Binter, Roman
(2012)
Applied probabilistic forecasting.
PhD thesis, London School of Economics and Political Science.
Abstract
In any actual forecast, the future evolution of the system is uncertain and the
forecasting model is mathematically imperfect. Both, ontic uncertainties in
the future (due to true stochasticity) and epistemic uncertainty of the model
(reflecting structural imperfections) complicate the construction and evaluation of probabilistic forecast. In almost all nonlinear forecast models, the
evolution of uncertainty in time is not tractable analytically and Monte Carlo
approaches (”ensemble forecasting”) are widely used. This thesis advances
our understanding of the construction of forecast densities from ensembles,
the evolution of the resulting probability forecasts and methods of establishing skill (benchmarks). A novel method of partially correcting the model
error is introduced and shown to outperform a competitive approach.
The properties of Kernel dressing, a method of transforming ensembles into
probability density functions, are investigated and the convergence of the
approach is illustrated. A connection between forecasting and Information
theory is examined by demonstrating that Kernel dressing via minimization
of Ignorance implicitly leads to minimization of Kulback-Leibler divergence.
The Ignorance score is critically examined in the context of other Information
theory measures.
The method of Dynamic Climatology is introduced as a new approach to establishing skill (benchmarking). Dynamic Climatology is a new, relatively
simple, nearest neighbor based model shown to be of value in benchmarking
of global circulation models of the ENSEMBLES project. ENSEMBLES is a
project funded by the European Union bringing together all major European
weather forecasting institutions in order to develop and test state-of-the-art
seasonal weather forecasting models. Via benchmarking the seasonal forecasts of the ENSEMBLES models we demonstrate that Dynamic Climatology
can help us better understand the value and forecasting performance of large
scale circulation models.
Lastly, a new approach to correcting (improving) imperfect model is presented, an idea inspired by [63]. The main idea is based on a two-stage
procedure where a second stage ‘corrective’ model iteratively corrects systematic parts of forecasting errors produced by a first stage ‘core’ model.
The corrector is of an iterative nature so that at a given time t the core
model forecast is corrected and then used as an input into the next iteration
of the core model to generate a time t + 1 forecast. Using two nonlinear
systems we demonstrate that the iterative corrector is superior to alternative
approaches based on direct (non-iterative) forecasts. While the choice of the
corrector model class is flexible, we use radial basis functions. Radial basis
functions are frequently used in statistical learning and/or surface approximations and involve a number of computational aspects which we discuss in
some detail.
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