Bayesian Model Comparison With the g-Prior

Abstract

Model comparison and selection is an important problem in many model-based 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 complex-valued 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 non-linear parameters. Moreover, we use this framework to give a new interpretation of the popular information criteria and relate their performance to the signal-to-noise 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.

On frequency domain models for TDOA estimation

“…If all the nonlinear parameters are unknown, an initial estimate of the fundamental frequency can be obtained by using a multi-channel pitch estimator such as the one suggested in [16]. If also the number L of harmonics are unknown, the joint fundamental frequency and model order estimator in [17] can easily be extended to cope with multi-channel data by using the model comparison framework suggested in [18]. If the attenuation β and ξ have been estimated (see the next two steps), the fundamental frequency can be re-estimated by maximising the cost function in (11).…”

Joint sparsity and frequency estimation for spectral compressive sensing

“…Based on the recently proposed framework in [15], we then formulate the probabilistic framework for jointly estimating the frequency parameters and detecting the sparsity level l. The latter is usually referred to as model selection and comparison. In the context of CS, an unknown level of sparsity is problematic since the number of measurements M should ideally be close to this level, which therefore often is assumed known.…”

Joint estimation of pitch and direction of arrival: improving robustness and accuracy for multi-speaker scenarios

“…The number of considered harmonics in Equation 12 was set to P = 5. In practice, the number of harmonics P is unknown or changes over time and has to be estimated [18][19][20]32]. The parameter β for the phase transform in Equation 16 was set to β = 0.2.…”

“…Traditional pitch estimation methods are based on, e.g., zero crossing rate analysis, detection of harmonics in the autocorrelation function, and cepstrum analysis [16]. Recently, a pitch estimation filter with amplitude compression (PEFAC) in the spectral domain has been proposed in [17], and methods for joint pitch and model order estimation have been proposed in [18][19][20]. Multipitch estimation has also become a topic of research, and several approaches are summarized in [21].…”