Modeling and Estimation for Self-Exciting Spatio-Temporal Models of Terrorist Activity

Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscript we will use existing theories on how violence spreads to create models that allow for both spatio-temporal diffusion in the process model as well as temporal diffusion, or self-excitation, in the data model. We will further demonstrate how Laplace approximations similar to their use in Integrated Nested Laplace Approximation can be used to quickly and accurately conduct inference of self-exciting spatio-temporal models allowing practitioners a new way of fitting and comparing multiple process models. We will illustrate this approach by fitting a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate how choice of process model leads to differing conclusions on the existence of self-excitation in the data and differing conclusions on how violence is spreading spatio-temporally

An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data

Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likelihood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial-temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fitting these models. We will demonstrate how to do this in a Bayesian setting for Self-Exciting Spatio-Temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how a more computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data

An Empirical Analysis of Agricultural Preservation Statutes in New York, Nebraska, and Minnesota

States passed agricultural preservation statutes in part to protect their agricultural heritage. Some scholars worry that right-to-farm statutes have not succeeded in achieving this goal. The agricultural preservation statutes of New York, Nebraska, and Minnesota show three different strategies toward agricultural preservation, all of which take different stances on the protections extended to small and large farms. Despite the structural differences among the states’ statutory approach to agricultural preservation, all three experienced similar agricultural demographic shifts since the 1980s—the number of large and small farms has increased while the number of medium-sized farms has decreased. The similarity in demographic trends suggests that none of the statutes are effective. Legislatures may be able to redirect their agricultural preservation statutes by empowering agricultural advisory boards to consider not only the soundness of farming practices but also the cultural and environmental value of individual farms

Biophysical, biochemical and structural characterization of Poly(ADP-ribose) Polymerase-1 (PARP-1) and its complexes with DNA-damage models and chromatin substrates, The

2013 Spring.Includes bibliographical references.Eukaryotic DNA is highly dynamic and must be compacted and organized with the help of cellular machines, proteins, into 'heterochromatin' state. At its basic level, chromatin is comprised of spool-like structures of protein complexes termed histones, which bind and organize DNA into larger fibrous structures. Cellular processes like transcription and DNA-damage repair require that chromatin be at least partially stripped of its protein components, which in turn allows for complete accessibility by DNA-repair or transcription machinery. A number of protein factors contribute to chromatin structure regulation. Poly(ADP-ribose) Polymerase-1 (PARP-1) is one of these proteins that exists in all eukaryotic organisms except for yeast. In its inactive form, it compacts chromatin, but performs its chromatin-opening function by covalently modifying itself and other nuclear proteins with long polymers of ADP-ribose in response to DNA damage. Thus, it also serves as a first responder to many types of DNA damage. The highly anionic polymers serve to disrupt protein-DNA interactions and thus allow for the creation of a temporary euchromatin structure. Contained herein are investigations aimed at addressing key questions regarding key differences between the interactions of PARP-1 and chromatin and its DNA-damage substrates. Our experiments show that human PARP-1 interacts with and is enzymatically activated to a similar level by a variety of different DNA substrates. In terms of chromatin, it appears that PARP-1 fails to interact with nucleosomes that do not have linker DNA. PARP-1 most effectively interacts with chromatin by simultaneously binding two DNA strands through contacts made by its two N-terminal Zn-finger domains. Small-Angle X-ray (SAXS) and Neutron Scattering (SANS) and molecular dynamics (MD) experiments were combined with biophysical and biochemical studies to better describe the structural effects of DNA binding on PARP-1. The average solution structure of PARP-1 indicates that the enzyme is a monomeric, non-spherical, elongated molecule with a radius of gyration (Rg) of ~55Å. The DNA-bound form of PARP-1 is also monomeric and binding DNA causes the molecule to become more elongated with an average Rg of ~80Å

Self-exciting spatio-temporal statistical models for count data with applications to modeling the spread of violence

In this dissertation we provide statistical models and inferential techniques for analyzing the number of violent or criminal events as they evolve over space and time. Our research focuses on a class of models we refer to as self-exciting spatio-temporal models. These are a class of parametric models that allow for dependence in a latent structure as well as dependence in the data model combining what is sometimes referred to as observation driven and parameter driven models. This class of models arise from straight-forward assumptions on how violence or crime evolves over space and time and has use in the statistical modeling of situations where there is an expected repeat or near-repeat victimization. In Chapter 2 we present the spatially correlated self-exciting model and the reaction-diffusion self-exciting model to analyze the number of violent events in different regions in Iraq. We also demonstrate how Laplace approximations can be used to conduct efficient Bayesian inference. We further show how the choice of the latent structure matters in this problem. In Chapter 3 we generalize the spatially correlated self-exciting model and show how it extends the classic integer generalized auto-regressive conditionally heteroskedastic, or INGARCH, model to account for spatial correlation and improves the second order properties of the INGARCH model. We refer to this new class of models as the spatially correlated INGARCH, or SPINGARCH, model. We show how the spatially correlated self-exciting model is similar to the SPINGARCH(0,1) model. Finally in Chapter 4 we present a fast extended Laplace approximation algorithm for fitting the SPINGARCH(0,1) model demonstrating empirically how the extended Laplace approximation method reduces a bias that exists in the Laplace approximation method while performing much quicker than Markov Chain Monte Carlo approaches