10,342 research outputs found
Predictive Inference for Spatio-temporal Precipitation Data and Its Extremes
Modelling of precipitation and its extremes is important for urban and
agriculture planning purposes. We present a method for producing spatial
predictions and measures of uncertainty for spatio-temporal data that is
heavy-tailed and subject to substaintial skewness which often arise in
measurements of many environmental processes, and we apply the method to
precipitation data in south-west Western Australia. A generalised hyperbolic
Bayesian hierarchical model is constructed for the intensity, frequency and
duration of daily precipitation, including the extremes. Unlike models based on
extreme value theory, which only model maxima of finite-sized blocks or
exceedances above a large threshold, the proposed model uses all the data
available efficiently, and hence not only fits the extremes but also models the
entire rainfall distribution. It captures spatial and temporal clustering, as
well as spatially and temporally varying volatility and skewness. The model
assumes that the regional precipitation is driven by a latent process
characterised by geographical and climatological covariates. Effects not fully
described by the covariates are captured by spatial and temporal structure in
the hierarchies. Inference is provided by MCMC using a Metropolis-Hastings
algorithm and spatial interpolation method, which provide a natural approach
for estimating uncertainty. Similarly both spatial and temporal predictions
with uncertainty can be produced with the model.Comment: Under review at Journal of the American Statistical Association. 27
pages, 10 figure
Algorithms for Estimating Trends in Global Temperature Volatility
Trends in terrestrial temperature variability are perhaps more relevant for
species viability than trends in mean temperature. In this paper, we develop
methodology for estimating such trends using multi-resolution climate data from
polar orbiting weather satellites. We derive two novel algorithms for
computation that are tailored for dense, gridded observations over both space
and time. We evaluate our methods with a simulation that mimics these data's
features and on a large, publicly available, global temperature dataset with
the eventual goal of tracking trends in cloud reflectance temperature
variability.Comment: Published in AAAI-1
A spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting
Renewable sources of energy such as wind power have become a sustainable
alternative to fossil fuel-based energy. However, the uncertainty and
fluctuation of the wind speed derived from its intermittent nature bring a
great threat to the wind power production stability, and to the wind turbines
themselves. Lately, much work has been done on developing models to forecast
average wind speed values, yet surprisingly little has focused on proposing
models to accurately forecast extreme wind speeds, which can damage the
turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto
model to forecast extreme and non-extreme wind speeds simultaneously. Our model
belongs to the class of latent Gaussian models, for which inference is
conveniently performed based on the integrated nested Laplace approximation
method. Considering a flexible additive regression structure, we propose two
models for the latent linear predictor to capture the spatio-temporal dynamics
of wind speeds. Our models are fast to fit and can describe both the bulk and
the tail of the wind speed distribution while producing short-term extreme and
non-extreme wind speed probabilistic forecasts.Comment: 25 page
An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data
Self-Exciting models are statistical models of count data where the
probability of an event occurring is influenced by the history of the process.
In particular, self-exciting spatio-temporal models allow for spatial
dependence as well as temporal self-excitation. For large spatial or temporal
regions, however, the model leads to an intractable likelihood. An increasingly
common method for dealing with large spatio-temporal models is by using Laplace
approximations (LA). This method is convenient as it can easily be applied and
is quickly implemented. However, as we will demonstrate in this manuscript,
when applied to self-exciting Poisson spatial-temporal models, Laplace
Approximations result in a significant bias in estimating some parameters. Due
to this bias, we propose using up to sixth-order corrections to the LA for
fitting these models. We will demonstrate how to do this in a Bayesian setting
for Self-Exciting Spatio-Temporal models. We will further show there is a
limited parameter space where the extended LA method still has bias. In these
uncommon instances we will demonstrate how a more computationally intensive
fully Bayesian approach using the Stan software program is possible in those
rare instances. The performance of the extended LA method is illustrated with
both simulation and real-world data
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