Simulation studies to compare bayesian wavelet shrinkage methods in aggregated functional data

TL;DR

This paper conducts simulation studies to compare various Bayesian wavelet shrinkage methods for estimating component curves from aggregated functional data, highlighting the influence of signal-to-noise ratio on performance.

Contribution

It provides a comparative analysis of five Bayesian wavelet shrinkage methods applied to aggregated functional data, including new insights into their performance under different noise conditions.

Findings

Performance varies with signal-to-noise ratio

Bayesian methods show different strengths depending on the prior used

Donoho-Johnstone test functions effectively evaluate method accuracy

Abstract

The present work describes simulation studies to compare the performances of bayesian wavelet shrinkage methods in estimating component curves from aggregated functional data. To do so, five methods were considered: the bayesian shrinkage rule under logistic prior by Sousa (2020), bayesian shrinkage rule under beta prior by Sousa et al. (2020), Large Posterior Mode method by Cutillo et al. (2008), Amplitude-scale invariant Bayes Estimator by Figueiredo and Nowak (2001) and Bayesian Adaptive Multiresolution Smoother by Vidakovic and Ruggeri (2001). Further, the so called Donoho-Johnstone test functions, Logit and SpaHet functions were considered as component functions. It was observed that the signal to noise ratio of the data had impact on the performances of the methods.