Bernoulli-Uniform model prior

Description

A mixture model prior with Bernoulli and uniform densities. See Scott and Berger (2010) for details.

Usage

Bernoulli_Uniform(ind,p)

Arguments

References

Scott, James G., and James O. Berger. "Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem." The Annals of Statistics 38.5 (2010): 2587-2619.

See Also

Uniform

Examples

p = 5000
ind = 1:3 
m = Bernoulli_Uniform(ind,p)
print(m)

Simplified shotgun stochastic search algorithm with screening (S5)

Description

The Simplified Shotgun Stochastic Search with Screening (S5) is proposed by Shin et al (2018), which is a scalable stochastic search algorithm for high-dimensonal Bayesian variable selection. It is a modified version of the Shotgun Stochasitic Search (SSS, Hans et al., 2007), aimed at rapidly identifying regions of high posterior probability and finding the maximum a posteriori (MAP) model. Also, the S5 provides an approximation of posterior probability of each model (including the marginal inculsion probabilities). For details, see Shin et al. (2018)

Usage

S5(X, y, ind_fun, model, tuning, tem, ITER = 20, S = 20, C0 = 5, verbose = TRUE)

Arguments

Details

Using the S5 (Shin et al., 2018), 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

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.

See Also

result, S5_parallel, SSS

Examples

p0 = 5000
n0= 100

indx.beta = 1:5
xd0 = rep(0,p0);xd0[indx.beta]=1
bt0 = rep(0,p0); 
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(n0*p0),n0,p0)
y = crossprod(t(X),bt0) + rnorm(n0)*sqrt(1.5)
X = scale(X)
y = y-mean(y)
y = as.vector(y)

### default setting
#fit_default = S5(X,y)
#res_default = result(fit_default)
#print(res_default$hppm) # the MAP model 
#print(res_default$hppm.prob) # the posterior probability of the hppm 
#plot(res_default$marg.prob,ylim=c(0,1),ylab="marginal inclusion probability") 
# the marginal inclusion probability 

### Nonlocal prior (piMoM prior) by S5
#C0 = 1 # 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 # the log-marginal likelihood of models based on piMoM prior
#model = Bernoulli_Uniform 
# the log-marginal likelihood of models based on piMoM prior 
#tem =  seq(0.4,1,length.out=20)^2 
# the temperatures schedule
#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)
#str(res_pimom)
#print(res_pimom$hppm) # the MAP model 
#print(res_pimom$hppm.prob) 
# the posterior probability of the hppm 
#plot(res_pimom$marg.prob,ylim=c(0,1),ylab="marginal inclusion probability") 
# the marginal inclusion probability 


### Get the estimated regression coefficients from Bayesian Model Avaeraging (BMA)
#est.LS = result_est_LS(res_pimom,X,y) # Averged over the Least Square estimators of the models.
#est.MAP = result_est_MAP(res_pimom,X,y,obj_fun_pimom,verbose=TRUE) 
# Averged over the maximum posteriori (MAP) estimators of the models.

Simplified shotgun stochastic search algorithm with screening (S5) for additive models

Description

This is the Simplified Shotgun Stochastic Search with Screening (S5) for high-dimensonal Bayesian variable selection under nonparameteric additive models, which is considered in "Nonlocal Functional Priors for Nonparametric Hypothesis Testing and High-dimensional Model Selection" by Shin and Bhattacharya (2020+). This function utilizes the inverse moment nonlocal functional prior, and see Shin and Bhattacharya (2020+) for details.

Usage

S5_additive(X, y, K=5, model, tuning = 0.5*nrow(X), tem, ITER = 20, S = 30, C0 = 5, 
verbose = TRUE)

Arguments

Details

Using the S5 (Shin et al., 2018), 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.

Unlike "S5" function that requires an extra step to get more information of the computation procedure, this function provides full information of the results.

Value

Author(s)

Shin Minsuk and Ruoxuan Tian

References

Shin, M. and Bhattacharya, A.(2020) Nonlocal Functional Priors for Nonparametric Hypothesis Testing and High-dimensional Model Selection.

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

See Also

result, S5_parallel, SSS

Examples

p0 = 500
n0 = 200

X = matrix(runif(n0*p0,-2,2),n0,p0)
mu = X[,1]^2 + 2*sin(X[,2]*2) + 2*cos(X[,3]*2) + X[,4]
y = mu + rnorm(n0)
X = scale(X)
y = as.vector(y)

#fit_additive = S5_additive(X,y, tuning = 0.1*ncol(X))
#print(fit_additive$ind.hppm) # the MAP model 
#print(fit_additive$hppm.prob) # the posterior probability of the hppm 
#plot(fit_additive$marg.prob,ylim=c(0,1),ylab="marginal inclusion probability") 
# the marginal inclusion probability 

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

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

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 

Shotgun stochastic search algorithm (SSS)

Description

The Shotgun Stochastic Search (SSS) was proposed by Hans et al. (2007), which is a stochastic search algorithm for Bayesian variable selection.

Usage

SSS(X,y,ind_fun,model,tuning,N=1000,C0=1,verbose=TRUE)

Arguments

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

Author(s)

Shin Minsuk and Ruoxuan Tian

References

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

See Also

result, S5_parallel, S5

Examples

p=100
n = 200

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)

### default setting
#fit_de_SSS = SSS(X,y)

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

Uniform model prior

Description

A uniform model prior that assigns the same prior mass on each model.

Usage

Uniform(ind,p)

Arguments

Examples

ind = 1:3 
m = Uniform(ind,p)
print(m)

Tuning parameter selection for nonlocal priors

Description

Hyper parameter tau selection for nonlocal priors using random sampling from the null distribution (Nikooienejad et al, 2016).

