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Computer intensive methods for statistical models with latent structures
Gerontogianni, Stavroula; Γεροντογιάννη, Σταυρούλα Δ.; Athens University of Economics and Business, Department of Statistics; Demiris, Nikolaos
Several methods have been proposed and applied to different data problems in order to makeBayesian inference for the unknown density of the parameters in interest. The most widelyused so far are the Markov Chain Monte Carlo methods, including Gibbs Sampling which willbe one of the algorithms in focus on this project. Moreover, contemporary methods such asVariational Inference and Hamiltonian Monte Carlo promise respectable results as regardsaccuracy and time speed. On account of this, they are considered to be quite useful alternativesin cases where their advantages tend to play a greater role than their disadvantages. In thisproject the three methods mentioned above, giving greater emphasis on the theory behindVariational Inference, are implemented in mixture models of Gaussians aiming at theircomparison, in terms of accuracy, statistical efficiency and computational cost. At this point,it is of crucial importance to highlight the different softwares used to implement the algorithms;Gibbs sampling run through OpenBugs and Variational Inference as well as HamiltonianMonte Carlo through the new probabilistic language Stan. Consequently, any differencesoccurring in the results may also be derivatives of the different softwares usage. At this stage,it is important to mention that Stan is on experimental level, especially for the VariationalInference algorithm; hence some inaccuracies in the results may occur. Nevertheless, it isinteresting to test its capabilities and the way it works, since it could be a quite useful tool soon.The interface for both softwares is chosen to be R; hence the R code is provided in theAppendix. It must be also noted that Stan provides a black box procedure for theaforementioned algorithms, which is discussed in detail for each method.