Sandwich algorithms for Bayesian variable selection

TLDR: It is proved that the Haar algorithm with the largest group that acts on the space of models is the optimum algorithm, within the parameter expansion data augmentation (PXDA) class of sandwich algorithms.

About: This article is published in Computational Statistics & Data Analysis.The article was published on 2015-01-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Markov chain Monte Carlo & Multicollinearity.

Figures

Figure 1: Estimates of marginal posterior inclusion probabilities, p(γj = 1 | Zo), for j = 1, . . . , 100, based on different algorithms, for the highly correlated simulated data.

Table 7: Estimates of relative efficiency of different algorithms with respect to the ODA algorithm in estimating p(γj = 1 | Zo), for the components of γ on which sandwich moves were employed, for the biscuit dough data.

Table 8: Running time adjusted estimates of relative efficiency of different algorithms with respect to the ODA algorithm in estimating p(γj = 1 | Zo), for the components of γ on which sandwich moves were employed, for the biscuit dough data.

Table 4: Running time adjusted estimates of relative efficiency of of different algorithms with respect to the ODA algorithm in estimating p(γj = 1 | Zo) for j = 1, . . . , 10, for the moderately correlated simulated data.

Table 3: Estimates of relative efficiency of different algorithms with respect to the ODA algorithm in estimating p(γj = 1 | Zo) for j = 1, . . . , 10, for the moderately correlated simulated data.

Table 6: Running time adjusted estimates of relative efficiency of different algorithms with respect to the ODA algorithm in estimating p(γj = 1 | Zo), for the components of γ on which sandwich moves were employed, for the protein data.

Frequently asked questions

Q1. What have the authors contributed in "Sandwich algorithms for bayesian variable selection" ?

The result provides theoretical insight but using the largest group is computationally prohibitive so two new computationally viable sandwich algorithms are developed, which are inspired by the Haar algorithm, but do not necessarily belong to the class of PXDA algorithms. 

Q2. What future works have the authors mentioned in the paper "Sandwich algorithms for bayesian variable selection" ?

It would be interesting to see in the future if parallel computing brings the Haar algorithm more advantage compared to MH approximations.