arXiv subjects

Jim Q. Smith

Publications and source records attributed to Jim Q. Smith.

At least 19 recordsLinked to original sources

arXiv2025

Structural Refinement of Bayesian Networks for Efficient Model Parameterisation

Many Bayesian network modelling applications suffer from the issue of data scarcity. Hence the use of expert judgement often becomes necessary to determine the parameters of the conditional probability tables (CPTs) throughout the network. There are usually a prohibitively large number of these parameters to determine, even when complementing any available data with expert judgements. To address this challenge, a number of CPT approximation methods have been developed that reduce the quantity and complexity of parameters needing to be determined to fully parameterise a Bayesian network. This paper provides a review of a variety of structural refinement methods that can be used in practice to efficiently approximate a CPT within a Bayesian network. We not only introduce and discuss the intrinsic properties and requirements of each method, but we evaluate each method through a worked example on a Bayesian network model of cardiovascular risk assessment. We conclude with practical guidance to help Bayesian network practitioners choose an alternative approach when direct parameterisation of a CPT is infeasible.

stat.ME↗

arXiv2025

Surjective Independence of Causal Influences for Local Bayesian Network Structures

The very expressiveness of Bayesian networks can introduce fresh challenges due to the large number of relationships they often model. In many domains, it is thus often essential to supplement any available data with elicited expert judgements. This in turn leads to two key challenges: the cognitive burden of these judgements is often very high, and there are a very large number of judgements required to obtain a full probability model. We can mitigate both issues by introducing assumptions such as independence of causal influences (ICI) on the local structures throughout the network, restricting the parameter space of the model. However, the assumption of ICI is often unjustified and overly strong. In this paper, we introduce the surjective independence of causal influences (SICI) model which relaxes the ICI assumption and provides a more viable, practical alternative local structure model that facilitates efficient Bayesian network parameterisation.

stat.ME↗

arXiv2024

Dynamic Bayesian Networks, Elicitation and Data Embedding for Secure Environments

Serious crime modelling typically needs to be undertaken securely behind a firewall where police knowledge and capabilities can remain undisclosed. Data informing an ongoing incident is often sparse, with a large proportion of relevant data only coming to light after the incident culminates or after police intervene - by which point it is too late to make use of the data to aid real-time decision making for the incident in question. Much of the data that is available to police to support real-time decision making is highly confidential so cannot be shared with academics, and is therefore missing to them. In this paper, we describe the development of a formal protocol where a graphical model is used as a framework for securely translating a model designed by an academic team to a model for use by a police team. We then show, for the first time, how libraries of these models can be built and used for real-time decision support to circumvent the challenges of data missingness and tardiness seen in such a secure environment. The parallel development described by this protocol ensures that any sensitive information collected by police, and missing to academics, remains secured behind a firewall. The protocol nevertheless guides police so that they are able to combine the typically incomplete data streams that are open source with their more sensitive information in a formal and justifiable way. We illustrate the application of this protocol by describing how a new entry - a suspected vehicle attack - can be embedded into such a police library of criminal plots.

stat.AP↗

arXiv2024

The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks

Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied modelling, it is critical to assess how robust the inferences on certain target variables are to changes in the model. In Bayesian networks, these analyses fall under the umbrella of sensitivity analysis, which is most commonly carried out by quantifying dissimilarities using Kullback-Leibler information measures. In this paper, we argue that robustness methods based instead on the familiar total variation distance provide simple and more valuable bounds on robustness to misspecification, which are both formally justifiable and transparent. We introduce a novel measure of dependence in conditional probability tables called the diameter to derive such bounds. This measure quantifies the strength of dependence between a variable and its parents. We demonstrate how such formal robustness considerations can be embedded in building a Bayesian network.

stat.ME↗

arXiv2024

Propagating moments in probabilistic graphical models with polynomial regression forms for decision support systems

Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide conditional and marginal distributions in closed form simplifying the inferential task. The Gaussianity and linearity assumptions are often adequate, yet can lead to poor performance when dealing with some practical applications. In this paper, we model each variable in graph G as a polynomial regression of its parents to capture complex relationships between individual variables and with a utility function of polynomial form. We develop a message-passing algorithm to propagate information throughout the network solely using moments which enables the expected utility scores to be calculated exactly. Our propagation method scales up well and enables to perform inference in terms of a finite number of expectations. We illustrate how the proposed methodology works with examples and in an application to decision problems in energy planning and for real-time clinical decision support.

