906 research outputs found
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
Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation
Integrated Nested Laplace Approximation provides a fast and effective method
for marginal inference on Bayesian hierarchical models. This methodology has
been implemented in the R-INLA package which permits INLA to be used from
within R statistical software. Although INLA is implemented as a general
methodology, its use in practice is limited to the models implemented in the
R-INLA package.
Spatial autoregressive models are widely used in spatial econometrics but
have until now been missing from the R-INLA package. In this paper, we describe
the implementation and application of a new class of latent models in INLA made
available through R-INLA. This new latent class implements a standard spatial
lag model, which is widely used and that can be used to build more complex
models in spatial econometrics.
The implementation of this latent model in R-INLA also means that all the
other features of INLA can be used for model fitting, model selection and
inference in spatial econometrics, as will be shown in this paper. Finally, we
will illustrate the use of this new latent model and its applications with two
datasets based on Gaussian and binary outcomes
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