Problem in Using target += function

Modeling
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1

Hi everyone,

I am trying to predict the failure probability as a part of structural reliability analysis. I want to use bayesian concept to predict the failure probability thus considering the joint distribution of influence paremeters directly in the failure surface. I tried first to use a very simple example with hypothetical values to see if the concept works or not then I devlope the original concept. This is my problem:

simple there is a failure surface G = x - y[i] while x is an uncertain parameter and y is the observation. I want to estimate the probability the G<0. I used target function in stan to tranfoming the G values to an increment log sacle and then in generate quantities tried to predic the posterior of G<0. one i use hypothetic data, surpring i see that always for all cases the values are G<0 no matter what value i use!! here is my simple code:

data {
  int<lower=0> N;       // Number of inputs
  vector[N] y;          // Inputs for y
}

parameters {
  real x;               // Parameter a
}

model {
  // Prior distribution for parameters a and b

  x ~ normal(0.5, 0.1); // Specify prior distribution for b

  for (i in 1:N) {
    real G = x - y[i];
    target += if_else(G < 0, 0, negative_infinity()); // Increment the log density when G < 0
  }
}

generated quantities {
  int<lower=0, upper=1> G_less_than_zero[N];  // Indicator variable for G < 0

  // Compute indicator variable
  for (i in 1:N) {
    real G = x - y[i];
    G_less_than_zero[i] = (G < 0) ? 1 : 0;
  }
}

i used these values to test the code:

N <- 100
y <- rnorm(N, mean = 0.4, sd = 0.1)

# Fit the Stan model to the data
fit <- sampling(stan_model, data = list(N = N, y = y))

# Extract the posterior samples for G_less_than_zero and G
G_less_than_zero_samples <- extract(fit)$G_less_than_zero
G_samples <- extract(fit)$G

# Compute the posterior probability that G < 0
posterior_prob_G_less_than_zero <- mean(G_less_than_zero_samples)

# Plot the posterior distribution for G < 0
hist(G_less_than_zero_samples, main = "Posterior Distribution for G < 0", xlab = "G < 0")

# Plot the posterior distribution for G
hist(G_samples, main = "Posterior Distribution for G", xlab = "G")

I will be thankful if you kindly advice me if I am doing wrong in using target function and have your valubale advice to solve the issue.

2

I’m not sure what you’re trying to do, but this:

target += if_else(G < 0, 0, negative_infinity());

is going to cause the sampler to reject the current proposal if G < 0. Maybe you want to just impose a penalty? Or not constrain at all and just count in generated quantities?

P.S. The more idiomatic way to code the target increment is

target += G < 0 ? 0 : negative_infinity();

or

if (G < 0)
  target += negative_infinity();

P.P.S. Rather than this,

  real x;               // Parameter a

I’d suggest just naming the parameter a.

  real a;