set_ssvs {bvhar} | R Documentation |
Stochastic Search Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and Cholesky Factor
Description
Set SSVS hyperparameters for VAR or VHAR coefficient matrix and Cholesky factor.
Usage
set_ssvs(
coef_spike = 0.1,
coef_slab = 5,
coef_mixture = 0.5,
coef_s1 = 1,
coef_s2 = 1,
mean_non = 0,
sd_non = 0.1,
shape = 0.01,
rate = 0.01,
chol_spike = 0.1,
chol_slab = 5,
chol_mixture = 0.5,
chol_s1 = 1,
chol_s2 = 1
)
## S3 method for class 'ssvsinput'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'ssvsinput'
knit_print(x, ...)
Arguments
coef_spike |
Standard deviance for Spike normal distribution (See Details). |
coef_slab |
Standard deviance for Slab normal distribution (See Details). |
coef_mixture |
Bernoulli parameter for sparsity proportion (See Details). |
coef_s1 |
First shape of coefficients prior beta distribution |
coef_s2 |
Second shape of coefficients prior beta distribution |
mean_non |
Prior mean of unrestricted coefficients |
sd_non |
Standard deviance for unrestricted coefficients |
shape |
Gamma shape parameters for precision matrix (See Details). |
rate |
Gamma rate parameters for precision matrix (See Details). |
chol_spike |
Standard deviance for Spike normal distribution, in the cholesky factor (See Details). |
chol_slab |
Standard deviance for Slab normal distribution, in the cholesky factor (See Details). |
chol_mixture |
Bernoulli parameter for sparsity proportion, in the cholesky factor (See Details). |
chol_s1 |
First shape of cholesky factor prior beta distribution |
chol_s2 |
Second shape of cholesky factor prior beta distribution |
x |
|
digits |
digit option to print |
... |
not used |
Details
Let be the vectorized coefficient,
.
Spike-slab prior is given using two normal distributions.
As spike-slab prior itself suggests, set small (point mass at zero: spike distribution)
and set
large (symmetric by zero: slab distribution).
is the proportion of the nonzero coefficients and it follows
-
coef_spike
: -
coef_slab
: -
coef_mixture
: -
: vectorized format corresponding to coefficient matrix
If one value is provided, model function will read it by replicated value.
-
coef_non
: vectorized constant term is given prior Normal distribution with variance. Here,
coef_non
is.
Next for precision matrix , SSVS applies Cholesky decomposition.
where is upper triangular.
Diagonal components follow the gamma distribution.
For each row of off-diagonal (upper-triangular) components, we apply spike-slab prior again.
-
shape
: -
rate
: -
chol_spike
: -
chol_slab
: -
chol_mixture
: -
: vectorized format corresponding to coefficient matrix
-
and
:
-
chol_
arguments can be one value for replication, vector, or upper triangular matrix.
Value
ssvsinput
object
References
George, E. I., & McCulloch, R. E. (1993). Variable Selection via Gibbs Sampling. Journal of the American Statistical Association, 88(423), 881–889.
George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553–580.
Koop, G., & Korobilis, D. (2009). Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. Foundations and Trends® in Econometrics, 3(4), 267–358.