|SULIK, JOHN - Former ARS Employee|
|NEWLANDS, NATHANIEL - Agriculture And Agri-Food Canada|
Submitted to: Frontiers in Environmental Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/22/2016
Publication Date: 1/9/2017
Publication URL: http://handle.nal.usda.gov/10113/5931570
Citation: Sulik, J.J., Newlands, N.K., Long, D.S. 2017. Encoding dependence in Bayesian causal networks. Frontiers in Environmental Science. 4:84. doi: 10.3389/fenvs.2016.00084.
Interpretive Summary: Bayesian networks (BNs) are mathematical models that organize a body of knowledge about a system by mapping out cause and effect relationships between key variables and describing the extent to which one variable is likely to affect another. The system might be a wheat field, weed community, stock market, etc. All states of the system are possible i.e., the crop can be normal or drought stressed, it's yield potential high or low, and so on. Some states will occur more frequently when other states are present. For example, if it is a dry year, the chances of low yield are higher. Typically, the variables represented in a BN are assumed to be randomly distributed in time and space. Yet the patterns are not random i.e., nearby locations experience similar intensities of yield over a farm field. This study explores the possibility of encoding such spatial dependence into BN models as needed to increase their usefulness in environmenal risk prediction and decision analysis.
Technical Abstract: Bayesian 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 time-slices. 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 spatio-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 of BNs can be decomposed into partition functions with spatial dependence encoded analogous to Markov Random Fields. In this way, the strength and direction of spatial dependence both locally and non-locally could be better validated against cross-scale monitoring data, while enabling BNs to better unravel the complex dependencies between large numbers of covariate, increasing their usefullness in environmental risk prediction and decision analysis.