calibrate_ER {systemicrisk}

Calibrate ER model to a given density

Description

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. Diagonal elements are being set to 0.

Usage

calibrate_ER(
  l,
  a,
  targetdensity,
  L_fixed = NA,
  nsamples_calib = 100,
  thin_calib = 100
)

Arguments

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

Value

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

Examples

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

# then reconstruct with a target density of 0.55
model <- calibrate_ER(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:(n/2),] <- NA
# then reconstruct with a target density of 0.9
model <- calibrate_ER(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$L[[10]][-(1:(n/2)),]>0) # known entries
mean(Lsamp$L[[10]][(1:(n/2)),]>0)  #reconstructed entries