Efficient estimation of decay parameters in acoustically coupled-spaces using slice sampling.
09 Sep 2009-Journal of the Acoustical Society of America (Acoustical Society of America)-Vol. 126, Iss: 3, pp 1269-1279
TL;DR: This work combines the SSMC algorithm and a fast search algorithm in order to efficiently determine decay parameters, their uncertainties, and inter-relationships with a minimum amount of required user tuning and interaction.
Abstract: Room-acoustic energy decay analysis of acoustically coupled-spaces within the Bayesian framework has proven valuable for architectural acoustics applications. This paper describes an efficient algorithm termed slice sampling Monte Carlo (SSMC) for room-acoustic decay parameter estimation within the Bayesian framework. This work combines the SSMC algorithm and a fast search algorithm in order to efficiently determine decay parameters, their uncertainties, and inter-relationships with a minimum amount of required user tuning and interaction. The large variations in the posterior probability density functions over multidimensional parameter spaces imply that an adaptive exploration algorithm such as SSMC can have advantages over the exiting importance sampling Monte Carlo and Metropolis–Hastings Markov Chain Monte Carlo algorithms. This paper discusses implementation of the SSMC algorithm, its initialization, and convergence using experimental data measured from acoustically coupled-spaces.
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TL;DR: In this article, the authors considered the efficiency of trans-dimensional (trans-D) Bayesian inversion based on reversible-jump Markov chain Monte Carlo (rjMCMC) sampling, with application to geophysical inverse problems for a depth-dependent earth or seabed model of an unknown number of layers.
Abstract: This paper considers the efficiency of trans-dimensional (trans-D) Bayesian inversion based on reversible-jump Markov-chain Monte Carlo (rjMCMC) sampling, with application to geophysical inverse problems for a depth-dependent earth or seabed model of an unknown number of layers (seabed acoustic reflectivity inversion is the specific example). Trans-D inversion is applied to sample the posterior probability density over geoacoustic/geophysical parameters for a variable number of layers, providing profile estimates with uncertainties that include the uncertainty in the model parameterization. However, the approach is computationally intensive. The efficiency of rjMCMC sampling is largely determined by the proposal schemes which are applied to generate perturbed values for existing parameters and new values for parameters assigned to layers added to the model. Several proposal schemes are considered here, some of which appear new for trans-D geophysical inversion. Perturbations of existing parameters are considered in a principal-component space based on an eigen-decomposition of the unit-lag parameter covariance matrix (computed from successive models along the Markov chain, a diminishing adaptation). The relative efficiency of proposing new parameters from the prior versus a Gaussian distribution focused near existing values is examined. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is also considered as a means to increase the acceptance rate of new layers. The relative efficiency of various proposal schemes is compared through repeated inversions with a pragmatic convergence criterion.
84 citations
TL;DR: The results indicate that the model in general can predict the growth of corrosion defects reasonably well and can be used to facilitate the development and application of reliability-based pipeline corrosion management.
76 citations
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TL;DR: This work investigates coupled-volume systems using acoustic scale-models of three coupled rooms and finds a fully parameterized Bayesian formulation capable of characterization of multiple-slope decays beyond the single-Slope and double-slopes of sound energy decays.
Abstract: Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.
41 citations
TL;DR: Taking the energy decay analysis in architectural acoustics as an example, this paper demonstrates that two different levels of inference, decay model-selection and decay parameter estimation, can be cohesively accomplished by the nested sampling algorithm.
Abstract: Room-acoustic energy decays often exhibit single-rate or multiple-rate characteristics in a wide variety of rooms/halls. Both the energy decay order and decay parameter estimation are of practical significance in architectural acoustics applications, representing two different levels of Bayesian probabilistic inference. This paper discusses a model-based sound energy decay analysis within a Bayesian framework utilizing the nested sampling algorithm. The nested sampling algorithm is specifically developed to evaluate the Bayesian evidence required for determining the energy decay order with decay parameter estimates as a secondary result. Taking the energy decay analysis in architectural acoustics as an example, this paper demonstrates that two different levels of inference, decay model-selection and decay parameter estimation, can be cohesively accomplished by the nested sampling algorithm.
27 citations
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07 Sep 2000
TL;DR: In this paper, a Markov chain is constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal ''slice'' defined by the current vertical position, or more generally with some update that leaves the uniform distribution over this slice invariant Variations on such slice sampling methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn.
Abstract: Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal `slice' defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant Variations on such `slice sampling' methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn This approach is often easier to implement than Gibbs sampling, and more efficient than simple Metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made It is therefore attractive for routine and automated use Slice sampling methods that update all variables simultaneously are also possible These methods can adaptively choose the magnitudes of changes made to each variable, based on the local properties of the density function More ambitiously, such methods could potentially allow the sampling to adapt to dependencies between variables by constructing local quadratic approximations Another approach is to improve sampling efficiency by suppressing random walks This can be done using `overrelaxed' versions of univariate slice sampling procedures, or by using `reflective' multivariate slice sampling methods, which bounce off the edges of the slice
1,285 citations
01 Jan 2003
TL;DR: In this paper, a Markov chain is constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant.
Abstract: Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using the principle that one can ample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant. Such "slice sampling" methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling and more efficient than simple Metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made. It is therefore attractive for routine and automated use. Slice sampling methods that update all variables simultaneously are also possible. These methods can adaptively choose the magnitudes of changes made to each variable, based on the local properties of the density function. More ambitiously, such methods could potentially adapt to the dependencies between variables by constructing local quadratic approximations. Another approach is to improve sampling efficiency by suppressing random walks. This can be done for univariate slice sampling by "overrelaxation," and for multivariate slice sampling by "reflection" from the edges of the slice.
968 citations
TL;DR: In this article, a new method of measuring reverberation time was described, which uses tone bursts (or filtered pistol shots) to excite the enclosure and a simple integral over the toneburst response of the enclosure yields, in a single measurement, the ensemble average of the decay curves that would be obtained with bandpass filtered noise as an excitation signal.
Abstract: A new method of measuring reverberation time is described. The method uses tone bursts (or filtered pistol shots) to excite the enclosure. A simple integral over the tone‐burst response of the enclosure yields, in a single measurement, the ensemble average of the decay curves that would be obtained with bandpass‐filtered noise as an excitation signal. The smooth decay curves resulting from the new method improve the accuracy of reverberation‐time measurements and facilitate the detection of nonexponential decays.
826 citations
TL;DR: Comparison of FGS, GS, and Monte Carlo integration for noisy synthetic benchmark test cases indicates that FGS provides rigorous estimates of PPD moments while requiring orders of magnitude less computation time.
Abstract: This paper develops a new approach to estimating seabed geoacoustic properties and their uncertainties based on a Bayesian formulation of matched-field inversion. In Bayesian inversion, the solution is characterized by its posterior probability density (PPD), which combines prior information about the model with information from an observed data set. To interpret the multi-dimensional PPD requires calculation of its moments, such as the mean, covariance, and marginal distributions, which provide parameter estimates and uncertainties. Computation of these moments involves estimating multi-dimensional integrals of the PPD, which is typically carried out using a sampling procedure. Important goals for an effective Bayesian algorithm are to obtain efficient, unbiased sampling of these moments, and to verify convergence of the sample. This is accomplished here using a Gibbs sampler (GS) approach based on the Metropolis algorithm, which also forms the basis for simulated annealing (SA). Although GS can be computationally slow in its basic form, just as modifications to SA have produced much faster optimization algorithms, the GS is modified here to produce an efficient algorithm referred to as the fast Gibbs sampler (FGS). An automated convergence criterion is employed based on monitoring the difference between two independent FGS samples collected in parallel. Comparison of FGS, GS, and Monte Carlo integration for noisy synthetic benchmark test cases indicates that FGS provides rigorous estimates of PPD moments while requiring orders of magnitude less computation time.
214 citations