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Article

Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework

by 1,*,†, 2 and 3,†
1
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
2
Department of Mathematics and Physics, SUNY Polytechnic Institute, Albany, NY 12203, USA
3
Naval Nuclear Laboratory, Schenectady, NY 12309, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Antonio M. Scarfone
Entropy 2021, 23(6), 674; https://doi.org/10.3390/e23060674
Received: 25 March 2021 / Revised: 26 May 2021 / Accepted: 26 May 2021 / Published: 27 May 2021
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise. It is common practice to first estimate the underlying system and then compute the gradient profile by taking the subsequent analytic derivative of the estimated system. The underlying system is often estimated by fitting or smoothing the data using other techniques. Taking the subsequent analytic derivative of an estimated function can be ill-posed. This becomes worse as the noise in the system increases. As a result, the uncertainty generated in the gradient estimate increases. In this paper, a theoretical framework for a method to estimate the gradient profile of discrete noisy data is presented. The method was developed within a Bayesian framework. Comprehensive numerical experiments were conducted on synthetic data at different levels of noise. The accuracy of the proposed method was quantified. Our findings suggest that the proposed gradient profile estimation method outperforms the state-of-the-art methods. View Full-Text
Keywords: computational techniques; inference methods; probability theory computational techniques; inference methods; probability theory
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MDPI and ACS Style

De Silva, K.; Cafaro, C.; Giffin, A. Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework. Entropy 2021, 23, 674. https://doi.org/10.3390/e23060674

AMA Style

De Silva K, Cafaro C, Giffin A. Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework. Entropy. 2021; 23(6):674. https://doi.org/10.3390/e23060674

Chicago/Turabian Style

De Silva, Kushani, Carlo Cafaro, and Adom Giffin. 2021. "Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework" Entropy 23, no. 6: 674. https://doi.org/10.3390/e23060674

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