The estimation of weather parameters such as attenuation and rainfall rates from weather radar data has been based mainly on deterministic regression models. The applications of a Bayesian approach to weather parameters classification and estimation have also been limited by a single Gaussian assumption. A computational intelligence model, i.e., Gaussian mixture model (GMM), is introduced in this work to characterize the prior distribution of weather parameters and the corresponding radar observation variables. Since a GMM would converge to any given distribution as the number of mixture increases, it provides an efficient way to accommodate extra information from antenna and frequency diversities and an omnipotent' solution to extract and model the knowledge' from training data. Hydrometeor classification and weather parameters estimation through a Bayesian approach are also made possible by the precisely represented prior distribution. A linear Bayesian estimator based on GMM, namely the Gaussian Mixture Parameter Estimator (GMPE), is then developed and tested in applications such as drop size distribution (DSD) retrieval, rainfall rate estimation and attenuation correction. The advantages of GMPE include 1) it is a best' estimator in terms of minimum-variance, unbiased performance; 2) it can easily include/exclude different radar observation variables and remains a best' estimator; 3) it provides a general framework that is applicable to different radar-meteorological applications. GMPE is further extended to explore the spatial relations with a Kalman Filter structure. Applications of the Kalman filter GMPE to rainfall rate estimation at X-band are analyzed and discussed.