Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES

Abstract

Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving an optimization problem where the cost function is assembled variously, for example, maximum likelihood and maximum a posteriori methods. However, these methods do not have exact solutions to most real-life problems. It is for this reason that Monte Carlo methods are preferred. In this paper, we treat the estimation of parameters which vary with space. We use the Metropolis-Hastings algorithm as a selection criterion for the maximum filter likelihood. Comparisons are made with the use of joint estimation of both the spatially varying parameters and the state. We illustrate the procedures employed in this paper by means of two hyperbolic SPDEs: the advection and the wave equation. The Metropolis-Hastings procedure registers better estimates.

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APA

David, A (2024). Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES. Afribary. Retrieved from https://afribary.com/works/estimation-of-spatially-varying-parameters-with-application-to-hyperbolic-spdes

MLA 8th

David, Angwenyi "Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES" Afribary. Afribary, 04 Jun. 2024, https://afribary.com/works/estimation-of-spatially-varying-parameters-with-application-to-hyperbolic-spdes. Accessed 21 Nov. 2024.

MLA7

David, Angwenyi . "Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES". Afribary, Afribary, 04 Jun. 2024. Web. 21 Nov. 2024. < https://afribary.com/works/estimation-of-spatially-varying-parameters-with-application-to-hyperbolic-spdes >.

Chicago

David, Angwenyi . "Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES" Afribary (2024). Accessed November 21, 2024. https://afribary.com/works/estimation-of-spatially-varying-parameters-with-application-to-hyperbolic-spdes

Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES

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