8,899 research outputs found
Probabilistic projections of HIV prevalence using Bayesian melding
The Joint United Nations Programme on HIV/AIDS (UNAIDS) has developed the
Estimation and Projection Package (EPP) for making national estimates and
short-term projections of HIV prevalence based on observed prevalence trends at
antenatal clinics. Assessing the uncertainty about its estimates and
projections is important for informed policy decision making, and we propose
the use of Bayesian melding for this purpose. Prevalence data and other
information about the EPP model's input parameters are used to derive a
probabilistic HIV prevalence projection, namely a probability distribution over
a set of future prevalence trajectories. We relate antenatal clinic prevalence
to population prevalence and account for variability between clinics using a
random effects model. Predictive intervals for clinic prevalence are derived
for checking the model. We discuss predictions given by the EPP model and the
results of the Bayesian melding procedure for Uganda, where prevalence peaked
at around 28% in 1990; the 95% prediction interval for 2010 ranges from 2% to
7%.Comment: Published at http://dx.doi.org/10.1214/07-AOAS111 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Probabilistic Interpretation of Linear Solvers
This manuscript proposes a probabilistic framework for algorithms that
iteratively solve unconstrained linear problems with positive definite
for . The goal is to replace the point estimates returned by existing
methods with a Gaussian posterior belief over the elements of the inverse of
, which can be used to estimate errors. Recent probabilistic interpretations
of the secant family of quasi-Newton optimization algorithms are extended.
Combined with properties of the conjugate gradient algorithm, this leads to
uncertainty-calibrated methods with very limited cost overhead over conjugate
gradients, a self-contained novel interpretation of the quasi-Newton and
conjugate gradient algorithms, and a foundation for new nonlinear optimization
methods.Comment: final version, in press at SIAM J Optimizatio
Probabilistic projections of HIV prevalence using Bayesian melding
The Joint United Nations Programme on HIV/AIDS (UNAIDS) has developed the
Estimation and Projection Package (EPP) for making national estimates and
short-term projections of HIV prevalence based on observed prevalence trends at
antenatal clinics. Assessing the uncertainty about its estimates and
projections is important for informed policy decision making, and we propose
the use of Bayesian melding for this purpose. Prevalence data and other
information about the EPP model's input parameters are used to derive a
probabilistic HIV prevalence projection, namely a probability distribution over
a set of future prevalence trajectories. We relate antenatal clinic prevalence
to population prevalence and account for variability between clinics using a
random effects model. Predictive intervals for clinic prevalence are derived
for checking the model. We discuss predictions given by the EPP model and the
results of the Bayesian melding procedure for Uganda, where prevalence peaked
at around 28% in 1990; the 95% prediction interval for 2010 ranges from 2% to
7%.Comment: Published at http://dx.doi.org/10.1214/07-AOAS111 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Probabilistic Modeling Paradigms for Audio Source Separation
This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems
A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms
The benefits of automating design cycles for Bayesian inference-based
algorithms are becoming increasingly recognized by the machine learning
community. As a result, interest in probabilistic programming frameworks has
much increased over the past few years. This paper explores a specific
probabilistic programming paradigm, namely message passing in Forney-style
factor graphs (FFGs), in the context of automated design of efficient Bayesian
signal processing algorithms. To this end, we developed "ForneyLab"
(https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message
passing-based inference in FFGs. We show by example how ForneyLab enables
automatic derivation of Bayesian signal processing algorithms, including
algorithms for parameter estimation and model comparison. Crucially, due to the
modular makeup of the FFG framework, both the model specification and inference
methods are readily extensible in ForneyLab. In order to test this framework,
we compared variational message passing as implemented by ForneyLab with
automatic differentiation variational inference (ADVI) and Monte Carlo methods
as implemented by state-of-the-art tools "Edward" and "Stan". In terms of
performance, extensibility and stability issues, ForneyLab appears to enjoy an
edge relative to its competitors for automated inference in state-space models.Comment: Accepted for publication in the International Journal of Approximate
Reasonin
Super-resolution Line Spectrum Estimation with Block Priors
We address the problem of super-resolution line spectrum estimation of an
undersampled signal with block prior information. The component frequencies of
the signal are assumed to take arbitrary continuous values in known frequency
blocks. We formulate a general semidefinite program to recover these
continuous-valued frequencies using theories of positive trigonometric
polynomials. The proposed semidefinite program achieves super-resolution
frequency recovery by taking advantage of known structures of frequency blocks.
Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum
Fast and scalable Gaussian process modeling with applications to astronomical time series
The growing field of large-scale time domain astronomy requires methods for
probabilistic data analysis that are computationally tractable, even with large
datasets. Gaussian Processes are a popular class of models used for this
purpose but, since the computational cost scales, in general, as the cube of
the number of data points, their application has been limited to small
datasets. In this paper, we present a novel method for Gaussian Process
modeling in one-dimension where the computational requirements scale linearly
with the size of the dataset. We demonstrate the method by applying it to
simulated and real astronomical time series datasets. These demonstrations are
examples of probabilistic inference of stellar rotation periods, asteroseismic
oscillation spectra, and transiting planet parameters. The method exploits
structure in the problem when the covariance function is expressed as a mixture
of complex exponentials, without requiring evenly spaced observations or
uniform noise. This form of covariance arises naturally when the process is a
mixture of stochastically-driven damped harmonic oscillators -- providing a
physical motivation for and interpretation of this choice -- but we also
demonstrate that it can be a useful effective model in some other cases. We
present a mathematical description of the method and compare it to existing
scalable Gaussian Process methods. The method is fast and interpretable, with a
range of potential applications within astronomical data analysis and beyond.
We provide well-tested and documented open-source implementations of this
method in C++, Python, and Julia.Comment: Updated in response to referee. Submitted to the AAS Journals.
Comments (still) welcome. Code available: https://github.com/dfm/celerit
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