BayesS5 (version 1.41)

S5_additive: 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

X

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

y

a response variable.

K

the degree of freedom for the B-spline basis

model

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

tuning

a tuning parameter for the objective function (tau for the inverse moment prior). The default is 0.5*n.

tem

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

ITER

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

S

a screening size of variables; default is 30.

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=5.

verbose

if TRUE, the function prints the currnet status of the S5 in each temperature; the default is TRUE.

Value

GAM

the binary vaiables of searched models by S5

OBJ

the corresponding log (unnormalized) posterior probability

phi

the matrix of B-spline basis functions

Knots

the boundaries of knots used in generating the B-spline matrix

K

the degree of freedom of the B-spline basis.

post

the corresponding (normalized) posterior model probabilities

marg.prob

the marginal inclusion probabilities

ind.MAP

the selected variables from the MAP model

ind.marg

the selected variables whose marginal inclusion probability is larger than 0.5

hppm.prob

the posterior probability of the MAP model

tuning

the tuning parameter used in the model selection

%% ...

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.

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

# NOT RUN {
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 
# }