1,556 research outputs found
Bayesian model selection for exponential random graph models via adjusted pseudolikelihoods
Models with intractable likelihood functions arise in areas including network
analysis and spatial statistics, especially those involving Gibbs random
fields. Posterior parameter es timation in these settings is termed a
doubly-intractable problem because both the likelihood function and the
posterior distribution are intractable. The comparison of Bayesian models is
often based on the statistical evidence, the integral of the un-normalised
posterior distribution over the model parameters which is rarely available in
closed form. For doubly-intractable models, estimating the evidence adds
another layer of difficulty. Consequently, the selection of the model that best
describes an observed network among a collection of exponential random graph
models for network analysis is a daunting task. Pseudolikelihoods offer a
tractable approximation to the likelihood but should be treated with caution
because they can lead to an unreasonable inference. This paper specifies a
method to adjust pseudolikelihoods in order to obtain a reasonable, yet
tractable, approximation to the likelihood. This allows implementation of
widely used computational methods for evidence estimation and pursuit of
Bayesian model selection of exponential random graph models for the analysis of
social networks. Empirical comparisons to existing methods show that our
procedure yields similar evidence estimates, but at a lower computational cost.Comment: Supplementary material attached. To view attachments, please download
and extract the gzzipped source file listed under "Other formats
Statistical Network Analysis with Bergm
Recent advances in computational methods for intractable models have made
network data increasingly amenable to statistical analysis. Exponential random
graph models (ERGMs) emerged as one of the main families of models capable of
capturing the complex dependence structure of network data in a wide range of
applied contexts. The Bergm package for R has become a popular package to carry
out Bayesian parameter inference, missing data imputation, model selection and
goodness-of-fit diagnostics for ERGMs. Over the last few years, the package has
been considerably improved in terms of efficiency by adopting some of the
state-of-the-art Bayesian computational methods for doubly-intractable
distributions. Recently, version 5 of the package has been made available on
CRAN having undergone a substantial makeover, which has made it more accessible
and easy to use for practitioners. New functions include data augmentation
procedures based on the approximate exchange algorithm for dealing with missing
data, adjusted pseudo-likelihood and pseudo-posterior procedures, which allow
for fast approximate inference of the ERGM parameter posterior and model
evidence for networks on several thousands nodes.Comment: 22 pages, 5 figure
Generalized Direct Sampling for Hierarchical Bayesian Models
We develop a new method to sample from posterior distributions in
hierarchical models without using Markov chain Monte Carlo. This method, which
is a variant of importance sampling ideas, is generally applicable to
high-dimensional models involving large data sets. Samples are independent, so
they can be collected in parallel, and we do not need to be concerned with
issues like chain convergence and autocorrelation. Additionally, the method can
be used to compute marginal likelihoods
A survey on independence-based Markov networks learning
This work reports the most relevant technical aspects in the problem of
learning the \emph{Markov network structure} from data. Such problem has become
increasingly important in machine learning, and many other application fields
of machine learning. Markov networks, together with Bayesian networks, are
probabilistic graphical models, a widely used formalism for handling
probability distributions in intelligent systems. Learning graphical models
from data have been extensively applied for the case of Bayesian networks, but
for Markov networks learning it is not tractable in practice. However, this
situation is changing with time, given the exponential growth of computers
capacity, the plethora of available digital data, and the researching on new
learning technologies. This work stresses on a technology called
independence-based learning, which allows the learning of the independence
structure of those networks from data in an efficient and sound manner,
whenever the dataset is sufficiently large, and data is a representative
sampling of the target distribution. In the analysis of such technology, this
work surveys the current state-of-the-art algorithms for learning Markov
networks structure, discussing its current limitations, and proposing a series
of open problems where future works may produce some advances in the area in
terms of quality and efficiency. The paper concludes by opening a discussion
about how to develop a general formalism for improving the quality of the
structures learned, when data is scarce.Comment: 35 pages, 1 figur
Sustainable energy governance in South Tyrol (Italy): A probabilistic bipartite network model
At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities.
These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective.
This research aimed to analyse a part of the sustainable energy governance composed of formal relationships between municipalities and public utilities and to investigate the opportunities to further spread sustainable energy development within a region.
In the case study from South Tyrol, Italy, the network structures and dynamics of this part of the actual energy governance were investigated through a social network analysis and Bayesian exponential random graph models.
The findings confirmed that almost all of the collaborations are based on spatial closeness relations and that the current network structures do not permit a further spread of the sustainable energy governance.
The methodological approach can be replicated in other case studies and the findings are relevant to support energy planning choices at regional and local scales
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl
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