On Latent Variable Models for Bayesian Inference with Stable Distributions and Processes
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Abstract
Extreme values and skewness in time-series are often observed in engineering, financial
and biological applications. This thesis is a study motivated by the need of efficient
and reliable Bayesian inference methods when the
The class of stable distributions is the limit of the generalized central limit
theorem (CLT), having a key role in representing phenomena that can be thought of
as the sum of many perturbations, with potentially unbounded variance. Besides the
ability to model heavy-tailedness, another consequence of the generalized CLT is a
further degree of freedom of stable distributions, namely their potential skewness.
However, stable distributions are, at the same time, highly intractable for inference
purposes. Several approximate methods are available in the literature, in both the
frequentist and Bayesian paradigms, but they suffer from a number of deficiencies,
the greatest of which is the lack of quantification of the approximation in place. This
thesis proposes Bayesian inference schemes for two different latent variable models,
with the aim of providing guarantees of accuracy when the
The focus of the second and central part of the thesis is the Poisson series
representation (PSR) of
In the third and final part of this thesis, an extension of the modified Poisson
series representation (MPSR) of linear continuous-time models driven by