readme_bvsgs

Bayes model averaging with selection of regressors - This program can be utilized for Bayesian Varia

************************************************************************
* bvsgs_sp: Bayesian Variable Selection - Gibbs Sampler, Selection prior
************************************************************************ 
			(Matlab version 5 required)

REFERENCE: Brown, P.J., Vannucci, M. and Fearn, T.
---------- JRSS Series B, 60(3), 1998, pp. 627-641.


		************************
		LIST OF MATLAB FUNCTIONS
		************************

bvsgs_sp.m	--	Main program
gibbs_sp.m	--	Gibbs sampler
itergs_sp.m     --	called by gibbs_sp
bernoulli.m	--	called by itergs_sp
gofg_sp.m	--	log relative probability function
repliche.m   	--	search for replicates
probord.m	--	posterior and marginal probs + ordering
pbvs_sp.m	--	prediction



		*****
		USAGE
		*****

[Gamma, GammD, logProb, logProbD, PostGamD, MargGam, SWITCH]= ...
bvsgs_sp(gamprec, X,Y, delta,k, w, v1)

Inputs:		gamprec,	starting binary vector.
-------				If gamprec=[] the program asks for r 
				to select a starting vector with first r
				elements equal to 1
 		X,		independent variables, n by p
 		Y,            	response variables, n by q
 		delta, k,     	hyperparameters Inverse Wishart
 		w,		Bernoulli priors with w_j = w, j=1...p        	
 		v1,            	hyperparameter normal selection prior
		                (column vector (p by 1) of standard deviations)


Outputs:	Gamma,        	all visited vectors (in sparse form)
--------			(Gamma(1,:) contains the starting vector)
		GammaD,		distinct visited vectors, ordered according 
				to their (normalized) relative post prob
				(matrix in sparse form)
 		logProb,	log-relative post probs of all visited
				vectors
		logProbD        log-relative posterior probabilities
               			of distinct visited vectors
 		PostGamD	normalized ordered relative probs
               			of distinct visited vectors
 		MargGam 	marginal probs of components
 		SWITCH,		number of component switches (out of p) 
				from iteration to iteration


Functions called by BVS_GSsP:
---------------------------
gofg_sp, gibbs_sp, repliche, probord


Notes:
------
_ Data must be centered
_ The programs asks for possible permuting of the data and for the
  Gibbs parameters (initial number of variables included, number of
  iterations)
_ QR matrices updated every m iterations (m provided by the user).
_ Programs use sparse matrices. To convert to the full form use
  the Matlab function full.m



			**********
			PREDICTION
			**********

[BayesPred,LSPred,ILS,IB]=pbvs_sp(X,Y,Xf,Yf,PostGamD,GammaD,numero)

Inputs:
-------
 X,            independent variables - calibration data
 Y,            response variables - calibration data
 Xf,           independent variables - future data
 Yf,           response variables - future data
 PostGamD,     normalized ordered relative probabilities
               of distinct visited vectors
 GammaD,       distinct visited vectors, ordered according to
               their (normalized) relative post. prob. (PostGamD)
 numero,       number of most likely models for Bayes prediction
             
Outputs:
--------
 BayesPred     Bayes prediction with the 'numero' most likely models
 LSPred        Least Squares prediction with the best model
 ILS           Indices of selected variables for LS prediction
 IB	       Indices of selected variables for Bayes prediction

                
                                
                        ***************
                        PARALLEL CHAINS
                        ***************

Use BVS_GSsP.m to obtain the chains
(ex. [Gamma1, GammD1, logProb1, logProbD1, PostGamD1, MargGam1, SWITCH1]= ...
		bvsgs_sp(gamprec, X,Y, delta,k, w, v1)
     [Gamma2, GammD2, logProb2, logProbD2, PostGamD2, MargGam2, SWITCH2]= ...
		bvsgs_sp(gamprec, X,Y, delta,k, w, v1)	)

Pool together distinct visited vectors
(ex. Gamma = [GammaD1' GammaD2']';   )

Pool together log-relative post probabilities of distinct visited vectors
(ex. logProb = cat(2, logProbD1, logProbD2);   )

Use repliche.m to search for replications
(ex. [GammaD, logProbD]=repliche(Gamma, logProb);  )

Use ProbOrd.m to get normalized posterior and marginal probs and
to order the distinct visited vectors according to probability
(ex. [GammaD, logProbD, PostGamD, MargGam]=probord(logProbD, GammaD);  )

Do prediction using PostGamD and GammaD


**********************************
Copyright (c) 1997 Marina Vannucci
**********************************