Implementation of the Stretch Move

[Noemi Manara]

Hi everyone,

I have a doubt about the implementation of the stretch move: in both Goodman & Weare (2010) and Foreman-Mackey et al. (2013) the density distribution g(z) of the scaling variable Z is chosen as proportional to 1/sqrt(z) with z in the range [1/a, a], with a an arbitrary constant, by default set to 2. 

From what I understand, the sampling of this distribution is implemented in line 30 of "emcee/src/emcee/moves/stretch.py" :

zz = ((self.a - 1.0) * random.rand(Ns) + 1) ** 2.0 / self.a

where the random variable is the z of the papers.

I have a hard time figuring out how to map this expression to one proportional to 1/sqrt(z), even looking at the following lines (31-33), where nothing else seems to happen to the variable zz before the actual move proposal:

factors = (ndim - 1.0) * np.log(zz)
rint = random.randint(Nc, size=(Ns,))
return c[rint] - (c[rint] - s) * zz[:, None], factors

Wouldn't the following edit of line 30 be more consistent with the distribution discussed in the papers? 

Z = random.uniform(1.0/self.a, self.a, Ns)
zz = 1.0 / np.sqrt(Z)

Thank you in advance, any help would be highly appreciated!

Noemi Manara

[Dan Foreman-Mackey]

Here's a notebook showing how you can derive and check this expression: https://gist.github.com/dfm/ed84d7aa9d039d95c42dd105ef5fae6e

Hope this helps!

Dan

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Dan Foreman-Mackey

Research Scientist

Flatiron Institute

https://dfm.io

[Noemi Manara]

Now everything is clear to me, thank you very much!

Noemi

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Noemi Manara

Junior Software Developer, Intern

noemi.manara@akamas.io