Compute a p value for the test of psi <= psi0 (lower = TRUE) or psi >= psi0 (lower = FALSE)

Compute a p value for the test of psi <= psi0 (lower = TRUE) or psi >= psi0 (lower = FALSE)

Usage

pvalue_psi0(
  psi0,
  psi,
  psi_hat,
  psi_obs,
  alternative = "two.sided",
  maxit,
  chunksize,
  p_target,
  SSpacearr,
  logC,
  d_k,
  psi_is_vectorized = FALSE,
  theta_sampler = runif_dk_vects,
  ga = FALSE,
  ga_gfactor = 1,
  ga_lrate = 0.01,
  ga_restart_every = 10,
  warn = TRUE
)

Arguments

psi0

The null hypothesis value for the parameter being tested.

psi

Function that takes in parameters and outputs a real valued number for each parameter. Can be vectorized rowwise for a matrix or not.

psi_hat

The vector of psi values at each element of the sample space

psi_obs

The observed estimate at the given data

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less"

maxit

Maximum number of iterations of the Monte Carlo procedure

chunksize

The number of samples to take from the parameter space at each iteration

p_target

If a p-value is found that is greater than p_target, terminate the algorithm early.

SSpacearr

The sample space matrix

logC

The log multinomial coefficients for each row of the sample space

d_k

The vector of dimensions

psi_is_vectorized

Is psi vectorized by row?

theta_sampler

Function to take samples from the \(Theta\) parameter space. Default is runif_dk_vects.

ga

Logical, if TRUE, uses gradient ascent.

ga_gfactor

Concentration parameter scale in the gradient ascent algorithm. A number or "adapt"

ga_lrate

The gradient ascent learning rate

ga_restart_every

Restart the gradient ascent after this number of iterations at a sample from

warn

If TRUE, will give a warning if no samples from the null space are found

Value

A vector with two p-values, one for the lower, and one for the greater

Examples

sspace_3_5 <- matrix(sspace_multinom(3, 5), ncol = 3, byrow = TRUE)
psi <- function(theta) max(theta)
logC <- apply(sspace_3_5, 1, log_multinom_coef, sumx = 5)
psi_hat <- apply(sspace_3_5, 1, \(x) psi(x / sum(x)))
pvalue_psi0(.3, psi, psi_hat, .4, maxit = 10, chunksize = 100,
 p_target = 1, SSpacearr = sspace_3_5, logC = logC, d_k = 3, warn = FALSE)
#>      null       alt 
#> 0.0010000 0.3702166 
#> attr(,"p.sequence")
#> attr(,"p.sequence")$p.null
#>  [1] 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
#> 
#> attr(,"p.sequence")$p.alt
#>  [1] 0.3650079 0.3681825 0.3681825 0.3681825 0.3681825 0.3702166 0.3702166
#>  [8] 0.3702166 0.3702166 0.3702166
#>