37,651 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
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
Determination of ferroelectric compositional phase transition using novel virtual crystal approach
We employ a new method for studying compositionally disordered ferroelectric
oxides. This method is based on the virtual crystal approximation (VCA), in
which two or more component potentials are averaged into a composite atomic
potential. In our method, we construct a virtual atom with the correctly
averaged atomic size and atomic eigenvalues. We have used our new method to
study the composition dependent phase transition in Pb(Zr_{1-x}Ti_x)O_3 lying
between x=0.5 and x=0.4. We correctly predict the experimentally determined
phase transition from the tetragonal phase to a low-temperature rhombohedral
phase between these two compositions.Comment: 7 pages, 2 figures, Proceedings for Fundamental Physics of
Ferroelectrics, Aspen, CO February 13-20, 200
Characters of the W3 algebra
Traces of powers of the zero mode in the W3 Algebra have recently been found
to be of interest, for example in relation to Black Hole thermodynamics, and
arise as the terms in an expansion of the full characters of the algebra. We
calculate the first few such powers in two cases. Firstly, we find the traces
in the 3-state Potts model by using null vectors to derive modular differential
equations for the traces. Secondly, we calculate the exact results for Verma
module representations. We compare our two methods with each other and the
result of brute-force diagonalisation for low levels and find complete
agreement.Comment: v2: Numerous small changes, version to appear in JHEP, 22 pages. v3:
Typos corrected, matches published version, 22 page
Substrate Induced Denitrification over or under Estimates Shifts in Soil N2/N2O Ratios
Funding: Funding was provided by the Biotechnology and Biological Sciences Research Council, BBSRC UK (http://www.bbsrc.ac.uk). Grant number BB/H013431/1. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD
Accurate construction of transition metal pseudopotentials
We generate a series of pseudopotentials to examine the relationship between
pseudoatomic properties and solid-state results. We find that lattice constants
and bulk moduli are quite sensitive to eigenvalue, total-energy difference and
tail norm errors, and clear correlations emerge. These trends motivate our
identification of two criteria for accurate transition metal pseudopotentials.
We find that both the preservation of all-electron derivative of tail norm with
respect to occupation and the preservation of all-electron derivative of
eigenvalue with respect to occupation {[Phys. Rev. B {\bf 48}, 5031 (1993)]}
are necessary to give accurate bulk metal lattice constants and bulk moduli. We
also show how the fairly wide range of lattice constant and bulk modulus
results found in the literature can be easily explained by pseudopotential
effects.Comment: submitted to Phys. Rev
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