Since the integration expression is present in the conjugate prior distribution

Bayesian estimation of the parameters in finite Beta-Liouville mixture models(BLM)is analytically intractable.In this paper

an approach based on the variational inference framework is proposed.Adopting gamma distributions to approximate the prior distributions of the parameter in BLM and using some reasonable non-linear approximations;the closed form solution for the posterior distribution of the parameters is obtained.Compared to the conventional expectation maximization(EM)algorithm

the proposed algorithm is able to simultaneously estimate the model parameters and determine the number of components;our method also avoids the problem of overfitting.Extensive experimental results based on the synthetic data sets and scenes classification show that the proposed method is efficient and feasible in terms of parameter estimation and model selection.