Evaluation of decay times in coupled spaces: Reliability analysis of Bayeisan decay time estimation

Abstract

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.

The effects of simple coupled volume geometry on the objective and subjective results from nonexponential decay

“…In the physical world, impedance effects at the boundary and considerations of wavelength compared to opening size could reduce the decay ratio values, so that the high values of decay ratio predicted theoretically would be invalid. Furthermore, high decay ratios are usually accompanied by higher uncertainty values in the Bayesian analysis, as explained by Xiang et al 20 Although the decay ratio and ⌬dB results from theory and from Bayesian analysis of the computer modeled impulse responses do not perfectly match, it is still of interest to use the simulated results to learn more about the subjective perception of DSE.…”

Optimum absorption and aperture parameters for realistic coupled volume spaces determined from computational analysis and subjective testing results

“…Bradley and Wang 1 tested two quantifiers that can theoretically identify DSE profiles more uniquely: the decay ratio ͑T 2 / T 1 ͒ and ⌬L. ⌬L is defined as the difference in decibels between the two y-intercepts in the DSE profile ͑referred to as ⌬dB in previous studies͒, calculated from data produced by a Bayesian analysis algorithm developed by Xiang et al 5,6,16 In this investigation, decay ratio and ⌬L showed trends similar to T30/T15, except for cases with the largest coupled volume size in which the results were harder to interpret. 1 In another study, Bradley and Wang 17 analyzed computational models of an existing coupled volume concert hall, and compared the DSE quantifiers listed above as well as a newly proposed quantifier, late decay time/early decay time ͑LDT/EDT͒.…”

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

“…The application of Bayesian inference in the acoustics of coupled rooms has been well documented in a series of papers by Xiang and Goggans [6]- [8] and Goggans et al [9]. Figure 2(A) and Figure 2(B) show plots of the likelihood function for the decay models of decay order two and one respectively which are denoted by H 1 and H 2 , the boundary of the plots also define the range of a normalized prior π(x|H i ) used in each calculation.…”