# Rejecting initial value: Log probability evaluates to log(0), i.e. negative infinity

Hello!
The error message “Rejecting initial value: Log probability evaluates to log(0), i.e. negative infinity.” came when I tried to run this Stan code … :(

Anyone who knows the reason?

``````data {
int<lower=1> N;
int<lower=1> T;
int<lower=1, upper=T> Tsubj[N];
int<lower=-1, upper=1> gamble[N, T];
int<lower=-2, upper=1> type[N, T];
real cert[N, T];
real<lower=0> gain[N, T];
real<lower=0> loss[N, T];
int<lower=-5,upper=5> happy[N,T];
}
transformed data {
}
parameters {
vector[5] mu_p;
vector<lower=0>[5] sigma;
vector[N] rho_p;
vector[N] lambda_p;
vector[N] tau_p;
vector[N] alpha_p;
vector[N] beta_p;
}
transformed parameters {
vector<lower=0, upper=2>[N] rho;
vector<lower=0, upper=5>[N] lambda;
vector<lower=0>[N] tau;
vector<lower=0, upper=1>[N] alpha;
vector<lower=0, upper=1>[N] beta;

for (i in 1:N) {
rho[i]    = Phi_approx(mu_p[1] + sigma[1] * rho_p[i]) * 2;
lambda[i] = Phi_approx(mu_p[2] + sigma[2] * lambda_p[i]) * 5;
alpha[i] = Phi_approx(mu_p[4] + sigma[4] * alpha_p[i]);
beta[i] = Phi_approx(mu_p[5] + sigma[5] * beta_p[i]);
}
tau = exp(mu_p[3] + sigma[3] * tau_p);
}
model {
mu_p  ~ normal(0, 1.0);
sigma ~ normal(0, 0.2);

rho_p    ~ normal(0, 1.0);
lambda_p ~ normal(0, 1.0);
tau_p    ~ normal(0, 1.0);
alpha_p ~ normal(0, 1.0);
beta_p ~ normal(0, 1.0);

for (i in 1:N) {
for (t in 1:Tsubj[i]) {
real evSafe;
real evGamble;
real pGamble;

if(type[i, t] == -1){
if(happy[i,t] < 0){
evSafe = -lambda[i] * pow(cert[i,t],rho[i]*(1+(-happy[i,t]*alpha[i])));
} if(happy[i,t] == 0){
evSafe = -lambda[i] * pow(cert[i, t], rho[i]);
} else {
evSafe = -lambda[i] * pow(cert[i, t], rho[i]*(1-(happy[i,t]*alpha[i])));
}
} else {
if(happy[i,t] < 0){
evSafe = pow(cert[i,t],rho[i]*(1+(-happy[i,t]*alpha[i])));
} if(happy[i,t] == 0){
evSafe   = pow(cert[i, t], rho[i]);
} else {
evSafe   = pow(cert[i,t],rho[i]*(1-(happy[i,t]*alpha[i])));
}
}

if(happy[i,t] < 0){
evGamble = 0.5 * (pow(gain[i, t], rho[i]*(1-(-happy[i,t]*beta[i]))) - lambda[i] * pow(loss[i, t], rho[i]*(1-(-happy[i,t]*beta[i]))));
} if(happy[i,t] == 0){
evGamble = 0.5 * (pow(gain[i, t], rho[i]) - lambda[i] * pow(loss[i, t], rho[i]));
} else {
evGamble = 0.5 * (pow(gain[i, t], rho[i]*(1+(happy[i,t]*beta[i]))) - lambda[i] * pow(loss[i, t], rho[i]*(1+(happy[i,t]*beta[i]))));
}
pGamble  = inv_logit(tau[i] * (evGamble - evSafe));
gamble[i, t] ~ bernoulli(pGamble);
}
}
}

generated quantities {
real<lower=0, upper=2> mu_rho;
real<lower=0, upper=5> mu_lambda;
real<lower=0>         mu_tau;
real<lower=0,upper=1> mu_alpha;
real<lower=0,upper=1> mu_beta;

real log_lik[N];

// For posterior predictive check
real y_pred[N, T];

// Set all posterior predictions to 0 (avoids NULL values)
for (i in 1:N) {
for (t in 1:T) {
y_pred[i, t] = -1;
}
}

mu_rho    = Phi_approx(mu_p[1]) * 2;
mu_lambda = Phi_approx(mu_p[2]) * 5;
mu_tau    = exp(mu_p[3]);
mu_alpha  = Phi_approx(mu_p[4]);
mu_beta = Phi_approx(mu_p[5]);

{ // local section, this saves time and space
for (i in 1:N) {
log_lik[i] = 0;
for (t in 1:Tsubj[i]) {
real evSafe;
real evGamble;
real pGamble;

if(type[i, t] == -1){
if(happy[i,t] < 0){
evSafe = -lambda[i] * pow(cert[i,t],rho[i]*(1+(-happy[i,t]*alpha[i])));
} if(happy[i,t] == 0){
evSafe = -lambda[i] * pow(cert[i, t], rho[i]);
} else {
evSafe = -lambda[i] * pow(cert[i, t], rho[i]*(1-(happy[i,t]*alpha[i])));
}
} else {
if(happy[i,t] < 0){
evSafe = pow(cert[i,t],rho[i]*(1+(-happy[i,t]*alpha[i])));
} if(happy[i,t] == 0){
evSafe   = pow(cert[i, t], rho[i]);
} else {
evSafe   = pow(cert[i,t],rho[i]*(1-(happy[i,t]*alpha[i])));
}
}

if(happy[i,t] < 0){
evGamble = 0.5 * (pow(gain[i, t], rho[i]*(1-(-happy[i,t]*beta[i]))) - lambda[i] * pow(loss[i, t], rho[i]*(1-(-happy[i,t]*beta[i]))));
} if(happy[i,t] == 0){
evGamble = 0.5 * (pow(gain[i, t], rho[i]) - lambda[i] * pow(loss[i, t], rho[i]));
} else {
evGamble = 0.5 * (pow(gain[i, t], rho[i]*(1+(happy[i,t]*beta[i]))) - lambda[i] * pow(loss[i, t], rho[i]*(1+(happy[i,t]*beta[i]))));
}
pGamble    = inv_logit(tau[i] * (evGamble - evSafe));
log_lik[i] = log_lik[i] + bernoulli_lpmf(gamble[i, t] | pGamble);

// generate posterior prediction for current trial
y_pred[i, t] = bernoulli_rng(pGamble);
}
}
}
}
``````

you can put the print statement, and check what is wrong in your program