ind_fun_g: Zellner's g-prior
In BayesS5: Bayesian Variable Selection Using Simplified Shotgun Stochastic Search with Screening (S5)
Description
Usage
Arguments
Author(s)
References
See Also
Examples
Description
a log-marginal likelhood value of a model, based on the Zellner's g-prior on the regression coefficients.
Usage
1
ind_fun_g(X.ind,y,n,p,tuning)
Arguments
X.ind
the subset of covariates in a model
y
the response variable
n
the sample size
p
the total number of covariates
tuning
a value of the tuning parameter
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
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
#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)
Example output
[1] "#################################"
[1] "S5 starts running"
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.16
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 9
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6106
[1] "The Number of Total Searched Models"
[1] 50
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.1862604
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 10
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6903
[1] "The Number of Total Searched Models"
[1] 69
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2145152
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 9
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6106
[1] "The Number of Total Searched Models"
[1] 80
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2447645
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 80
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2770083
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6 7
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -267.5921
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3112465
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3474792
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3857064
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.425928
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.468144
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.5123546
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.5585596
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 10
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6903
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.606759
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.6569529
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.7091413
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6769
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.7633241
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.8195014
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6769
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.8776731
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.9378393
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 1
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
user system elapsed
0.896 0.008 0.906
[1] "#################################"
[1] "Post-process starts"
[1] "#################################"
[1] "Done!"
BayesS5 documentation built on March 26, 2020, 7:14 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Author(s) References See Also Examples
Description
a log-marginal likelhood value of a model, based on the Zellner's g-prior on the regression coefficients.
Usage
1 | ind_fun_g(X.ind,y,n,p,tuning)
|
Arguments
X.ind |
the subset of covariates in a model |
y |
the response variable |
n |
the sample size |
p |
the total number of covariates |
tuning |
a value of the tuning parameter |
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
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | #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)
|
Example output
[1] "#################################"
[1] "S5 starts running"
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.16
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 9
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6106
[1] "The Number of Total Searched Models"
[1] 50
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.1862604
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 10
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6903
[1] "The Number of Total Searched Models"
[1] 69
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2145152
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 9
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6106
[1] "The Number of Total Searched Models"
[1] 80
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2447645
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 80
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.2770083
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6 7
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -267.5921
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3112465
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3474792
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.3857064
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 86
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.425928
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.468144
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.5123546
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.5585596
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 10
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6903
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.606759
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 92
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.6569529
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.7091413
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6769
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.7633241
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.8195014
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 6
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -265.6769
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.8776731
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5 8
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -264.4167
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 0.9378393
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
[1] "#################################"
[1] "Inverse Temperature"
[1] 1
[1] "The Selected Variables in the Searched MAP Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Searched MAP Model"
[1] -263.4072
[1] "Current Model"
[1] 1 2 3 4 5
[1] "The Evaluated Object Value at the Current Model"
[,1]
[1,] -263.4072
[1] "The Number of Total Searched Models"
[1] 97
user system elapsed
0.896 0.008 0.906
[1] "#################################"
[1] "Post-process starts"
[1] "#################################"
[1] "Done!"
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