49,604 research outputs found
Improving power posterior estimation of statistical evidence
The statistical evidence (or marginal likelihood) is a key quantity in
Bayesian statistics, allowing one to assess the probability of the data given
the model under investigation. This paper focuses on refining the power
posterior approach to improve estimation of the evidence. The power posterior
method involves transitioning from the prior to the posterior by powering the
likelihood by an inverse temperature. In common with other tempering
algorithms, the power posterior involves some degree of tuning. The main
contributions of this article are twofold -- we present a result from the
numerical analysis literature which can reduce the bias in the estimate of the
evidence by addressing the error arising from numerically integrating across
the inverse temperatures. We also tackle the selection of the inverse
temperature ladder, applying this approach additionally to the Stepping Stone
sampler estimation of evidence.Comment: Revised version (to appear in Statistics and Computing). This version
corrects the typo in Equation (17), with thanks to Sabine Hug for pointing
this ou
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
Accounting for choice of measurement scale in extreme value modeling
We investigate the effect that the choice of measurement scale has upon
inference and extrapolation in extreme value analysis. Separate analyses of
variables from a single process on scales which are linked by a nonlinear
transformation may lead to discrepant conclusions concerning the tail behavior
of the process. We propose the use of a Box--Cox power transformation
incorporated as part of the inference procedure to account parametrically for
the uncertainty surrounding the scale of extrapolation. This has the additional
feature of increasing the rate of convergence of the distribution tails to an
extreme value form in certain cases and thus reducing bias in the model
estimation. Inference without reparameterization is practicably infeasible, so
we explore a reparameterization which exploits the asymptotic theory of
normalizing constants required for nondegenerate limit distributions. Inference
is carried out in a Bayesian setting, an advantage of this being the
availability of posterior predictive return levels. The methodology is
illustrated on both simulated data and significant wave height data from the
North Sea.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS333 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian Methods for Exoplanet Science
Exoplanet research is carried out at the limits of the capabilities of
current telescopes and instruments. The studied signals are weak, and often
embedded in complex systematics from instrumental, telluric, and astrophysical
sources. Combining repeated observations of periodic events, simultaneous
observations with multiple telescopes, different observation techniques, and
existing information from theory and prior research can help to disentangle the
systematics from the planetary signals, and offers synergistic advantages over
analysing observations separately. Bayesian inference provides a
self-consistent statistical framework that addresses both the necessity for
complex systematics models, and the need to combine prior information and
heterogeneous observations. This chapter offers a brief introduction to
Bayesian inference in the context of exoplanet research, with focus on time
series analysis, and finishes with an overview of a set of freely available
programming libraries.Comment: Invited revie
- âŠ