A list of sample counts of a Bernoulli variable with (unnormalized) success and failure probabilities given by Prob{ind=r} and Prob{ind=r+1}.
ind_prob
A list of two-element integer vectors.
The samples have been found with the HMC sampler Stan with a model that simulates the eigenvalues of a Gaussian orthogonal/unitary/symplectic ensemble with index constrained to {r,r+1}. The code below shows how this data can be generated.
The values of the parameters beta, n, r are specified in the names of the list
elements, which are of the form beta=_,n=_,r=_
with _ replaced by
values. The list contains all combinations of beta=1,2,4
, n=4,5,...,10
,
and r
between floor((n+1)/2)
and n-2
. The remaining values
can be found through the relation Prob{ind=r}=Prob{ind=n-r}.
Package: symconivol
# NOT RUN { library(rstan) ind_prob <- list() nmin <- 4 nmax <- 10 filename <- "tmp.stan" N <- 1e6 warmup <- 1e3 for (n in nmin:nmax) { for (beta in c(1,2,4)) { for (r in floor((n+1)/2):(n-2)) { index <- str_c("beta=",beta,",n=",n,",r=",r) M <- constr_eigval(beta, n, r, r+1, filename=filename) stan_samp <- stan( file = filename, data = M$data, chains = 1, warmup = warmup, iter = N+warmup, cores = 2, refresh = 1e4 ) ef <- rstan::extract(stan_samp)$ef indprob[[index]] <- c(length(which(ef<0)),length(which(ef>0))) } } } file.remove(filename) # }