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Title: State-space based mass event-history model I: many decision-making agents with one target

item Shapiro Ilan, David
item Campbell, James - Jim

Submitted to: Annals of Applied Statistics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/3/2008
Publication Date: 12/1/2008
Citation: Fushing, H., Shapiro Ilan, D.I., Campbell, J.F., Lewis, E. 2008. State-space based mass event-history model I: many decision-making agents with one target. Annals of Applied Statistics. 2:1503-1522.

Interpretive Summary: Entomopathogenic (insect-killing) nematodes are environmentally friendly natural bio-insecticides that can control a number of important insect pests. In order to develop methods to improve insect suppression using these nematodes, it is important to understand the nematode’s basic biology. One area of basic biology that is in need of further study is nematode infection decisions, i.e., understanding why a nematode infects. We have observed that the nematodes tend to a “follow the leader” or “herding” behavior when it comes to infecting. That is, a nematode seems more likely to enter an insect that has been recently infected compared to a non-infected insect. The objective of this manuscript was to develop a mathematical model of this herding behavior. Thus, such a model was developed and when tested appears to describe nematode infection behavior quite well. The model can now be tested further and used to predict infection behavior of the nematodes in the field. With a better understanding and ability to predict infections we can develop superior pest management tactics using the nematodes.

Technical Abstract: A dynamic decision-making system that includes a mass of indistinguishable agents could manifest impressive heterogeneity. This kind of non-homogeneity is postulated to result from macroscopic behavioral tactics employed by almost all involved agents. A state-space based (SSB) mass event-history model is developed here to explore the potential existence of such macroscopic behaviors. By imposing an unobserved internal state-space variable into the system, each individual’s event-history is made into a composition of a common state duration and an individual specific time to action. With the common state modeling of the macroscopic behavior, parametric statistical inferences are derived under the interval censorship and conditional independence assumptions. Identifiability and computation related problems are also addressed. From the dynamic perspectives of system-wise heterogeneity, this SSB mass event history model is shown to be very distinct from a random effect model via the Principle Component Analysis (PCA) in a numerical experiment. Real data showing the mass invasion by two species of parasitic nematode into two species of host larvae is also analyzed. The analysis results are not only are found to be coherent in the context of the biology of the nematode as a parasite, but also include new quantitative interpretations.