3 research outputs found
A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting
Extreme streamflow is a key indicator of flood risk, and quantifying the
changes in its distribution under non-stationary climate conditions is key to
mitigating the impact of flooding events. We propose a non-stationary process
mixture model (NPMM) for annual streamflow maxima over the central US (CUS)
which uses downscaled climate model precipitation projections to forecast
extremal streamflow. Spatial dependence for the model is specified as a convex
combination of transformed Gaussian and max-stable processes, indexed by a
weight parameter which identifies the asymptotic regime of the process. The
weight parameter is modeled as a function of the annual precipitation for each
of the two hydrologic regions within the CUS, introducing spatio-temporal
non-stationarity within the model. The NPMM is flexible with desirable tail
dependence properties, but yields an intractable likelihood. To address this,
we embed a neural network within a density regression model which is used to
learn a synthetic likelihood function using simulations from the NPMM with
different parameter settings. Our model is fitted using observational data for
1972--2021, and inference carried out in a Bayesian framework. The two regions
within the CUS are estimated to be in different asymptotic regimes based on the
posterior distribution of the weight parameter. Annual streamflow maxima
estimates based on global climate models for two representative climate pathway
scenarios suggest an overall increase in the frequency and magnitude of extreme
streamflow for 2006-2035 compared to the historical period of 1972-2005
Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation
Stochastic precipitation generators (SPGs) are a class of statistical models
which generate synthetic data that can simulate dry and wet rainfall stretches
for long durations. Generated precipitation time series data are used in
climate projections, impact assessment of extreme weather events, and water
resource and agricultural management. We construct an SPG for daily
precipitation data that is specified as a semi-continuous distribution at every
location, with a point mass at zero for no precipitation and a mixture of two
exponential distributions for positive precipitation. Our generators are
obtained as hidden Markov models (HMMs) where the underlying climate conditions
form the states. We fit a 3-state HMM to daily precipitation data for the
Chesapeake Bay watershed in the Eastern coast of the USA for the wet season
months of July to September from 2000--2019. Data is obtained from the
GPM-IMERG remote sensing dataset, and existing work on variational HMMs is
extended to incorporate semi-continuous emission distributions. In light of the
high spatial dimension of the data, a stochastic optimization implementation
allows for computational speedup. The most likely sequence of underlying states
is estimated using the Viterbi algorithm, and we are able to identify
differences in the weather regimes associated with the states of the proposed
model. Synthetic data generated from the HMM can reproduce monthly
precipitation statistics as well as spatial dependency present in the
historical GPM-IMERG data
Semiparametric Estimation of the Shape of the Limiting Multivariate Point Cloud
We propose a model to flexibly estimate joint tail properties by exploiting
the convergence of an appropriately scaled point cloud onto a compact limit
set. Characteristics of the shape of the limit set correspond to key tail
dependence properties. We directly model the shape of the limit set using
B\'ezier splines, which allow flexible and parsimonious specification of shapes
in two dimensions. We then fit the B\'ezier splines to data in pseudo-polar
coordinates using Markov chain Monte Carlo, utilizing a limiting approximation
to the conditional likelihood of the radii given angles. By imposing
appropriate constraints on the parameters of the B\'ezier splines, we guarantee
that each posterior sample is a valid limit set boundary, allowing direct
posterior analysis of any quantity derived from the shape of the curve.
Furthermore, we obtain interpretable inference on the asymptotic dependence
class by using mixture priors with point masses on the corner of the unit box.
Finally, we apply our model to bivariate datasets of extremes of variables
related to fire risk and air pollution