Description Details Author(s) See Also Examples

The package implements a fast gibbs sampler for the multivariate nomral with affine constraints. For the d-dimensional Z~Normal(mu,sigma), the linear_part matrix A in d x r, and offset vector b in 1 x r define a multivariate normal with affine constraints in {Z| A*Z<= b}.

Sampling is implemented in the main function, `sample_from_constraints`

. It is parameterized by the parameters of the normal (`mean_param`

and `covariance`

), parameters of the restriction (`linear_part`

and `offset`

), and the number of samples `ndraw`

. The user also
needs to specify an initial point that satisfies the constraints.
`thresh2constraints`

is a helper function that translates coordinate-wise truncations into the affine form.

Jonathan Taylor and Yuval Benjamini.

Maintainer: Yuval Benjamini <yuval.benjamini@mail.huji.ac.il>

The package was originally part of the github selective-inference code base.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
constr = thresh2constraints(3, lower = c(0.2,0.2,0.2))
covariance = matrix(c(1,0.5,0,0.5,1,0.5,0,0.5,1),nc=3)
samp = sample_from_constraints(linear_part = constr$linear_part,
offset= constr$offset,
mean_param = c(0,0,0),
covariance = covariance,
initial_point = c(1,1,1),
ndraw=20000,
burnin=2000)
# all points should be >= 0.2
stopifnot(all(samp>=0.2))
mean_restricted = colMeans(samp)
# compare to rejection of multivariate normals
library("MASS")
full_samp = mvrnorm(n=100000,mu = c(0,0,0),Sigma = covariance)
# Add restrictions:
pass_restrictions = apply(full_samp, 1,
function(x){all(constr$linear_part%*% x - constr$offset <=0 )})
cond_samp = full_samp[pass_restrictions,]
mean_restricted_rej = colMeans(cond_samp)
stopifnot(all(abs(mean_restricted - mean_restricted_rej)<=0.05))
``` |

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