SPASESHIP

SPArSe Estimation using SHrInkage Priors (SPASESHIP)

• Course Instructor: Dr. Anirban Bhattacharya (TAMU Statistics)

This repository contains the R codes used in STAT 633 Project Report on: Efficient Bayesian Computation using Variational Inference for a Shrinkage Prior. The details are as follows:

• Armagan_GDP_Gibbs.R: performs the data-augmented Gibbs sampler as outlined in Armagan et al. (2013), with the GDP prior endowed upon the model regression coefficients.
• Horseshoe.R: considers using the monomvn package in R to compute the posterior mean estimates, by putting a Horseshoe prior over the model regression coefficients, where the prior hierarchy follows from Section 1.1 of Carvalho et al. (2010).
• LAPLACE_BLASSO.R: once again uses the monomvn package in R to consider implementing the Bayesian LASSO framework, with the LASSO parameter having a Gamma prior with shape and rate parameters as: 2 and 0.1 respectively.
• NORMAL_BRIDGE.R: performs the Bayesian ridge regression, using the monomvn package in R. The ridge parameter is endowed upon with an inverse-Gamma prior having scale and shape parameters as: 1/1000.
• SCAD.R: uses the SCAD penalty from Fan and Li (2001), which is implemented using the SIS package in R.
• TAVIE_GDP.R: implements the VI (TAVIE) algorithm for the GDP prior.