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Woods Hole Coastal and Marine Science Center

Woods Hole Coastal and Marine Science Center > Sea-Level Rise Hazards and Decision Support > Bayesian Networks

Bayesian Networks

A principal focus of this project is to bring together historical and modern observations, such as records of long-term sea level changes and rates of shoreline change, and results of numerical simulations into a Bayesian Network to evaluate the probability of sea level rise impacts to the coastal environment (see Shoreline Change and Landloss for an example). The Bayesian approach has been used in the artificial intelligence, medical, and ecological communities to evaluate and translate scientific information and/or expert judgments into probabilistic terms (see review by Berger, 2000). More recently, Bayesian Networks have been used in the earth and environmental sciences, particularly to address ecological questions.

A Bayesian Network provides a framework to evaluate the probability of a specific outcome based on causal relationships between variables identified as important by users. Bayes’ Theorem relates the probability of one event R given the occurrence of another event O (Bayes, 1763; Gelman and others, 2004):

equation for Bayes Theorem

On the left side of this equation, p(Ri|Oj) is the conditional probability of a particular response, Ri, given a set of observations Oj. For example, a particular response might be the joint occurrence of a particular rate of sea level rise and a particular rate of shoreline change. The ith response scenario is just one of a finite number of such scenarios that can be considered. Likewise, the jth observation set represents one of many possible observations sets such as wave height, rate of sea level rise, or other. On the right side of this equation, p(Oi|Rj)  is the likelihood of the observations for a known response. In essence, this term indicates the strength of the correlation between observation and response (for example rate of sea level rise and shoreline change). The correlation is high if the observations are accurate and if the particular response variables are actually sensitive to the observed variables. The second term in the numerator is the prior probability of the response. That is, it is the probability of a particular response integrated over all expected observation scenarios. Lastly, the denominator is a normalization factor to account for the likelihood of the observations.

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