# Econometric Information Recovery in Behavioral Networks
## 1 Introduction  
By tradition, our ability to measure evidence and make predictions relative to economic behavioral systems has been linked to reductionist parametric econometric models and ad hoc sampling model designs. Using traditional estimation and inference methods with fragile static econometric models and dynamic sample data often leads to probability parameter estimation biases, incorrect inferences and obscures the intervention-treatment-causal path effects information that one hopes to measure. This traditional methodological focus has led to fragile economic theories and questionable inferences and has failed in terms of prediction and the extraction of quantitative information relative to the nature of underlying economic behavioral systems.  
To go beyond traditional reductionist modeling and mathematical anomalies, a network paradigm is developing under the name of Network Science (for example, see [1; 2; 3]). This new paradigm recognizes that the network representation of economic processes arise quite naturally from microeconomic theory where markets and weighted and binary linked networks are equivalent and is based on observed adaptive behavior data sets that are by nature indirect, incomplete and noisy. There are several things that make this approach attractive for information recovery in economics and in other social sciences. First of all, in the economic behavioral sciences, everything seems to depend on everything else, and this fits the interconnectedness-simultaneity of the nonlinear dynamic network paradigm. There is also a close link in economic behavioral systems between information recovery and inference in random network models and adaptive intelligent behavior, causal entropy maximization and information theoretic methods.  
A problem of great interest across the sciences in general and network recovery in particular, is how to infer, given noisy limited data, the mathematical form of the corresponding probabilitydistribution function. In this context with information recovery and inference in mind, we propose an adaptive intelligent behavior framework that permits the interpretation of behavioral networks in terms of causal entropy maximization and entropy based inference methods. To address the unknown nature of the probability sampling model in recovering behavior related preference-choice network pathway information from limited noisy observational data, we use the Cressie-Read (CR)-information theoretic entropy family of divergence measures as a distributional basis for linking the data and the unknown and unobservable behavioral network edge-path probabilities. This permits the recovery of estimates of the unknown link parameters and pathway probabilities across the network ensemble that can be computed analytically without sampling the configuration space.  
In the sections ahead, we consider econometrics as an exercise in inference and recognize that the observed samples of network data come from complex dynamic adaptive behavior systems that are non-deterministic in nature, involve information and uncertainty, and are driven toward a certain optimal stationary state. To recover econometric-network behavior related choice-preference information from samples of indirect, incomplete and noisy observational or quasi-controlled samples of behavioral data, we use random network models to demonstrate the nature of the entropy based information theoretic approach to recovering the unknown mathematical form of the underlying probability distribution and pathway probabilities of the behavioral network system. Finally, we note that the emergence of large data sets and recovery methods linked to causal entropy maximization and information theoretic methods appear to offer a promising new paradigm to the quantitative analysis of behavioral structural and network systems. In Appendices, we (i) illustrate the connection between a simple network and corresponding adjacency matrices; and (ii) discuss an information theoretic approach to statistical network models.