Encoding Dependence in Bayesian Causal Networks

Abstract

Bayesian (belief, learning, or causal) networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable "states" with a testable causal interaction model. Typically, they assume random variables are discrete in time and space, with a static network structure that may evolve over time, according to a prescribed set of changes over a successive set of discrete model time-slices (i.e., snap-shots). But the observations that are analyzed are not necessarily independent and are autocorrelated due to their locational positions in space and time. Such BN models are not truly spatial-temporal, as they do not allow for autocorrelation in the prediction of the dynamics of a sequence of data. We begin by discussing Bayesian causal networks and explore how such data dependencies could be embedded into BN models from the perspective of fundamental assumptions governing space-time dynamics. We show how the joint probability distribution for BNs can be decomposed into partition functions with spatial dependence encoded, analogous to Markov Random Fields (MRFs). In this way, the strength and direction of spatial dependence both locally and non-locally could be validated against cross-scale monitoring data, while enabling BNs to better unravel the complex dependencies between large numbers of covariates, increasing their usefulness in environmental risk prediction and decision analysis.Keywords: Bayesian, causal, clique, dependence, GIS, network ENVIRONMENTAL INFORMATICSA wide array of statistical modeling approaches are available for exploring real-world complex spatio-temporal phenomena including multivariate regression, multivariate analysis of variance (MANOVA), principal components analysis (PCA), canonical correlation analysis (CCA), factor analysis, spectral analysis, vector autoregressive models (VARs), and machine-learning tree and expert rule-based techniques-to name just a few (Izenman, 2013). Deciding which technique to employ relies heavily on the main purpose of a model in a given application context (e.g., estimation, prediction, and problem dimensional-reduction), the availability and quality of data and auxiliary information, and the level of accuracy required to aid in decision-making. Given the large uncertainties facing environmental decision making, and the need for more robust prediction methods, Bayesian-hierarchical, causal-learning, and copula-based network techniques are increasingly being employed to better resolve interactions and trade-offs in observed, latent, and decision-making variables. These models also provide a tractable way to integrate both tradition and more modern forms of data-from station monitoring networks, sensor-networks, and remote-sensing/satellite imagery, and can prove computationally challenging to solve numerically and to validate in the case of high-dimensional model systems.

A Review of Recent Machine Learning Advances for Forecasting Harmful Algal Blooms and Shellfish Contamination

“…Alongside the remarkable development of machine learning algorithms to model time-series data, there is a growing need to understand the causal temporal relationships in complex systems. Temporal probabilistic graphical models have been proposed to infer the direction of temporal relationships, which show particularly promising for environmental risk prediction and decision analysis [66]. Pioneering work in causal discovery is rooted in Bayesian Network (BN) theory [67].…”

“…BNs encode probabilistic relations within a set of variables, {X 1 , ..., X n }, to simplify the representation of their joint distribution [66]. A BN is represented by a directed acyclic graph (DAG), where the variables are represented by nodes, with edges between the variables corresponding to a causal relationship represented by directed arrows.…”

Comparing Random Forest to Bayesian Networks as nitrogen management decision support systems

“…Therefore, a BN with structure based on expert opinion and stakeholder input can integrate theoretical assumptions about complex dependencies. Environmental data often carries complex dependencies across time and space (Sulik et al., 2017) and BN can introduce simplifying assumptions in order to facilitate forecasts of environmental outcomes such as crop disease risk to weather (Lu et al., 2020), wheat yield response to fungicide (Tari, 1996), and many other applications in natural resource management (McCann et al., 2006).…”