109 research outputs found
Spatial Statistics and Computational Methods
Abstracts not available for BookReview
Hidden Gibbs random fields model selection using Block Likelihood Information Criterion
Performing model selection between Gibbs random fields is a very challenging
task. Indeed, due to the Markovian dependence structure, the normalizing
constant of the fields cannot be computed using standard analytical or
numerical methods. Furthermore, such unobserved fields cannot be integrated out
and the likelihood evaluztion is a doubly intractable problem. This forms a
central issue to pick the model that best fits an observed data. We introduce a
new approximate version of the Bayesian Information Criterion. We partition the
lattice into continuous rectangular blocks and we approximate the probability
measure of the hidden Gibbs field by the product of some Gibbs distributions
over the blocks. On that basis, we estimate the likelihood and derive the Block
Likelihood Information Criterion (BLIC) that answers model choice questions
such as the selection of the dependency structure or the number of latent
states. We study the performances of BLIC for those questions. In addition, we
present a comparison with ABC algorithms to point out that the novel criterion
offers a better trade-off between time efficiency and reliable results
ABC likelihood-freee methods for model choice in Gibbs random fields
Gibbs random fields (GRF) are polymorphous statistical models that can be
used to analyse different types of dependence, in particular for spatially
correlated data. However, when those models are faced with the challenge of
selecting a dependence structure from many, the use of standard model choice
methods is hampered by the unavailability of the normalising constant in the
Gibbs likelihood. In particular, from a Bayesian perspective, the computation
of the posterior probabilities of the models under competition requires special
likelihood-free simulation techniques like the Approximate Bayesian Computation
(ABC) algorithm that is intensively used in population genetics. We show in
this paper how to implement an ABC algorithm geared towards model choice in the
general setting of Gibbs random fields, demonstrating in particular that there
exists a sufficient statistic across models. The accuracy of the approximation
to the posterior probabilities can be further improved by importance sampling
on the distribution of the models. The practical aspects of the method are
detailed through two applications, the test of an iid Bernoulli model versus a
first-order Markov chain, and the choice of a folding structure for two
proteins.Comment: 19 pages, 5 figures, to appear in Bayesian Analysi
Dismantling the Mantel tests
The simple and partial Mantel tests are routinely used in many areas of
evolutionary biology to assess the significance of the association between two
or more matrices of distances relative to the same pairs of individuals or
demes. Partial Mantel tests rather than simple Mantel tests are widely used to
assess the relationship between two variables displaying some form of
structure.
We show that contrarily to a widely shared belief, partial Mantel tests are
not valid in this case, and their bias remains close to that of the simple
Mantel test.
We confirm that strong biases are expected under a sampling design and
spatial correlation parameter drawn from an actual study.
The Mantel tests should not be used in case auto-correlation is suspected in
both variables compared under the null hypothesis. We outline alternative
strategies. The R code used for our computer simulations is distributed as
supporting material
Simulation-based model selection for dynamical systems in systems and population biology
Computer simulations have become an important tool across the biomedical
sciences and beyond. For many important problems several different models or
hypotheses exist and choosing which one best describes reality or observed data
is not straightforward. We therefore require suitable statistical tools that
allow us to choose rationally between different mechanistic models of e.g.
signal transduction or gene regulation networks. This is particularly
challenging in systems biology where only a small number of molecular species
can be assayed at any given time and all measurements are subject to
measurement uncertainty. Here we develop such a model selection framework based
on approximate Bayesian computation and employing sequential Monte Carlo
sampling. We show that our approach can be applied across a wide range of
biological scenarios, and we illustrate its use on real data describing
influenza dynamics and the JAK-STAT signalling pathway. Bayesian model
selection strikes a balance between the complexity of the simulation models and
their ability to describe observed data. The present approach enables us to
employ the whole formal apparatus to any system that can be (efficiently)
simulated, even when exact likelihoods are computationally intractable.Comment: This article is in press in Bioinformatics, 2009. Advance Access is
available on Bioinformatics webpag
Introducing the Spatial Conflict Dynamics indicator of political violence
Modern armed conflicts have a tendency to cluster together and spread
geographically. However, the geography of most conflicts remains under-studied.
To fill this gap, this article presents a new indicator that measures two key
geographical properties of subnational political violence: the conflict
intensity within a region on the one hand, and the spatial distribution of
conflict within a region on the other. We demonstrate the indicator in North
and West Africa between 1997 to 2019 to show that it can clarify how conflicts
can spread from place to place and how the geography of conflict changes over
time
Multiplicative random walk Metropolis-Hastings on the real line
In this article we propose multiplication based random walk Metropolis
Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH)
algorithm. This algorithm, even if simple to apply, was not studied earlier in
Markov chain Monte Carlo literature. The associated kernel is shown to have
standard properties like irreducibility, aperiodicity and Harris recurrence
under some mild assumptions. These ensure basic convergence (ergodicity) of the
kernel. Further the kernel is shown to be geometric ergodic for a large class
of target densities on . This class even contains realistic target
densities for which random walk or Langevin MH are not geometrically ergodic.
Three simulation studies are given to demonstrate the mixing property and
superiority of RDMH to standard MH algorithms on real line. A share-price
return data is also analyzed and the results are compared with those available
in the literature
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