Results 1  10
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35
Bayesian Model Assessment In Factor Analysis
, 2004
"... Factor analysis has been one of the most powerful and flexible tools for assessment of multivariate dependence and codependence. Loosely speaking, it could be argued that the origin of its success rests in its very exploratory nature, where various kinds of datarelationships amongst the variable ..."
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Cited by 64 (10 self)
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Factor analysis has been one of the most powerful and flexible tools for assessment of multivariate dependence and codependence. Loosely speaking, it could be argued that the origin of its success rests in its very exploratory nature, where various kinds of datarelationships amongst the variables at study can be iteratively verified and/or refuted. Bayesian inference in factor analytic models has received renewed attention in recent years, partly due to computational advances but also partly to applied focuses generating factor structures as exemplified by recent work in financial time series modeling. The focus of our current work is on exploring questions of uncertainty about the number of latent factors in a multivariate factor model, combined with methodological and computational issues of model specification and model fitting. We explore reversible jump MCMC methods that build on sets of parallel Gibbs samplingbased analyses to generate suitable empirical proposal distributions and that address the challenging problem of finding e#cient proposals in highdimensional models. Alternative MCMC methods based on bridge sampling are discussed, and these fully Bayesian MCMC approaches are compared with a collection of popular model selection methods in empirical studies.
Using particles to track varying numbers of interacting people
 In CVPR
, 2005
"... In this paper, we present a Bayesian framework for the fully automatic tracking of a variable number of interacting targets using a fixed camera. This framework uses a joint multiobject statespace formulation and a transdimensional Markov Chain Monte Carlo (MCMC) particle filter to recursively est ..."
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Cited by 49 (3 self)
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In this paper, we present a Bayesian framework for the fully automatic tracking of a variable number of interacting targets using a fixed camera. This framework uses a joint multiobject statespace formulation and a transdimensional Markov Chain Monte Carlo (MCMC) particle filter to recursively estimate the multiobject configuration and efficiently search the statespace. We also define a global observation model comprised of color and binary measurements capable of discriminating between different numbers of objects in the scene. We present results which show that our method is capable of tracking varying numbers of people through several challenging realworld tracking situations such as full/partial occlusion and entering/leaving the scene. 1.
Bayesian Harmonic Models for Musical Signal Analysis
 in Bayesian Statistics 7
, 2002
"... This paper is concerned with the Bayesian analysis of musical signals. The ultimate aim is to use Bayesian hierarchical structures in order to infer quantities at the highest level, including such quantities as musical pitch, dynamics, timbre, instrument identity, etc. Analysis of real musical si ..."
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Cited by 44 (8 self)
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This paper is concerned with the Bayesian analysis of musical signals. The ultimate aim is to use Bayesian hierarchical structures in order to infer quantities at the highest level, including such quantities as musical pitch, dynamics, timbre, instrument identity, etc. Analysis of real musical signals is complicated by many things, including the presence of transient sounds, noises and the complex structure of musical pitches in the frequency domain. The problem is truly Bayesian in that there is a wealth of (often subjective) prior knwowledge about how musical signals are constructed, which can be exploited in order to achieve more accurate inference about the musical structure. Here we propose developments to an earlier Bayesian model which describes each component `note' at a given time in terms of a fundamental frequency, partials (`harmonics'), and amplitude. This basic model is modified for greater realism to include nonwhite residuals, timevarying amplitudes and partials `detuned' from the natural linear relationship. The unknown parameters of the new model are simulated using a variable dimension MCMC algorithm, leading to a highly sophisticated analysis tool. We discuss how the models and algorithms can be applied for feature extraction, polyphonic music transcription, source separation and restoration of musical sources
Estimating the integrated likelihood via posterior simulation using the harmonic mean identity
 Bayesian Statistics
, 2007
"... The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison a ..."
