Density Estimation and Wavelet Thresholding via Bayesian Methods: A Wavelet Probability Band and Related Metrics Approach to Assess Agitation and Sedation in ICU Patients

Density estimation by wavelet thresholding

10.1214/aos/1032894451 ◽

1996 ◽

Vol 24 (2) ◽

pp. 508-539 ◽

Cited By ~ 343

Author(s):

David L. Donoho ◽

Iain M. Johnstone ◽

Gérard Kerkyacharian ◽

Dominique Picard

Keyword(s):

Density Estimation ◽

Wavelet Thresholding

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Global L2 error of wavelet density estimator with truncated and strong mixing observations

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691314500337 ◽

2014 ◽

Vol 12 (03) ◽

pp. 1450033 ◽

Cited By ~ 2

Author(s):

Yu-Ye Zou ◽

Han-Ying Liang

Keyword(s):

Convergence Rate ◽

Rate Of Convergence ◽

Density Estimation ◽

Linear Estimator ◽

Strong Mixing ◽

Density Estimator ◽

Wavelet Thresholding ◽

Independent Data ◽

Wavelet Estimator ◽

Optimal Rate Of Convergence

In this paper, we discuss the global L2-error of the nonlinear wavelet estimator of density in the Besov space [Formula: see text] for the truncation model when the data exhibit strong mixing assumption, and prove that the estimator can achieve the optimal rate of convergence, which is similar to that in the complete and independent data case with term-by-term thresholding of the empirical wavelet coefficients (D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Ann. Statist.24 (1996) 508–539). In addition, the conclusion shows that the convergence rate of the nonlinear estimator is faster than that of its linear estimator in some range.

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Bayesian Applications in Auditory Research

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-h-astm-18-0228 ◽

2019 ◽

Vol 62 (3) ◽

pp. 577-586 ◽

Cited By ~ 9

Author(s):

Garnett P. McMillan ◽

John B. Cannon

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Bayesian Methods ◽

Prior Distribution ◽

Interim Analysis ◽

Iterative Process ◽

Bayes Theorem ◽

Sound Therapy ◽

The Many ◽

Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

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