables that are a fraction or a proportion. It is shown how to fit these models and they are applied to a Loss Given Default dataset from insurance to which they provide a good fi
Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models
Spatially varying coefficient (SVC) models are a type of regression models for spatial data where covariate effects vary over space. If there are several covariates, a natural question is which covariates have a spatially varying effect and which not. We present a new variable selection approach for Gaussian process-based SVC models. It relies on a penalized maximum likelihood estimation and allows joint variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach in a simulation study as well as a real world data set. In the simulation study, the penalized maximum likelihood estimation correctly identifies zero fixed and random effects, while the penalty-induced bias of non-zero estimates is negligible. In the real data application, our proposed penalized maximum likelihood estimation yields sparser SVC models and achieves a smaller information criterion than classical maximum likelihood estimation. In a cross-validation study applied on the real data, we show that our proposed penalized maximum likelihood estimation consistently yields the sparsest SVC models while achieving similar predictive performance compared to other SVC modeling methodologies