result_est_LS {BayesS5}

Posterior inference results from the object of S5

Description

Using the object of S5, the Least Square (LS) estimator of the MAP model and Bayesian Model Averaged (BMA) LS estimators of the regression coefficients are provided.

Usage

result_est_LS(res,X,y,verbose = TRUE)

Arguments

res

an object of the 'S5' function.

X

the covariates.

y

the response varaible.

verbose

logical; default is TRUE.

Value

intercept.MAP

the least square estimator of the intercept in the MAP model.

beta.MAP

the least square estimator of the regression coefficients in the MAP model.

intercept.BMA

the Baeysian model averaged over the least square estimator of the intercept.

beta.BMA

the Bayesian model averaged over the least square estimator of the regression coefficients.

Author(s)

Shin Minsuk and Ruoxuan Tian

References

Shin, M., Bhattacharya, A., Johnson V. E. (2018) A Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings, Statistica Sinica.

Hans, C., Dobra, A., and West, M. (2007). Shotgun stochastic search for large p regression. Journal of the American Statistical Association, 102, 507-516.

Nikooienejad,A., Wang, W., and Johnson V.E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using non-local priors. Bioinformatics, 32(9), 1338-45.

Examples

p=5000
n = 100

indx.beta = 1:5
xd0 = rep(0,p);xd0[indx.beta]=1
bt0 = rep(0,p); 
bt0[1:5]=c(1,1.25,1.5,1.75,2)*sample(c(1,-1),5,replace=TRUE)
xd=xd0
bt=bt0
X = matrix(rnorm(n*p),n,p)
y = X%*%bt0 + rnorm(n)*sqrt(1.5)
X = scale(X)
y = y-mean(y)
y = as.vector(y)

### piMoM  
#C0 = 2 # the number of repetitions of S5 algorithms to explore the model space
#tuning = 10 # tuning parameter
#tuning = hyper_par(type="pimom",X,y,thre = p^-0.5)
#print(tuning)
#ind_fun = ind_fun_pimom # choose the prior on the regression coefficients (pimom in this case)
#model = Bernoulli_Uniform # choose the model prior 
#tem =  seq(0.4,1,length.out=20)^2 # the sequence of the temperatures

#fit_pimom = S5(X,y,ind_fun=ind_fun,model = model,tuning=tuning,tem=tem,C0=C0)
#fit_pimom$GAM # the searched models by S5
#fit_pimom$OBJ # the corresponding log (unnormalized) posterior probability

#res_pimom = result(fit_pimom)
#est.LS = result_est_LS(res_pimom,X,y,obj_fun_pimom,verbose=TRUE)
#plot(est.LS$beta.MAP,est.LS$beta.BMA)
#abline(0,1,col="red")