Nothing
minimal_model_MRMC3 <- function() {
# Make a dataset
# modality ID
m <-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3
,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5
,5,5,5,5,5,5,5,5,5,5,5,5)
# reader ID
q <-c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1
,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2
,2,2,3,3,3,3,3,4,4,4,4,4)
# confidence level
c<-c(5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2
,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3
,2,1,5,4,3,2,1,5,4,3,2,1)
# FP ( false alarm)
f<-c(
0,4,20,29,21,0,0,6,15,22,1,15,18,31,19,1,2,4,16,17,1,1,21,24,23,1,1,5,30
,40,2,19,31,56,42,2,0,2,30,32,1,7,13,28,19,0,1,7,7,31,7,15,28,41,9,0,2,5
,24,31,1,4,18,21,23,1,1,0,11,35,6,14,37,36,18,0,2,4,18,25,0,2,19,23,18,0,2
,6,10,30,2,25,40,29,24,1,1,4,24,32
)
# TP (hit)
h<-c(
50,30,11,5,1,15,29,29,1,0,39,31,8,10,3,10,8,25,45,14,52,25,13,4,1,27,28,29,1
,0,53,29,13,2,4,9,16,22,43,14,43,29,11,6,0,18,29,21,0,0,43,29,6,7,1,10,14,19
,32,23,61,19,12,9,3,16,29,34,1,0,52,29,10,4,3,10,16,23,43,15,35,29,18,9,0,17,27
,24,0,0,34,33,7,13,2,12,16,21,35,15
)
C<-5 # the number of confidence levels
M<-5 # the number of modalities
Q<-4 # the number of readers
NI<-199 # the number of images
NL<-142 # the number of lesions
# the length of the dataset
N <-C*M*Q
# make an array format hits data
ff <- numeric(N) #Initialization of Cumulative False alarm
harray<-array(0,dim=c(C,M,Q));
for(md in 1:M) {
for(cd in 1:C) {
for(qd in 1 : Q){
for(n in 1:cd){
ff[cd+(md-1)*C*Q+(qd-1)*C]<-ff[cd+(md-1)*C*Q+(qd-1)*C]+f[n+(md-1)*C*Q+(qd-1)*C]
}
harray[cd,md,qd] <- h[cd+(md-1)*C*Q+(qd-1)*C]
}}}
# make a data to be passed to sampling()
data <- list(N=N,Q=Q, M=M,m=m ,C=C , NL=NL,NI=NI
,c=c,q=q,
h=h, f=f,
ff=ff,
harray=harray
)
# Make a Stan model
Stan.model <- rstan::stan_model( model_code="
data{
int <lower=0>N;
int <lower=0>M;
int <lower=0>C;
int <lower=0>Q;
int <lower=0>h[N];
int <lower=0>f[N];
int <lower=0>q[N];
int <lower=0>c[N];
int <lower=0>m[N];
int <lower=0>NL;
int <lower=0>NI;
int <lower=0>ff[N];
int <lower=0>harray[C,M,Q];
int ModifiedPoisson;
}
transformed data {
int <lower=0> NX;
if(ModifiedPoisson==0) NX = NI;
if(ModifiedPoisson==1) NX =NL;
}
parameters{
real w;
real <lower =0 > dz[C-1];
real mu[M,Q];
real <lower=0> v[M,Q];
}
transformed parameters {
real <lower =0> dl[C];
real <lower=0,upper=1> ppp[C,M,Q];
real <lower =0> l[C];
real z[C];
real aa[M,Q];
real <lower =0> bb[M,Q];
real <lower=0,upper=1> AA[M,Q];
real deno[C-1,M,Q];
real hit_rate[C,M,Q];
real <lower=0,upper=1>A[M];
z[1]=w;
for(md in 1 : M) {
for(qd in 1 : Q) {
aa[md,qd]=mu[md,qd]/v[md,qd];
bb[md,qd]=1/v[md,qd];
for(cd in 1 : C-1) z[cd+1] = z[cd] + dz[cd];
ppp[C,md,qd] = 1- Phi((z[C] -mu[md,qd])/v[md,qd]);
for(cd in 1 : C-1) ppp[cd,md,qd] = Phi((z[cd+1] -mu[md,qd])/v[md,qd]) - Phi((z[cd ] -mu[md,qd])/v[md,qd]);
for(cd in 1 : C) l[cd] = (-1)*log(Phi(z[cd]));
dl[C] = fabs(l[C]-0);
for(cd in 1:C-1) dl[cd]= fabs(l[cd]-l[cd+1]);
}
}
for(md in 1 : M) {
for(qd in 1 : Q) {
AA[md,qd]=Phi( (mu[md,qd]/v[md,qd])/sqrt((1/v[md,qd])^2+1) );//Measures of modality performance
}}
for(md in 1 : M) {
A[md] = 0;
for(qd in 1 : Q) {
A[md] = A[md] + AA[md,qd];
}
A[md]= A[md]/M;
}
for(md in 1 : M) {
for(qd in 1 : Q) {
deno[C-1,md,qd]=1-ppp[C,md,qd];
for(cd in 3:C){ deno[c[cd],md,qd]=deno[c[cd-1],md,qd]-ppp[c[cd-1],md,qd]; }
}}
for(md in 1 : M) {
for(qd in 1 : Q) {
for(cd in 1:C-1){
hit_rate[cd,md,qd]=ppp[cd,md,qd]/deno[cd,md,qd];
}
hit_rate[C,md,qd]=ppp[C,md,qd];
}}
}
model{
int s=0;
for(n in 1:N) {
target += poisson_lpmf(ff[n]|l[c[n]]*NX);
}
for(qd in 1 : Q) {
for(md in 1 : M) {
s=0;
for(cd in 1 : C){
target += binomial_lpmf(harray[cd,md,qd] | NL-s, hit_rate[c[cd],md,qd] );
s = s + harray[cd,md,qd]; }
}}
w ~ uniform(-3,3);
for(cd in 1:C-1) dz[cd] ~ uniform(0.001,7);
for(md in 1 : M) { for(qd in 1 : Q) {
mu[md,qd] ~ uniform(-11,11);
v[md,qd] ~ uniform(0.01,11);
}}
}
")
# Fit a model to data
fit <- rstan::sampling(
object= Stan.model, data=data, verbose = FALSE,
seed=1234567, chains=1, warmup=111, iter=1111
, control = list(adapt_delta = 0.9999999,
max_treedepth = 15)
# ,init = initial
)
rstan::traceplot(fit,pars=c("w"))
rstan::check_hmc_diagnostics(fit)
}#function
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