stat.ME↗

arXiv2024

On the Stability of General Bayesian Inference

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from the decision-maker but a level of interpolation is required to arrive at a likelihood model. As a result, an often computationally convenient canonical form is used in place of the decision-maker's true beliefs. Equally, in practice, observational datasets often contain unforeseen heterogeneities and recording errors and therefore do not necessarily correspond to how the process was idealised by the decision-maker. Acknowledging such imprecisions, a faithful Bayesian analysis should ideally be stable across reasonable equivalence classes of such inputs. We are able to guarantee that traditional Bayesian updating provides stability across only a very strict class of likelihood models and data generating processes, requiring the decision-maker to elicit their beliefs and understand how the data was generated with an unreasonable degree of accuracy. On the other hand, a generalised Bayesian alternative using the $β$-divergence loss function is shown to be stable across practical and interpretable neighbourhoods, providing assurances that posterior inferences are not overly dependent on accidentally introduced spurious specifications or data collection errors. We illustrate this in linear regression, binary classification, and mixture modelling examples, showing that stable updating does not compromise the ability to learn about the data generating process. These stability results provide a compelling justification for using generalised Bayes to facilitate inference under simplified canonical models.

stat.ME↗

arXiv2024

Causal chain event graphs for remedial maintenance

The analysis of system reliability has often benefited from graphical tools such as fault trees and Bayesian networks. In this article, instead of conventional graphical tools, we apply a probabilistic graphical model called the chain event graph (CEG) to represent the failures and processes of deterioration of a system. The CEG is derived from an event tree and can flexibly represent the unfolding of asymmetric processes. For this application we need to define a new class of formal intervention we call remedial to model causal effects of remedial maintenance. This fixes the root causes of a failure and returns the status of the system to as good as new. We demonstrate that the semantics of the CEG are rich enough to express this novel type of intervention. Furthermore through the bespoke causal algebras the CEG provides a transparent framework with which guide and express the rationale behind predictive inferences about the effects of various different types of remedial intervention. A back-door theorem is adapted to apply to these interventions to help discover when a system is only partially observed.

stat.ME↗

arXiv2024

A comparison of graphical methods in the case of the murder of Meredith Kercher

We compare three graphical methods for displaying evidence in a legal case: Wigmore Charts, Bayesian Networks and Chain Event Graphs. We find that these methods are aimed at three distinct audiences, respectively lawyers, forensic scientists and the police. The methods are illustrated using part of the evidence in the case of the murder of Meredith Kercher. More specifically, we focus on representing the list of propositions, evidence, testimony and facts given in the first trial against Raffaele Sollecito and Amanda Knox with these graphical methodologies.

stat.AP↗

arXiv2023

Resource Adequacy and Capacity Procurement: Metrics and Decision Support Analysis

Resource adequacy studies typically use standard metrics such as Loss of Load Expectation and Expected Energy Unserved to quantify the risk of supply shortfalls. This paper critiques present approaches to adequacy assessment and capacity procurement in terms of their relevance to decision maker interests, before demonstrating alternatives including risk-averse metrics and visualisations of wider risk profile. This is illustrated with results for a Great Britain example, in which the risk profile varies substantially with the installed capacity of wind generation. This paper goes beyond previous literature through its critical discussion of how current practices reflect decision maker interests; and how decision making can be improved using a broader range of outputs available from standard models.

stat.AP↗

arXiv2023

Using infinite server queues with partial information for occupancy prediction

Motivated by demand prediction for the custodial prison population in England and Wales, this paper describes an approach to the study of service systems using infinite server queues, where the system has non-empty initial state and the elapsed time of individuals initially present is not known. By separating the population into initial content and new arrivals, we can apply several techniques either separately or jointly to those sub-populations, to enable both short-term queue length predictions and longer-term considerations such as managing congestion and analysing the impact of potential interventions. The focus in the paper is the transient behaviour of the $M_t/G/\infty$ queue with a non-homogeneous Poisson arrival process and our analysis considers various possible simplifications, including approximation. We illustrate the approach in that domain using publicly available data in a Bayesian framework to perform model inference.

stat.AP↗

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

Propagating uncertainty in a network of energy models

Computer models are widely used in decision support for energy systems operation, planning and policy. A system of models is often employed, where model inputs themselves arise from other computer models, with each model being developed by different teams of experts. Gaussian Process emulators can be used to approximate the behaviour of complex, computationally intensive models and used to generate predictions together with a measure of uncertainty about the predicted model output. This paper presents a computationally efficient framework for propagating uncertainty within a network of models with high-dimensional outputs used for energy planning. We present a case study from a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. The system model considered for this case study is simple, however the framework can be applied to larger networks of more complex models.

