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Bayesian Model Comparison with the gPrior
"... Abstract—Model comparison and selection is an important problem in many modelbased signal processing applications. Often, very simple information criteria such as the Akaike information criterion or the Bayesian information criterion are used despite their shortcomings. Compared to these methods, D ..."
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Abstract—Model comparison and selection is an important problem in many modelbased signal processing applications. Often, very simple information criteria such as the Akaike information criterion or the Bayesian information criterion are used despite their shortcomings. Compared to these methods, Djuric’s asymptotic MAP rule was an improvement, and in this paper we extend the work by Djuric in several ways. Specifically, we consider the elicitation of proper prior distributions, treat the case of real and complexvalued data simultaneously in a Bayesian framework similar to that considered by Djuric, and develop new model selection rules for a regression model containing both linear and nonlinear parameters. Moreover, we use this framework to give a new interpretation of the popular information criteria and relate their performance to the signaltonoise ratio of the data. By use of simulations, we also demonstrate that our proposed model comparison and selection rules outperform the traditional information criteria both in terms of detecting the true model and in terms of predicting unobserved data. The simulation code is available online. Index Terms—Bayesian model comparison, Zellner’s gprior, AIC, BIC, Asymptotic MAP. I.
On frequency domain models for TDOA estimation
 in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process
, 2015
"... Timedifferenceofarrival (TDOA) estimation is an important problem in many microphone signal processing applications. Traditionally, this problem is solved by using a crosscorrelation method, but in this paper we show that the crosscorrelation method is actually a restricted special case of a ..."
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Timedifferenceofarrival (TDOA) estimation is an important problem in many microphone signal processing applications. Traditionally, this problem is solved by using a crosscorrelation method, but in this paper we show that the crosscorrelation method is actually a restricted special case of a much more general method. In this connection, we establish the conditions under which the crosscorrelation method is a statistically efficient estimator. One of the conditions is that the source signal is periodic with a known fundamental frequency of 2pi/N radians per sample, where N is the number of data points, and a known number of harmonics. The more general method only relies on that the source signal is periodic and is, therefore, able to outperform the crosscorrelation method in terms of estimation accuracy on both synthetic data and artificially delayed speech data. The simulation code is available online.
A FAST ALGORITHM FORMAXIMUM LIKELIHOODBASED FUNDAMENTAL FREQUENCY ESTIMATION
"... Periodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood ..."
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Periodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood (ML) approach. Unfortunately, the ML estimator has a very high computational complexity, and the more inaccurate, but faster correlationbased estimators are therefore often used instead. In this paper, we propose a fast algorithm for the evaluation of the ML cost function for complexvalued data over all frequencies on a Fourier grid and up to a maximum model order. The proposed algorithm significantly reduces the computational complexity to a level not far from the complexity of the popular harmonic summation method which is an approximate ML estimator. Index Terms — Fundamental frequency estimation, Levinson algorithm, Durbin algorithm, nonlinear least squares,
INITIALIZATIONROBUST BAYESIAN MULTIPITCH ANALYZER BASED ON PSYCHOACOUSTICAL AND MUSICAL CRITERIA
"... We present a new Bayesian multipitch analyzer that dispenses with a precise optimization of parameter initialization or hyperparameters. Our method uses a new family of prior distribution, characteristic prior; it efficiently restricts the existence region of the latent variables, that is, the prod ..."
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We present a new Bayesian multipitch analyzer that dispenses with a precise optimization of parameter initialization or hyperparameters. Our method uses a new family of prior distribution, characteristic prior; it efficiently restricts the existence region of the latent variables, that is, the product of a conjugate prior and a characteristic function. The update formulas become a simple form that is actually suitable for Gibbs sampling. We construct characteristic priors of harmonic structures based on psychoacoustical and musical knowledge and apply them to nonnegative harmonic factorization. Experimental results improve 5.2 points in Fmeasure under a tough condition, random initialization with no hyperparameter optimization. Index Terms — multipitch estimation, nonnegative matrix factorization, harmonic clustering, overtone corpus, Bayesian analysis 1.