12,699 research outputs found
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that
is capable of sampling from the posterior distribution of non-linear state
space models for both the unobserved latent states and the unknown model
parameters. We apply this novel methodology to five population growth models,
including models with strong and weak Allee effects, and test if it can
efficiently sample from the complex likelihood surface that is often associated
with these models. Utilising real and also synthetically generated data sets we
examine the extent to which observation noise and process error may frustrate
efforts to choose between these models. Our novel algorithm involves an
Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm
(AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional
spaces efficiently, and is therefore superior to standard Gibbs or Metropolis
Hastings algorithms that are known to converge very slowly when applied to the
non-linear state space ecological models considered in this paper.
Additionally, we show how the AdPMCMC algorithm can be used to recursively
estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive
expressions for these Cram\'er-Rao Bounds and estimate them for the models
considered. Our results demonstrate a number of important features of common
population growth models, most notably their multi-modal posterior surfaces and
dependence between the static and dynamic parameters. We conclude by sampling
from the posterior distribution of each of the models, and use Bayes factors to
highlight how observation noise significantly diminishes our ability to select
among some of the models, particularly those that are designed to reproduce an
Allee effect
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
INLA or MCMC? A Tutorial and Comparative Evaluation for Spatial Prediction in log-Gaussian Cox Processes
We investigate two options for performing Bayesian inference on spatial
log-Gaussian Cox processes assuming a spatially continuous latent field: Markov
chain Monte Carlo (MCMC) and the integrated nested Laplace approximation
(INLA). We first describe the device of approximating a spatially continuous
Gaussian field by a Gaussian Markov random field on a discrete lattice, and
present a simulation study showing that, with careful choice of parameter
values, small neighbourhood sizes can give excellent approximations. We then
introduce the spatial log-Gaussian Cox process and describe MCMC and INLA
methods for spatial prediction within this model class. We report the results
of a simulation study in which we compare MALA and the technique of
approximating the continuous latent field by a discrete one, followed by
approximate Bayesian inference via INLA over a selection of 18 simulated
scenarios. The results question the notion that the latter technique is both
significantly faster and more robust than MCMC in this setting; 100,000
iterations of the MALA algorithm running in 20 minutes on a desktop PC
delivered greater predictive accuracy than the default \verb=INLA= strategy,
which ran in 4 minutes and gave comparative performance to the full Laplace
approximation which ran in 39 minutes.Comment: This replaces the previous version of the report. The new version
includes results from an additional simulation study, and corrects an error
in the implementation of the INLA-based method
Causal inference for social network data
We describe semiparametric estimation and inference for causal effects using
observational data from a single social network. Our asymptotic result is the
first to allow for dependence of each observation on a growing number of other
units as sample size increases. While previous methods have generally
implicitly focused on one of two possible sources of dependence among social
network observations, we allow for both dependence due to transmission of
information across network ties, and for dependence due to latent similarities
among nodes sharing ties. We describe estimation and inference for new causal
effects that are specifically of interest in social network settings, such as
interventions on network ties and network structure. Using our methods to
reanalyze the Framingham Heart Study data used in one of the most influential
and controversial causal analyses of social network data, we find that after
accounting for network structure there is no evidence for the causal effects
claimed in the original paper
Optimal experimental design for mathematical models of haematopoiesis.
The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters
Hierarchical Gaussian process mixtures for regression
As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported
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