map estimate of Pareto falls outside support

[grinsted]

Description of your problem

The map estimate of the Pareto falls outside the support for the distribution.

minimal example.

import pymc3 as pm
testmodel = pm.Model()
with testmodel:
    q = pm.Pareto('q',alpha=1,m=10)

map_estimate = pm.find_MAP(model=testmodel, start={'q':11})
map_estimate

output

{'q_log__': array(1.3978952727983707), 'q': array(4.046673852885866)}

This cannot be right as the Pareto distribution is zero below the m-value. https://docs.pymc.io/api/distributions/continuous.html#pymc3.distributions.continuous.Pareto

• PyMC3 Version: 3.4.1
• Theano Version: 1.0.1
• Python Version: 3.6.5

[grinsted]

Is this a bug or am i misunderstanding something?

[grinsted]

@junpenglao posted a solution/workaround which can be found on discourse: https://discourse.pymc.io/t/how-do-i-use-the-pareto-distribution/1425