# R/hit.and.run.samples.multivariate.model.R In prototest: Inference on Prototypes from Clusters of Features

#### Defines functions hit.and.run.samples.multivariate.model

```#### generates hit-and-run samples for the multivariate model
#### y = mu + sum_{k != test.group}theta_k.P_k(y-mu) + eps
#### conditions on the projection of y onto the column space of the nuisance (i.e. non-test.group) columns
#### distinguishes between cases where we know mu and where we do not (conditioning on additional information when mu is NULL)
#### assumes we know sigma
hit.and.run.samples.multivariate.model <-
function(x, y, groups, test.group, A, b, mu, sigma, hr.iter, hr.burn.in){
n = length(y)

### find P2.tilde -- the projection matrix onto the nuisance columns
nuisance.selector = groups != test.group
if (sum(nuisance.selector) == 0){ # no columns selected in the nuisance groups
if (is.null(mu)){
P2 = matrix (1/n, nrow=n, ncol=n)
}else{
P2 = matrix (0, nrow=n, ncol=n)
}
}else{
if (is.null(mu)){
X2 = cbind(rep(1, n), x[,nuisance.selector,drop=FALSE])
}else{
X2 = x[,nuisance.selector,drop=FALSE]
}
P2 = X2%*%ginv(X2)
}

### constraint matrices
A.row.sum = apply (A, 1, sum)
A.tilde = sigma*A%*%(diag(n) - P2)
if (is.null(mu)){
delta = P2%*%y
b.tilde = b - A%*%delta
y.init = (y - delta)/sigma
}else{
delta = P2%*%(y-mu)
b.tilde = b - mu*A.row.sum - A%*%delta
y.init = (y - mu - delta)/sigma
}

### generate hit-and-run samples for the random part
eps.hr = sigma*rcpp_generate_hit_and_run_samples (num_samples=hr.iter, burn_in=hr.burn.in, init_y = y.init, A=A.tilde, b=b.tilde)
y.hr = eps.hr - P2%*%eps.hr # adjust the covariance matrix

### add back the conditioned on part
y.hr = apply (y.hr, 2, function(col){col + delta}) # add back the projection onto the nuisance columns
if (!is.null(mu)){y.hr = y.hr + mu} # if we have a mean, add it back

return (y.hr)
}
```

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prototest documentation built on May 2, 2019, 4:02 p.m.