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Cited by 26 (2 self)
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The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the harmonic mean identity, which says that the reciprocal of the integrated likelihood is equal to the posterior harmonic mean of the likelihood. The simplest estimator based on the identity is thus the harmonic mean of the likelihoods. While this is an unbiased and simulationconsistent estimator, its reciprocal can have infinite variance and so it is unstable in general. We describe two methods for stabilizing the harmonic mean estimator. In the first one, the parameter space is reduced in such a way that the modified estimator involves a harmonic mean of heaviertailed densities, thus resulting in a finite variance estimator. The resulting
Transdimensional Markov Chains: A Decade of Progress and Future Perspectives
, 2005
"... The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current ..."
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Cited by 20 (2 self)
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The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current state of the art and evaluate some of the most recent advances in this field. We also discuss future research perspectives in the context of the drive to develop sampling mechanisms with high degrees of both efficiency and automation.
Bayesian Analysis of Polyphonic Western Tonal Music
 JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
, 2006
"... This paper deals with the computational analysis of musical audio from recorded audio waveforms. This general problem includes, as subtasks, music transcription, extraction of musical pitch, dynamics, timbre, instrument identity, and source separation. Analysis of real musical signals is a highly ..."
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Cited by 18 (4 self)
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This paper deals with the computational analysis of musical audio from recorded audio waveforms. This general problem includes, as subtasks, music transcription, extraction of musical pitch, dynamics, timbre, instrument identity, and source separation. Analysis of real musical signals is a highly illposed task which is made complicated by the presence of transient sounds, background interference or the complex structure of musical pitches in the timefrequency domain. This paper focuses on models and algorithms for computer transcription of multiple musical pitches in audio, elaborated from previous work by two of the authors. The audio data are supposedly presegmented into fixed pitch regimes such as individual chords. The models presented apply to pitched (tonal) music and are formulated via a Gabor representation of nonstationary signals. A Bayesian probabilistic structure is employed for representation of prior information about the parameters of the notes. This paper introduces a numerical Bayesian inference strategy for estimation of the pitches and other parameters of the waveform. The improved algorithm is much quicker, and makes the approach feasible in realistic sitautions. Results are
Computational advances for and from Bayesian analysis
 Statist. Sci
, 2004
"... Abstract. The emergence in the past years of Bayesian analysis in many methodological and applied fields as the solution to the modeling of complex problems cannot be dissociated from major changes in its computational implementation. We show in this review how the advances in Bayesian analysis and ..."
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Cited by 10 (0 self)
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Abstract. The emergence in the past years of Bayesian analysis in many methodological and applied fields as the solution to the modeling of complex problems cannot be dissociated from major changes in its computational implementation. We show in this review how the advances in Bayesian analysis and statistical computation are intermingled. Key words and phrases: Monte Carlo methods, importance sampling, Markov chain Monte Carlo (MCMC) algorithms.
The mode oriented stochastic search (MOSS) algorithm for loglinear models with conjugate priors
, 2008
"... ..."
Bayesian model selection for heteroskedastic models
 Advances in Econometrics
, 2008
"... It is well known that volatility asymmetry exists in financial markets. This paper reviews and investigates recently developed techniques for Bayesian estimation and model selection applied to a large group of modern asymmetric heteroskedastic models. These include the GJRGARCH, threshold autoregr ..."
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Cited by 5 (0 self)
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It is well known that volatility asymmetry exists in financial markets. This paper reviews and investigates recently developed techniques for Bayesian estimation and model selection applied to a large group of modern asymmetric heteroskedastic models. These include the GJRGARCH, threshold autoregression with GARCH errors, threshold GARCH and Double threshold heteroskedastic model with auxiliary threshold variables. Further we briefly review recent methods for Bayesian model selection, such as: reversible jump Markov chain Monte Carlo, Monte Carlo estimation via independent sampling from each model and importance sampling methods. Seven heteroskedastic models are then compared, for three long series of daily Asian market returns, in a model selection study illustrating the preferred model selection method. Major evidence of nonlinearity in mean and volatility is found, with the preferred model having a weighted threshold variable of local and international market news.