Introduction

Bayesian network modelling is a data analysis technique which is ideally suited to messy, highly correlated and complex datasets. This methodology is rather distinct from other forms of statistical modelling in that its focus is on structure discovery – determining an optimal graphical model which describes the inter-relationships in the underlying processes which generated the data. It is a multivariate technique and can used for one or many dependent variables. This is a data driven approach, as opposed to, rely only on subjective expert opinion to determine how variables of interest are inter-related (for example: structural equation modelling). An example can be found in the American Journal of Epidemiology where this approach was used to investigate risk factors for child diarrhoea. A special issue of Preventive Veterinary Medicine on graphical modelling features a number of articles which use abn to fit epidemiological data. An introduction to this methodology can be found in Emerging Themes in Epidemiology.

This website provides some cookbook type examples of how to perform Bayesian network structure discovery analyses with observational data. The particular type of Bayesian network models considered here are additive Bayesian networks. These are rather different, mathematically speaking, from the standard form of Bayesian network models (for binary or categorical data) presented in the academic literature, which typically use an analytically elegant, but arguably interpretation-wise opaque, contingency table parametrization. An additive Bayesian network model is simply a multidimensional regression model, e.g. directly analogous to generalised linear modelling but with all variables potentially dependent. All examples presented use an extension library for R called abn.

Contact abn package maintainer by email: gilles.kratzer at math.uzh.ch

Contributors: Gilles Kratzer, Marta Pittavino, Fraser Lewis and Reinhard Furrer

Installation

abn R package can easily be installed from CRAN using:

install.packages("abn", dependencies = TRUE)

However further libraries could be necessary to best profit from the abn features.

Quickstart

Simple examples provide illustrations of how to perform data analyses using additive Bayesian networks with abn ( installation procedure). The data sets used are provided with abn. Many more examples are given at the end of the relevant manual pages in R, e.g. see ?fitabn, ?buildscorecache, ?mostprobable, ?search.hillclimber. More realistic examples are given in case studies.

Case studies

More case studies will be presented as additional features will be added in abn. The general approach for structure discovery is broadly similar and relatively independent of the specific problem data. While Bayesian network modelling is computationally intensive, comparing across potentially large numbers of different models, it should not be treated as a black box approach as each individual data set has its own quirks and difficulties.

Case study Zero presents ten case study analyses which are used to validate the robustness and accuracy of the implementation of the numerical methods used in abn.
Case Study One gives a fairly typical and complete example for a data problem in which there are sufficiently few variables (around 20 or less) then an exact search is feasible, along with parametric bootstrapping to address overfitting. This uses real (anonymised), as opposed to artificially generated data and as such has some quirks. For example, due to small sample sizes some of the distributions cannot be reliably estimated and it may be sensible to drop one or more variables from the analyses. This example also includes a correction for grouped (correlated data) as a final step, for non-grouped data this step can be ignored.

Literature

General note

Typical BN models involving binary nodes, arguably the most commonly used type of BN, use a contingency table rather than additive parameter formulation. This facilities mathematical elegance and means that key metrics like model goodness of fit and marginal posterior parameters can be estimated analytically (e.g. from a formula) rather than numerically (an approximation). The downside being that this parametrisation is likely far from parsimonious, and the interpretation of the model parameters is less clear than the usual GLM type models (which are common across all areas of science). This is, while practically important, a fairly low level technical distinction as the key aspect of BN modelling is that this is a form of graphical modelling – that is a model of the joint probability distribution of the data. It is this joint – multidimensional – aspect which makes this methodology so attractive for analyses of complex data and what discriminates it from the more standard regression techniques, e.g. glm’s, glmm’s etc, which are only one dimensional in that the covariates are all assumed independent. The latter is entirely reasonable in a classical experimental design scenario, but completely unrealistic for many observational studies in medicine, veterinary science, ecology and biology.

Technical articles

Kratzer et al. (2020) Bayesian Networks modeling applied to Feline Calicivirus infection among cats in Switzerland
Kratzer et al. (2018): Comparison between Suitable Priors for Additive Bayesian Networks
Koivisto et al. (2004): Exact Bayesian structure discovery in Bayesian networks
Friedman et al. (2003): Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks
Friedman et al. (1999): Data analysis with Bayesian networks: A bootstrap approach
Heckerman et al. (1995): Learning Bayesian Networks – The Combination of Knowledge And Statistical-Data

Application articles

Guinat et al. (2020) Biosecurity risk factors for highly pathogenic avian influenza (H5N8) virus infection in duck farms, France
Hartnack et al. (2019) Additive Bayesian networks for antimicrobial resistance and potential risk factors in non-typhoidal Salmonella isolates from layer hens in Uganda
Ruchti et al. (2019): Progression and risk factors of pododermatitis in part-time group housed rabbit does in Switzerland
Comin et al. (2019) Revealing the structure of the associations between housing system, facilities, management and welfare of commercial laying hens using Additive Bayesian Networks
Ruchti et al. (2018): Pododermatitis in group housed rabbit does in Switzerland – prevalence, severity and risk factors
Pittavino et al. (2017): Comparison between generalized linear modelling and additive Bayesian network; identification of factors associated with the incidence of antibodies against Leptospira interrogans sv Pomona in meat workers in New Zealand
Hartnack et al. (2017): Attitudes of Austrian veterinarians towards euthanasia in small animal practice: impacts of age and gender on views on euthanasia
Lewis et al. (2012): Revealing the Complexity of Health Determinants in Resource-poor Settings
Lewis et al. (2011): Structure discovery in Bayesian networks: An analytical tool for analysing complex animal health data

Further ressources

Workshops

Causality:

4 December 2018, Beate Sick & Gilles Kratzer of the 1st Causality workshop talk, Bayesian Networks meet Observational data. (UZH, Switzerland)

ABN modeling:

07 July 2021, workshop at the UseR! Conference on Additive Bayesian Networks Modeling. (Online)
29 March 2019, workshop at the SVEPM conference on Multivariate analysis using Additive Bayesian Networks. (Utrecht, Netherland)

Presentations

4 October 2018, talk in Nutricia (Danone). Multivariable analysis: variable and model selection in system epidemiology. (Utrecht, Netherland)
30 May 2018. Brown Bag Seminar in ZHAW. Presentation: Bayesian Networks Learning in a Nutshell. (Winterthur, Switzerland)