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

Entropy

Carlo Cafaro¹  Kushani De Silva²  Adom Giffin³ 

[1] Department of Mathematics and Physics, SUNY Polytechnic Institute, Albany, NY 12203, USA;Department of Mathematics, Iowa State University, Ames, IA 50011, USA;Naval Nuclear Laboratory, Schenectady, NY 12309, USA;

关键词: computational techniques;    inference methods;    probability theory;   

DOI  :  10.3390/e23060674

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown