15,609 research outputs found
Computational statistics using the Bayesian Inference Engine
This paper introduces the Bayesian Inference Engine (BIE), a general
parallel, optimised software package for parameter inference and model
selection. This package is motivated by the analysis needs of modern
astronomical surveys and the need to organise and reuse expensive derived data.
The BIE is the first platform for computational statistics designed explicitly
to enable Bayesian update and model comparison for astronomical problems.
Bayesian update is based on the representation of high-dimensional posterior
distributions using metric-ball-tree based kernel density estimation. Among its
algorithmic offerings, the BIE emphasises hybrid tempered MCMC schemes that
robustly sample multimodal posterior distributions in high-dimensional
parameter spaces. Moreover, the BIE is implements a full persistence or
serialisation system that stores the full byte-level image of the running
inference and previously characterised posterior distributions for later use.
Two new algorithms to compute the marginal likelihood from the posterior
distribution, developed for and implemented in the BIE, enable model comparison
for complex models and data sets. Finally, the BIE was designed to be a
collaborative platform for applying Bayesian methodology to astronomy. It
includes an extensible object-oriented and easily extended framework that
implements every aspect of the Bayesian inference. By providing a variety of
statistical algorithms for all phases of the inference problem, a scientist may
explore a variety of approaches with a single model and data implementation.
Additional technical details and download details are available from
http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GPL.Comment: Resubmitted version. Additional technical details and download
details are available from http://www.astro.umass.edu/bie. The BIE is
distributed under the GNU GP
Unbiased Monte Carlo estimate of stochastic differential equations expectations
We develop a pure Monte Carlo method to compute where is a
bounded and Lipschitz function and an Ito process. This approach extends
a previously proposed method to the general multidimensional case with a SDE
with varying coefficients. A variance reduction method relying on interacting
particle systems is also developped.Comment: 32 pages, 14 figure
Opinion influence and evolution in social networks: a Markovian agents model
In this paper, the effect on collective opinions of filtering algorithms
managed by social network platforms is modeled and investigated. A stochastic
multi-agent model for opinion dynamics is proposed, that accounts for a
centralized tuning of the strength of interaction between individuals. The
evolution of each individual opinion is described by a Markov chain, whose
transition rates are affected by the opinions of the neighbors through
influence parameters. The properties of this model are studied in a general
setting as well as in interesting special cases. A general result is that the
overall model of the social network behaves like a high-dimensional Markov
chain, which is viable to Monte Carlo simulation. Under the assumption of
identical agents and unbiased influence, it is shown that the influence
intensity affects the variance, but not the expectation, of the number of
individuals sharing a certain opinion. Moreover, a detailed analysis is carried
out for the so-called Peer Assembly, which describes the evolution of binary
opinions in a completely connected graph of identical agents. It is shown that
the Peer Assembly can be lumped into a birth-death chain that can be given a
complete analytical characterization. Both analytical results and simulation
experiments are used to highlight the emergence of particular collective
behaviours, e.g. consensus and herding, depending on the centralized tuning of
the influence parameters.Comment: Revised version (May 2018
Differential equation approximations for Markov chains
We formulate some simple conditions under which a Markov chain may be
approximated by the solution to a differential equation, with quantifiable
error probabilities. The role of a choice of coordinate functions for the
Markov chain is emphasised. The general theory is illustrated in three
examples: the classical stochastic epidemic, a population process model with
fast and slow variables, and core-finding algorithms for large random
hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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