Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/6/674 |
| _version_ | 1797532479042617344 |
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| author | Kushani De Silva Carlo Cafaro Adom Giffin |
| author_facet | Kushani De Silva Carlo Cafaro Adom Giffin |
| author_sort | Kushani De Silva |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T10:59:44Z |
| format | Article |
| id | doaj.art-bc46b511d93c44ed91c7d24d9d5a5836 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T10:59:44Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bc46b511d93c44ed91c7d24d9d5a58362023-11-21T21:36:56ZengMDPI AGEntropy1099-43002021-05-0123667410.3390/e23060674Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian FrameworkKushani De Silva0Carlo Cafaro1Adom Giffin2Department of Mathematics, Iowa State University, Ames, IA 50011, USADepartment of Mathematics and Physics, SUNY Polytechnic Institute, Albany, NY 12203, USANaval Nuclear Laboratory, Schenectady, NY 12309, USAAttaining 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.https://www.mdpi.com/1099-4300/23/6/674computational techniquesinference methodsprobability theory |
| spellingShingle | Kushani De Silva Carlo Cafaro Adom Giffin Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework Entropy computational techniques inference methods probability theory |
| title | Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework |
| title_full | Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework |
| title_fullStr | Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework |
| title_full_unstemmed | Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework |
| title_short | Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework |
| title_sort | gradient profile estimation using exponential cubic spline smoothing in a bayesian framework |
| topic | computational techniques inference methods probability theory |
| url | https://www.mdpi.com/1099-4300/23/6/674 |
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