Using Nested Sampling in the Analysis of Multi-Rate Sound Energy Decay in Acoustically Coupled Rooms

Abstract

Nested Sampling is a method introduced by Skilling[1] as a bayesian sampling method for model selection and parameter estimation. We present a view of Nested Sampling as an approximate method for computing the Lebesgue Integral of a function. We then apply Nested Sampling to the problem of estimating the decay order and decay time as applied to the acoustics of coupled rooms.

Nested sampling applied in Bayesian room-acoustics decay analysis

“…The slice sampling MCMC algorithm 14,32 which has the ability to automatically tune a proposal distribution in order to correct for cases where scaling may lead to inefficient sampling, seems particularly suited for nested sampling. 12 Any MCMC approach used will be problematic in that the samples w 1 s ; …; w rðiÞ s generated will be dependent (although the dependence between samples can be minimized by choosing samples which are uncorrelated). As the proofs in the Appendixes rely on independent samples w 1 s ; …; w rðiÞ s using a MCMC approach violates the assumptions at the heart of the nested sampling algorithm.…”

“…This paper applies the nested sampling algorithm proposed by Skilling 17,18 to Bayesian room-acoustics energy decay analysis. The paper presents the nested sampling algorithm as a numerical implementation of the Lebesgue integral as originally proposed by Jasa and Xiang 12 in order to provide acousticians an alternative understanding of the nested sampling algorithm's theoretical foundation.…”

“…Bayesian methods have been utilized in a wide range of acoustics applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] with increasing attention being given to the task of performing Bayesian model selection. A few of the most recent applications of Bayesian model selection can be found in such acoustics applications as roomacoustics energy decay analysis 1 and geo-acoustics inversion, 2,3 where the model selection problems are tackled separately from that of parameter estimation.…”

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

“…Other methods exist, including the recently proposed method of nested sampling 29 which has been applied to a variety of problems, including one application to acoustics. 9 Further, several methods to approximate evidence by predictive distributions and by analytical examination of asymptotic behavior can be found in the literature. 30,31 Several other approaches discussed in the literature can suffer from large or even infinite variance of the evidence estimate.…”

“…However, Bayesian model selection, a fundamental component of Bayesian inference, has seen only limited applications in acoustics. [8][9][10][11][12] Both parameter inference and model selection are intrinsic parts of estimating parameter uncertainty.…”