Mixture of Gaussian functions

Modeling
6

I think you’re trying to fit what is typically called a non-linear least squares model, not a mixture model.

That should be straightforward in Stan. Something like (untested):

functions {
    real phi(real x, real mu, real sigma){
        return 1 / (sigma * sqrt(2 * pi())) * exp(-(x - mu)^2/(2 * sigma^2)); 
    }
data {
    ...
}
parameters { 
    ordered[2] m; 
    real<lower=0> s[2];

    real<lower=0> sigma; 
}
model {
    // Priors
    ...

    // Likelihood
    for(i in 1:N){
        y[i] ~ normal(phi(x[i], m[1], s[1]) + phi(x[i], m[2], s[2]), sigma); 
    }
}

There’s a lot you can do to speed this up (vectorizing phi() is the obvious thing) and I’d imagine the posterior is a bit difficult, but this should get you started.

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