Von_mises documentation suggestion

General
15

Again thanks.
Here is an example of working code for a von Mises distribution, using the unit vector.
It eats periodic data. It gives you an angle from -pi to pi for the centre.
It does not ask you to tolerate multi-model posteriors and stan’s convergence statistics remain meaningful.
It allows you to put a von Mises prior on mu, the distribution centre.
It does not need a jacobian correction. The prior is a wrapper which acts on the unit vector directly.
it is suitable for vegans

functions {
    real von_mises_prior_lpdf (vector in_vec, real mu, real kappa) {
        real angle = atan2(in_vec[2], in_vec[1]);
        return (von_mises_lpdf (angle| mu, kappa));
    }
}

data {
    int NP;
    vector [NP] angles;
}

parameters {
    unit_vector [2] mu_vec;
    real <lower = 0> kappa;
}

transformed parameters {
    real mu = atan2(mu_vec[2], mu_vec[1]);
}

model {
    kappa ~  normal (4, 3);  // My kappa's are not more than 7 or 8
    mu_vec ~ von_mises_prior (3, 1);  // prior, centred on 3, kappa = 1
    angles ~ von_mises (mu, kappa);
}

Imagine you are working with a simple von Mises distribution.
Is there any reason not to do it this way routinely ?

This thread started with a suggestion for the manual. This version is better, but maybe it is too long. Maybe it is overkill for just fitting to circular data, when convergence is not an issue and you don’t mind unwrapping your posteriors. If this is going into part of a model with more terms, then I think it is important.

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