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The LMS algorithm is one of the most popular adaptive filter algorithms. Many variants of the algorithm have been developed for different applications. In this paper, we propose a unified model-based approach for developing LMS algorithms. We use a number of probability density functions to model the filtering error and the filter coefficients. The filter coefficients are determined by maximizing the posterior distribution function. We demonstrate that using this approach, we can not only develop existing LMS algorithms with further insights, we can also explore a number of new algorithms with certain desired properties such as robustness and sparseness.