Usage

hyper_par(type, X, y, thre)

Arguments

Details

Nikooienejad et al. (2016) proposed a novel approach to choose the hyperparameter tau for nonlocal priors. They first derive the null distribution of the regression coefficient by randomly sampling the covariates, and shuffle the index of the samples in the covariates. Then, they calculate the MLE from the sampled covariates that are shuffled. This process is repeated large enough times to approximate the null distribution of the MLE under the situation where all true regression coefficients are zero. They compare the nonlocal density with different values of the parameter to the null distribution so that the overlap of these densities falls below the threshold; see Nikooienejad et al. (2016) for further details.

Value

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.

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

ind_fun_pimom, ind_fun_pemom

Examples

p=50
n = 200

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)

# piMoM  
C0 = 1 # 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)

the log-marginal likelhood function based on the invers moment functional priors and inverse gamma prior (0.01,0.01)

Description

a log-marginal likelhood value of a model, based on the peMoM prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

ind_fun_NLfP(ind2, y, phi, n, p, K, IP.phi, C.prior1, tuning)

Arguments

References

Shin, M. and Bhattacharya, A.(2020) Nonlocal Functional Priors for Nonparametric Hypothesis Testing and High-dimensional Model Selection.

Zellner's g-prior

Description

a log-marginal likelhood value of a model, based on the Zellner's g-prior on the regression coefficients.

Usage

ind_fun_g(X.ind,y,n,p,tuning)

Arguments

Author(s)

Shin Minsuk and Ruoxuan Tian

References

Zellner, Arnold. "On assessing prior distributions and Bayesian regression analysis with g-prior distributions." Bayesian inference and decision techniques: Essays in Honor of Bruno De Finetti 6 (1986): 233-243.

See Also

ind_fun_pimom, ind_fun_g

Examples

#p=5000
p = 10
n = 200

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)

C0 = 1 # the number of repetitions of S5 algorithms to explore the model space
tuning = p^2 # tuning parameter g for g-prior
ind_fun = ind_fun_g # choose the pror on the regression coefficients (g-prior in this case)
model = Uniform #choose the model prior (Uniform prior in this cases)
tem =  seq(0.4,1,length.out=20)^2 # the sequence of the temperatures

fit_g = S5(X,y,ind_fun=ind_fun,model=model, tuning=tuning,tem=tem,C0=C0)

the log-marginal likelhood function based on peMoM priors and inverse gamma prior (0.01,0.01)

Description

a log-marginal likelhood value of a model, based on the peMoM prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

ind_fun_pemom(X.ind,y,n,p,tuning)

Arguments

References

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

Rossell, D., Telesca, D., and Johnson, V. E. (2013) High-dimensional Bayesian classifiers using non-local priors, Statistical Models for Data Analysis, 305-313.

See Also

ind_fun_g, ind_fun_pimom

the log-marginal likelhood function based on piMoM priors

Description

a log-marginal likelhood value of a model, based on the piMoM prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

ind_fun_pimom(X.ind,y,n,p,tuning)

Arguments

References

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

Johnson, V. E. and Rossell, D. (2012) Bayesian model selection in high-dimensional settings , David, Journal of the American Statistical Association, 107 (498), 649-660.

See Also

ind_fun_g, ind_fun_pemom

the log posterior distribution based on g-priors and inverse gamma prior (0.01,0.01)

Description

a log posterior density value at regression coefficients of a model, based on the g-prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

obj_fun_g(ind,X,y,n,p,tuning)

Arguments

References

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

Rossell, D., Telesca, D., and Johnson, V. E. (2013) High-dimensional Bayesian classifiers using non-local priors, Statistical Models for Data Analysis, 305-313.

See Also

obj_fun_pimom, obj_fun_pemom

the log posterior distribution based on peMoM priors and inverse gamma prior (0.01,0.01)

Description

a log posterior density value at regression coefficients of a model, based on the peMoM prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

obj_fun_pemom(ind,X,y,n,p,tuning)

Arguments

References

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

Rossell, D., Telesca, D., and Johnson, V. E. (2013) High-dimensional Bayesian classifiers using non-local priors, Statistical Models for Data Analysis, 305-313.

See Also

obj_fun_g, obj_fun_pimom

the log posterior distribution based on piMoM priors and inverse gamma prior (0.01,0.01)

Description

a log posterior density value at regression coefficients of a model, based on the piMoM prior on the regression coefficients and inverse gamma prior (0.01,0.01) on the variance.

Usage

obj_fun_pimom(ind,X,y,n,p,tuning)

Arguments

References

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

Rossell, D., Telesca, D., and Johnson, V. E. (2013) High-dimensional Bayesian classifiers using non-local priors, Statistical Models for Data Analysis, 305-313.

See Also

obj_fun_g, obj_fun_pemom

Posterior inference results from the object of S5

Description

Using the object of S5, the maximum a posteriori (MAP) model, its posterior probability, and the marginal inclusion probabilities are provided.

Usage

result(fit)

Arguments

Value

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 = 200

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)
#str(res_pimom)
#print(res_pimom$hppm) 
#print(res_pimom$hppm.prob)  
#plot(res_pimom$marg.prob,ylim=c(0,1)) 

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

Value

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")

Posterior inference results from the object of S5

Description

Using the object of S5, the maximum a posteriori (MAP) estimator and Bayesian Model Averaged (BMA) estimators of the regression coefficients are provided.

Usage

result_est_MAP(res,X,y,obj_fun,verbose = TRUE)

Arguments

Value

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