stat.AP↗

arXiv2022

A Bayesian Decision Support System in Energy Systems Planning

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of networks of connected GP emulators. In this paper, we combine these recent methodological advances with classical state-space models to construct a Bayesian decision support system. This approach gives a coherent probability model that produces predictions with the measure of uncertainty in terms of two first moments and enables the propagation of uncertainty from individual decision components. This methodology is used to produce a decision support tool for a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. In particular, we demonstrate how to couple information from an energy model, a heating demand model, and gas and electricity price time-series to quantitatively assess the impact on operational costs of various policy choices and changes in the energy market.

stat.AP↗

arXiv2021

Constructing a Chain Event Graph from a Staged Tree

Chain Event Graphs (CEGs) are a recent family of probabilistic graphical models - a generalisation of Bayesian Networks - providing an explicit representation of structural zeros, structural missing values and context-specific conditional independences within their graph topology. A CEG is constructed from an event tree through a sequence of transformations beginning with the colouring of the vertices of the event tree to identify one-step transition symmetries. This coloured event tree, also known as a staged tree, is the output of the learning algorithms used for this family. Surprisingly, no general algorithm has yet been devised that automatically transforms any staged tree into a CEG representation. In this paper we provide a simple iterative backward algorithm for this transformation. Additionally, we show that no information is lost from transforming a staged tree into a CEG. Finally, we demonstrate that with an optimal stopping criterion, our algorithm is more efficient than the generalisation of a special case presented in Silander and Leong (2013). We also provide Python code using this algorithm to obtain a CEG from any staged tree along with the functionality to add edges with sampling zeros.

stat.ML↗

arXiv2021

A Bayesian decision support system for counteracting activities of terrorist groups

Activities of terrorist groups present a serious threat to the security and well-being of the general public. Counterterrorism authorities aim to identify and frustrate the plans of terrorist groups before they are put into action. Whilst the activities of terrorist groups are likely to be hidden and disguised, the members of such groups need to communicate and coordinate to organise their activities. Such observable behaviour and communications data can be utilised by the authorities to estimate the threat posed by a terrorist group. However, to be credible, any such statistical model needs to fold in the level of threat posed by each member of the group. Unlike in other benign forms of social networks, considering the members of terrorist groups as exchangeable gives an incomplete picture of the combined capacity of the group to do harm. Here we develop a Bayesian integrating decision support system that can bring together information relating to each of the members of a terrorist group as well as the combined activities of the group.

cs.SI↗

arXiv2021

Hierarchical Causal Analysis of Natural Languages on a Chain Event Graph

Various graphical models are widely used in reliability to provide a qualitative description of domain experts hypotheses about how a system might fail. Here we argue that the semantics developed within standard causal Bayesian networks are not rich enough to fully capture the intervention calculus needed for this domain and a more tree-based approach is necessary. We instead construct a Bayesian hierarchical model with a chain event graph at its lowest level so that typical interventions made in reliability models are supported by a bespoke causal calculus. We then demonstrate how we can use this framework to automate the process of causal discovery from maintenance logs, extracting natural language information describing hypothesised causes of failures. Through our customised causal algebra we are then able to make predictive inferences about the effects of a variety of types of remedial interventions. The proposed methodology is illustrated throughout with examples drawn from real maintenance logs.

math.ST↗

arXiv2021

Partial Correlation Graphical LASSO

Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardises the observed data to unit sample variances. We show that such standardisation can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, $L_0$ and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an $L_{1}$ penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference.

stat.ME↗

arXiv2021

Lexical semantic change for Ancient Greek and Latin

Change and its precondition, variation, are inherent in languages. Over time, new words enter the lexicon, others become obsolete, and existing words acquire new senses. Associating a word's correct meaning in its historical context is a central challenge in diachronic research. Historical corpora of classical languages, such as Ancient Greek and Latin, typically come with rich metadata, and existing models are limited by their inability to exploit contextual information beyond the document timestamp. While embedding-based methods feature among the current state of the art systems, they are lacking in the interpretative power. In contrast, Bayesian models provide explicit and interpretable representations of semantic change phenomena. In this chapter we build on GASC, a recent computational approach to semantic change based on a dynamic Bayesian mixture model. In this model, the evolution of word senses over time is based not only on distributional information of lexical nature, but also on text genres. We provide a systematic comparison of dynamic Bayesian mixture models for semantic change with state-of-the-art embedding-based models. On top of providing a full description of meaning change over time, we show that Bayesian mixture models are highly competitive approaches to detect binary semantic change in both Ancient Greek and Latin.

cs.CL↗