Abstract

Interaction Models of Probabilistic Networks Suggested by Statistical Mechanics

John E. Gray, (Naval Surface Warfare Center ), ` john.e.gray@navy.mil`

**Abstract**

Statistical Mechanics has proven to be useful model for drawing inferences about the collective behavior of individual objects that interact according to a known force law (which for more general usage is referred to as interacting units.). Collective behavior is determined not by computing F=ma for each interacting unit because the problem is mathematically intractable. Instead, one computes the partition function for the collection of interacting units and predicts statistical behavior from the partition function. Statistical mechanics was unified with Bayesian inference by Jaynes who demonstrated that the partition function assignment of probabilities via the interaction Hamiltonian is the solution to a Bayesian assignment of probabilities based on the maximum entropy method with known means and standard deviations. Once this technique has been applied to a variety of problems and obtained a solution, one can, of course, solve the inverse problem of to determine the solution to an inverse problem to determine what interaction model gives rise to a given probability assignment. Probabilistic networks are important modeling tools in a variety of applications including social networks. I explore the usage of statistical mechanics as a mechanism to solve the inverse problem for a probabilistic network to determine what the underlying interaction model that gives rise to probabilistic network. Then I explore how one can draw general inferences about the network by defining, energy, heat capacity, temperature and other thermodynamic characteristics of the network.

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