Robust Bayesian Estimation of Mixed Normal Dirichlet Models to Study the Effect of Some Climatic Factors on Evaporation

Abstract

This study proposes and validates a robust Bayesian model based on a Dirichlet process mixture of normals (DMNM) for probability density estimation and missing data imputation in multivariate datasets. The primary focus is on addressing the challenge of incomplete data by providing a flexible and accurate estimation of their underlying probability density function. To fit the model, three Bayesian estimation algorithms are implemented and compared: the Expectation-Maximization (EM) algorithm, the Markov Chain Monte Carlo (MCMC) method, and a Traditional Bayesian (TB) algorithm. The framework is applied to real-world climaticdata (temperature, humidity, wind speed, and evaporation) obtained from the Meteorological Service in Basra,Iraq, with artificially introduced missing values at rates of 10%, 20%, and 40%. Model performance isevaluated using two key metrics: the Mean Squared Error (MSE) for imputation accuracy and computationalexecution time. The results demonstrate that the EM algorithm achieves the highest estimation accuracy(lowest MSE), while the TB method is the most computationally efficient. This work provides a practicaltoolkit for the statistical analysis of incomplete multivariate data in fields such as environmental modeling,hydrology, and agriculture.