Approaches for Behavior Intensity Estimation in Groups of Heterogeneous Individuals: Precision and Applicability for Data with Uncertainty

In socially oriented areas, there arises the problem of assessing the cumulative characteristics of behavior, such as intensity, that are realized in groups of individuals. All individuals vary in their behavior and the available data is limited and may be associated with significant uncertainty: only a few episodes may be known and only a few individualsi the group may be observed. Mathematical models of behavior are used for estimation of key characteristics of the behavior. One of them is based on the gamma–Poisson point process, that reflects the heterogeneity of individuals in a form of a mixing distribution. This general model allows to formulate several methods of frequency estimation: the Cox regression, estimation of the copula parameter, and a posteriori inference in Bayesian belief networks. The aim of the paper is to assess their determine the precision of these methods based on the Kantorovich–Rubinstein distance between estimates and the true distribution of the desired parameter. The analysis of assumptions of those methods allows to formulate rules, that allow to chose the appropriate method in various sutuations of data availability. It has been shown that the copula-based approach provides the most accurate estimates and has the mild assumptions for the number of observed objects, but it cannot take into account external factors that may influence the behavior. Among methods that can take into account process covariants, estimates based on a posteriori inference in hybrid Bayesian belief networks have the highest precision. The paper considers a method for quantification of a hybrid BBNs with the approximation of mixtures of truncated exponents, that is data-demanding at the stage of calculating a priori estimates. However, it is noted that there are other approaches to setting hybrid BSDs in which a priori estimates can be set completely expertly.