arXiv subjects

Peter Strong

Publications and source records attributed to Peter Strong.

6 recordsLinked to original sources

arXiv2022

cegpy: Modelling with Chain Event Graphs in Python

Chain event graphs (CEGs) are a recent family of probabilistic graphical models that generalise the popular Bayesian networks (BNs) family. Crucially, unlike BNs, a CEG is able to embed, within its graph and its statistical model, asymmetries exhibited by a process. These asymmetries might be in the conditional independence relationships or in the structure of the graph and its underlying event space. Structural asymmetries are common in many domains, and can occur naturally (e.g. a defendant vs prosecutor's version of events) or by design (e.g. a public health intervention). However, there currently exists no software that allows a user to leverage the theoretical developments of the CEG model family in modelling processes with structural asymmetries. This paper introduces cegpy, the first Python package for learning and analysing complex processes using CEGs. The key feature of cegpy is that it is the first CEG package in any programming language that can model processes with symmetric as well as asymmetric structures. cegpy contains an implementation of Bayesian model selection and probability propagation algorithms for CEGs. We illustrate the functionality of cegpy using a structurally asymmetric dataset.

stat.ME↗

arXiv2022

Scalable Model Selection for Staged Trees: Mean-posterior Clustering and Binary Trees

Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these either do not scale efficiently as the number of variables considered increases, a priori restrict the set of models, or they do not find comparable models to existing methods. Here, we define an alternative algorithm based on a totally ordered hyperstage. We demonstrate how it can be used to obtain a quadratically-scaling structural learning algorithm for staged trees that restricts the model space a-posteriori. Through comparative analysis, we show that through the ordering provided by the mean posterior distributions, we can outperform existing methods in both computational time and model score. This method also enables us to learn more complex relationships than existing model selection techniques by expanding the model space and illustrates how this can embellish inferences in a real study.

stat.ME↗

arXiv2022

Score Equivalence for Staged Trees

Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the equivalence class of a given staged tree. Here, two staged trees are said to be statistically equivalent when they represent the same set of distributions. Probabilistic graphical models such as staged trees are increasingly being used for causal analyses. Staged trees which are within the same equivalence class can encode very different causal hypotheses but data alone cannot help us distinguish between these. Therefore, in using score-based methods to learn the model structure and distributions from data for causal analyses, we should expect that a suitable scoring function is one which assigns the same score to statistically equivalent models. No scoring function has yet been proven to have this desirable property for staged trees. In this paper, we present a novel Bayesian Dirichlet scoring function based on path uniformity and mass conversation, and prove that this new scoring function is score-equivalent for staged trees.

stat.ME↗

arXiv2022

Bayesian Model Averaging of Chain Event Graphs for Robust Explanatory Modelling

Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model selection literature on CEGs has largely focused on obtaining the maximum a posteriori (MAP) CEG. However, MAP selection is well-known to ignore model uncertainty. Here, we explore the use of Bayesian model averaging over this class. We demonstrate how this approach can quantify model uncertainty and leads to more robust inference by identifying shared features across multiple high-scoring models. Because the space of possible CEGs is huge, scoring models exhaustively for model averaging in all but small problems is prohibitive. However, we provide a simple modification of an existing model selection algorithm, that samples the model space, to illustrate the efficacy of Bayesian model averaging compared to more standard MAP modelling.

stat.ME↗

arXiv2021

A Bayesian Analysis of Migration Pathways using Chain Event Graphs of Agent Based Models

Agent-Based Models (ABMs) are often used to model migration and are increasingly used to simulate individual migrant decision-making and unfolding events through a sequence of heuristic if-then rules. However, ABMs lack the methods to embed more principled strategies of performing inference to estimate and validate the models, both of which are of significant importance for real-world case studies. Chain Event Graphs (CEGs) can fill this need: they can be used to provide a Bayesian framework which represents an ABM accurately. Through the use of the CEG, we illustrate how to transform an elicited ABM into a Bayesian framework and outline the benefits of this approach.

stat.AP↗

arXiv2021

Building A Bayesian Decision Support System for Evaluating COVID-19 Countermeasure Strategies

Decision making in the face of a disaster requires the consideration of several complex factors. In such cases, Bayesian multi-criteria decision analysis provides a framework for decision making. In this paper, we present how to construct a multi-attribute decision support system for choosing between countermeasure strategies, such as lockdowns, designed to mitigate the effects of COVID-19. Such an analysis can evaluate both the short term and long term efficacy of various candidate countermeasures. The expected utility scores of a countermeasure strategy capture the expected impact of the policies on health outcomes and other measures of population well-being. The broad methodologies we use here have been established for some time. However, this application has many novel elements to it: the pervasive uncertainty of the science; the necessary dynamic shifts between regimes within each candidate suite of countermeasures; and the fast moving stochastic development of the underlying threat all present new challenges to this domain. Our methodology is illustrated by demonstrating in a simplified example how the efficacy of various strategies can be formally compared through balancing impacts of countermeasures, not only on the short term (e.g. COVID-19 deaths) but the medium to long term effects on the population (e.g increased poverty).

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