S5_parallel {BayesS5}

Parallel version of S5

Description

The parallel version of the S5. Multiple S5 chains independently explore the model space to enhance the capacity of searching interesting region of the model space.

Usage

S5_parallel(NC,X,y,ind_fun,model,tuning,tem,ITER=20,S=20,C0=2)

Arguments

NC

a number of cores (the number of parallel S5 chains) to be used.

X

a covariate matrix (a standardization is recommneded for nonlocal priors).

y

a response variable.

ind_fun

a log-marginal likelihood function of models, which is resulted from a pred-specified priors on the regression coefficients. The default is piMoM

model

a model prior; Uniform or Bernoulli_Uniform. The default is Bernoulli_Uniform

tuning

a tuning parameter for the objective function (tau for piMoM and peMoM priors; g for the g-prior).

tem

a temperature schedule. The default is seq(0.4,1,length.out=20)^-2.

ITER

a number of iterations in each temperature; default is 20.

S

a screening size of variables; default is 20.

C0

a number of repetition of the S5 algorithm C0 times,default is 2. When the total number of variables is huge and real data sets are considered, using a large number of C0 is recommended, e.g., C0=10.

Details

Using the S5 (Shin et al., 2016+), you will get all the models searched by S5 algorithm, and their corresponding log (unnormalized) posterior probabilities, and also this function can receive searched model for g-prior,piMoM,and peMoM.

After obtaining the object of the S5 function, by using the 'result' function, you can obtain the posterior probabilities of the searched models including the MAP model and the marginal inclusion probabilities of each variable.

By using the procedure of Nikooienejad et al. (2016), the 'hyper_par' function chooses the tuning parameter for nonlocal priors (piMoM or peMoM priors).

Value

GAM

the binary vaiables of searched models by S5

OBJ

the corresponding log (unnormalized) posterior probability

tuning

the tuning parameter used in the model selection

Author(s)

Shin Minsuk and Ruoxuan Tian

References

Shin, M., Bhattacharya, A., Johnson V. E. (2016+) A Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings, under revision in 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.

See Also

result, S5

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 = crossprod(t(X),bt0) + rnorm(n)*sqrt(1.5)
X = scale(X)
y = y-mean(y)
y = as.vector(y)

### parallel version of S5 (defalut)
#fit_parallel = S5_parallel(NC=2,X,y)
 

#fit_parallel$GAM # the searched models by S5
#fit_parallel$OBJ # the corresponding log (unnormalized) posterior probability

#res_parallel = result(fit_parallel)
#str(res_parallel)
#print(res_parallel$hppm) # the MAP model 
#print(res_parallel$hppm.prob) # the posterior probability of the hppm 
#plot(res_parallel$marg.prob,ylim=c(0,1),ylab="marginal inclusion probability") 
# the marginal inclusion probability 

### parallel version of S5 (temperature rescheduling)
#NC = 2 # the number of cores for the prallel computing
#C0 = 5 # the number of repetitions of S5 algorithms to explore the model space
#tuning = hyper_par(type="pimom",X,y,thre = p^-0.5)  
# tuning parameter selection for nonlocal priors
#print(tuning) 

#ind_fun = ind_fun_pimom 
#model = Bernoulli_Uniform 
# the log-marginal likelihood of models based on piMoM prior 
#('Uniform' or 'Bernoulli_Uniform').
#tem =  seq(0.4,1,length.out=20)^2 
# the temperatures schedule
#fit_parallel = S5_parallel(NC=2,X,y,ind_fun,model,tuning,tem,C0=C0)
 

#fit_parallel$GAM # the searched models by S5
#fit_parallel$OBJ # the corresponding log (unnormalized) posterior probability

#res_parallel = result(fit_parallel)
#str(res_parallel)
#print(res_parallel$hppm) # the MAP model 
#print(res_parallel$hppm.prob) # the posterior probability of the hppm 
#plot(res_parallel$marg.prob,ylim=c(0,1),ylab="marginal inclusion probability") 
# the marginal inclusion probability