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(
  spike_grid = 100L,
  slab_shape = 0.01,
  slab_scl = 0.01,
  s1 = c(1, 1),
  s2 = c(1, 1),
  shape = 0.01,
  rate = 0.01
)

## S3 method for class 'ssvsinput'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

is.ssvsinput(x)

## S3 method for class 'ssvsinput'
knit_print(x, ...)

Arguments

spike_grid

Griddy gibbs grid size for scaling factor (between 0 and 1) of spike sd which is Spike sd = c * slab sd

slab_shape

Inverse gamma shape for slab sd

slab_scl

Inverse gamma scale for slab sd

s1

First shape of coefficients prior beta distribution

s2

Second shape of coefficients prior beta distribution

shape

Gamma shape parameters for precision matrix (See Details).

rate

Gamma rate parameters for precision matrix (See Details).

x

Any object

digits

digit option to print

...

not used

Details

Let \alpha be the vectorized coefficient, \alpha = vec(A). Spike-slab prior is given using two normal distributions.

\alpha_j \mid \gamma_j \sim (1 - \gamma_j) N(0, \tau_{0j}^2) + \gamma_j N(0, \tau_{1j}^2)

As spike-slab prior itself suggests, set \tau_{0j} small (point mass at zero: spike distribution) and set \tau_{1j} large (symmetric by zero: slab distribution).

\gamma_j is the proportion of the nonzero coefficients and it follows

\gamma_j \sim Bernoulli(p_j)

Next for precision matrix \Sigma_e^{-1}, SSVS applies Cholesky decomposition.

\Sigma_e^{-1} = \Psi \Psi^T

where \Psi = \{\psi_{ij}\} is upper triangular.

Diagonal components follow the gamma distribution.

\psi_{jj}^2 \sim Gamma(shape = a_j, rate = b_j)

For each row of off-diagonal (upper-triangular) components, we apply spike-slab prior again.

\psi_{ij} \mid w_{ij} \sim (1 - w_{ij}) N(0, \kappa_{0,ij}^2) + w_{ij} N(0, \kappa_{1,ij}^2)

w_{ij} \sim Bernoulli(q_{ij})

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.

Ishwaran, H., & Rao, J. S. (2005). Spike and slab variable selection: Frequentist and Bayesian strategies. The Annals of Statistics, 33(2).

Koop, G., & Korobilis, D. (2009). Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. Foundations and TrendsĀ® in Econometrics, 3(4), 267-358.


[Package bvhar version 2.3.0 Index]