Bayesian estimation of copula parameters for wind speed models of dependence

Abstract

Modelling the uncertainty of wind speed is essential in power flow analysis. Having abundant knowledge of the wind speed in an area is critical. A low volume of data can increase uncertainty in wind speed analysis. Spatial dependencies are often modelled before running probabilistic power flow and load flow analysis. Copulas are a popular way of capturing spatial dependence between multiple wind farms. Using NREL data from seven Northeastern United States wind farm sites, Bayesian inference will be used to determine the copula parameter uncertainty between weekly, daily, and hourly wind speed observations. This approach will be used on elliptical and single parameter Archimedean copulas. For each possible wind farm pair, an uninformative prior will be placed on the copula parameter. The resulting posterior will contain a distribution of copula parameter values based on the prior and the observed wind speed data. The posterior's credible interval is reviewed to determine the uncertainty in parameter estimation. The results show that using a data volume considerably more petite than 8760 hourly data points will result in more uncertainty in parameter estimation and inaccuracies in wind speed forecasting if using non‐Bayesian methods for copula parameter estimation.

Estimation of the Correlation Between Temperature and Precipitation in Bafra Plain Using Copula

“…Table 9 provides information about the copula families used in the study and their characteristics. Here, Φ 𝑛 is the 𝑛- 𝜃 is Pickand's dependence function (Gumbel, 1960;Joe, 1997;Trivedi and Zimmer, 2007;Franc et al, 2011;Nadarajah et al, 2017;Henderson et al, 2021;BenMim and BenSaïda, 2023). Some copula families may not have the ability to capture relationships in both directions.…”

Joint distribution of lightning and wind speed and its impact on the transmission system

“…Under the influence of relevance, the statistical characteristics of the joint probability distribution of lightning and wind speed may be significantly different from the univariate distribution (Khoubseresht et al, 2023). Sklar proposed the copula theory, which can decompose the multidimensional joint distribution function into multiple marginal distribution functions and one copula function, and the copula function can describe the relevance characteristics among variables (Henderson et al, 2021). In recent years, relevant theories and methods have been developed rapidly and successfully applied to financial risk assessment and flood peak impact analysis.…”

“…Copula function C (u 1 , u 2 , •••, u N ) denotes the connection function of the joint distribution function F (x 1 , x 2 ,•••, x N ) of multidimensional random variables and corresponding edge distribution functions Khoubseresht et al, 2023). The definition of the binary copula function C(u, v) corresponding to the joint distribution of binary random variables is as follows (Henderson et al, 2021):…”

Estructuras estocásticas notables en procesos puntuales espacio-temporales y medidas de riesgo bivariantes

“…Esto es debido a que toda distribución multivariante admite una representación en términos de una cópula y un conjunto de distribuciones marginales (Joe, 2015). El propósito de utilizar cópulas es encontrar familias paramétricas flexibles para ser utilizadas como descriptores de las estructuras de dependencia evidentes en los datos (Joe, 2015;Henderson et al, 2021). Las cópulas permiten simular fácilmente distribuciones bivariantes y analizar su estructura.…”

“…Como resultado, se espera que el parámetro de la cópula extrema de Gumbel-Hougaard capture la dependencia localizada entre los dos patrones de delitos. Es importante tener en cuenta que un volumen pequeño de datos no proporciona suficientes observaciones para formar una estructura de dependencia distintiva (Henderson et al, 2021).…”