calibrate_ER.nonsquare: Calibrate ER model to a given density with a nonsquare matrix
In systemicrisk: A Toolbox for Systemic Risk

Description Usage Arguments Value Examples

The model is an Erdos-Renyi model for the existence of links (a link exists independently of other links with a fixed probability) and the weight of each existing link follows an exponential distribution with a fixed rate parameter. This function chooses the two parameters such that the density of the network (the average proportion of existing links) is a certain desired value. This function does not set diagonal values to 0.

1 2	calibrate_ER.nonsquare(l, a, targetdensity, L_fixed = NA, nsamples_calib = 100, thin_calib = 100)

`l`	row sums of matrix to be reconstructed
`a`	column sum of matrix to be reconstructed
`targetdensity`	desired proportion of reconstructed entries to be positive
`L_fixed`	Matrix containing known values of L, where NA signifies that an element is not known. If `L_fixed` equates to `NA` (the default) then no values are assumed to be known.
`nsamples_calib`	number of matrices to generate during calibration.
`thin_calib`	amount of thinning to use during calibration

Model that can be used to generate the desired samples using sample_HierarchicalModel.

## first generate a true network
nrow <- 10 # size of network
ncol <- 8 # size of network
p <- 0.45
lambda <- 0.1
L <- matrix(nrow=nrow,rbinom(nrow*ncol,prob=p,size=1)*rexp(nrow*ncol,rate=lambda))

# then reconstruct with a target density of 0.55
model <- calibrate_ER.nonsquare(l=rowSums(L),a=colSums(L),
                      targetdensity=0.55,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),model=model,
                                    nsamples=10,thin=1e2)
# check row sums
rowSums(L)
rowSums(Lsamp$L[[10]])
# check calibration
mean(Lsamp$L[[10]]>0)

# now an example with some fixed entries
L_fixed <- L
L_fixed[1:(nrow/2),] <- NA
# then reconstruct with a target density of 0.9
model <- calibrate_ER.nonsquare(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
                              targetdensity=0.9,nsamples_calib=10)
Lsamp <- sample_HierarchicalModel(l=rowSums(L),a=colSums(L),L_fixed=L_fixed,
                                  model=model,nsamples=10,thin=1e2)
mean(Lsamp$L[[10]][-(1:(nrow/2)),]>0) # known entries
mean(Lsamp$L[[10]][(1:(nrow/2)),]>0)  #reconstructed entries