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Generate a v0 ladder

Source: R/helpers.R
make_v0_ladder.Rd

Creates a decreasing sequence of spike variances v0 for ssjgl, log-spaced in the ratio lambda1/v0. With the defaults it returns the ladder that ssjgl() uses when v0s is not given: three steps from lambda1/v0 = 10 to 100, i.e. lambda1 / c(10, 31.6, 100).

Usage

make_v0_ladder(
  lambda1,
  n_steps = 3,
  min_ratio = 10,
  max_ratio = 100,
  start_sparse = TRUE
)

Arguments

lambda1

Positive scalar; the off-diagonal penalty used in ssjgl. The ladder is scaled to this value.

n_steps

Integer number of v0 values in the ladder. Default 3.

min_ratio

Ratio lambda1/v0 at the first (weakest-spike, densest) step. Default 10.

max_ratio

Ratio lambda1/v0 at the last (strongest-spike, sparsest) step. Default 100.

start_sparse

Logical. If TRUE (default), the sequence is decreasing in v0 (increasing in lambda1/v0), which is the direction the warm starts of the dynamic posterior exploration need. If FALSE, returns an increasing sequence.

Value

A numeric vector of n_steps v0 values, decreasing by default.

Details

In SSJGL the spike and slab are Laplace priors on each off-diagonal precision entry \(\omega_{jk}\), with rates lambda1/v0 (spike) and lambda1/v1 (slab); the spike's scale is v0/lambda1. So v0 only matters through lambda1/v0, and this function is parameterised by that ratio. (sqrt(v0) is not a standard deviation of anything in the model.)

Along the ladder, the spike penalty on a non-edge grows from lambda1 * min_ratio to lambda1 * max_ratio. In the M-step it soft-thresholds sample covariances (sample correlations, for standardised data) at roughly lambda1/(n v0), for group sample size n.

The default end point lambda1/v0 = 100 was chosen by a simulation study (see vignette("parameter-exploration")): by that point the solution path has stabilised and F1 at PIP > 0.5 has reached its plateau, while longer ladders (up to 500) took longer and gave no better graphs. For exploring the whole path, use e.g. n_steps = 10, min_ratio = 5, max_ratio = 500 with plot_stability and plot_path.

See also

ssjgl(), plot_stability()

Examples

# Default ladder (what ssjgl() uses) for lambda1 = 1
make_v0_ladder(lambda1 = 1)
#> [1] 0.10000000 0.03162278 0.01000000
# A longer exploration ladder
v0s <- make_v0_ladder(lambda1 = 1, n_steps = 10, min_ratio = 5, max_ratio = 500)
data.frame(v0 = v0s, ratio = 1 / v0s, spike_scale = v0s / 1)
#>             v0      ratio spike_scale
#> 1  0.200000000   5.000000 0.200000000
#> 2  0.119896850   8.340503 0.119896850
#> 3  0.071876273  13.912797 0.071876273
#> 4  0.043088694  23.207944 0.043088694
#> 5  0.025830993  38.713184 0.025830993
#> 6  0.015485274  64.577483 0.015485274
#> 7  0.009283178 107.721735 0.009283178
#> 8  0.005565119 179.690683 0.005565119
#> 9  0.003336201 299.742125 0.003336201
#> 10 0.002000000 500.000000 0.002000000