arXiv subjects

Matthew Griffiths

Publications and source records attributed to Matthew Griffiths.

4 recordsLinked to original sources

arXiv2024

Regularisation of cylindrical L\'evy processes in Besov spaces

In this work, we quantify the irregularity of a given cylindrical L\'evy process $L$ in $L^2({\mathbb R}^d)$ by determining the range of weighted Besov spaces $B$ in which $L$ has a regularised version $Y$, that is a stochastic process $Y$ in the classical sense with values in $B$. Our approach is based on characterising L\'evy measures on Besov spaces. As a by-product, we determine those Besov spaces $B$ for which the embedding of $L^2({\mathbb R}^d)$ into $B$ is $0$-Radonifying and $p$-Radonifying for $p>1$.

math.PR↗

arXiv2022

Nested sampling for physical scientists

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS.

stat.CO↗

arXiv2021

PyAutoFit: A Classy Probabilistic Programming Language for Model Composition and Fitting

A major trend in academia and data science is the rapid adoption of Bayesian statistics for data analysis and modeling, leading to the development of probabilistic programming languages (PPL). A PPL provides a framework that allows users to easily specify a probabilistic model and perform inference automatically. PyAutoFit is a Python-based PPL which interfaces with all aspects of the modeling (e.g., the model, data, fitting procedure, visualization, results) and therefore provides complete management of every aspect of modeling. This includes composing high-dimensionality models from individual model components, customizing the fitting procedure and performing data augmentation before a model-fit. Advanced features include database tools for analysing large suites of modeling results and exploiting domain-specific knowledge of a problem via non-linear search chaining. Accompanying PyAutoFit is the autofit workspace (see https://github.com/Jammy2211/autofit_workspace), which includes example scripts and the HowToFit lecture series which introduces non-experts to model-fitting and provides a guide on how to begin a project using PyAutoFit. Readers can try PyAutoFit right now by going to the introduction Jupyter notebook on Binder (see https://mybinder.org/v2/gh/Jammy2211/autofit_workspace/HEAD) or checkout our readthedocs(see https://pyautofit.readthedocs.io/en/latest/) for a complete overview of PyAutoFit's features.

astro-ph.IM↗

arXiv2019

Modelling Levy space-time white noises

Based on the theory of independently scattered random measures, we introduce a natural generalisation of Gaussian space-time white noise to a Levy-type setting, which we call Levy-valued random measures. We determine the subclass of cylindrical Levy processes which correspond to Levy-valued random measures, and describe the elements of this subclass uniquely by their characteristic function. We embed the Levy-valued random measure, or the corresponding cylindrical Levy process, in the space of general and tempered distributions. For the latter case, we show that this embedding is possible if and only if a certain integrability condition is satisfied. Similar to existing definitions, we introduce Levy-valued additive sheets, and show that integrating a Levy-valued random measure in space defines a Levy-valued additive sheet. This relation is manifested by the result, that a Levy-valued random measure can be viewed as the weak derivative of a Levy-valued additive sheet in the space of distributions.

math.PR↗