def pymc_objective(objective):
"""
Creates a pymc3 model from an Objective. Will not be able to use the NUTS
sampler because gradients aren't evaluable.
Requires theano and pymc3 be installed. This is an experimental feature.
Parameters
----------
objective: refnx.analysis.Objective
Returns
-------
model: pymc3.Model
Notes
-----
The varying parameters are renamed 'p0', 'p1', etc, as it's vital in pymc3
that all parameters have their own unique name.
"""
import pymc3 as pm
import theano.tensor as T
from theano.compile.ops import as_op
basic_model = pm.Model()
wrapped_obj = _pymc_objective_wrapper(objective)
pars = objective.varying_parameters()
wrapped_pars = []
with basic_model:
# Priors for unknown model parameters
for i, par in enumerate(pars):
name = 'p%d' % i
p = _to_pymc3_distribution(name, par)
wrapped_pars.append(p)
# Expected value of outcome
try:
v = wrapped_obj(*wrapped_pars)
except Exception:
print("Falling back, theano autodiff won't work on function"
" object")
o = as_op(itypes=[T.dscalar] * len(pars),
otypes=[T.dvector])(wrapped_obj)
v = o(*wrapped_pars)
# Likelihood (sampling distribution) of observations
y_obs = pm.Normal('Y_obs',
mu=v,
sd=objective.data.y_err,
observed=objective.data.y)
if not y_obs:
return None
return basic_model
def _to_pymc3_distribution(name, par):
"""
Create a pymc3 continuous distribution from a Bounds object.
Parameters
----------
name : str
Name of parameter
par : refnx.analysis.Parameter
The parameter to wrap
Returns
-------
d : pymc3.Distribution
The pymc3 distribution
"""
import pymc3 as pm
import theano.tensor as T
from theano.compile.ops import as_op
dist = par.bounds
# interval and both lb, ub are finite
if (isinstance(dist, Interval) and
np.isfinite([dist.lb, dist.ub]).all()):
return pm.Uniform(name, dist.lb, dist.ub)
# no bounds
elif (isinstance(dist, Interval) and
np.isneginf(dist.lb) and
np.isinf(dist.lb)):
return pm.Flat(name)
# half open uniform
elif isinstance(dist, Interval) and not np.isfinite(dist.lb):
return dist.ub - pm.HalfFlat(name)
# half open uniform
elif isinstance(dist, Interval) and not np.isfinite(dist.ub):
return dist.lb + pm.HalfFlat(name)
# it's a PDF
if isinstance(dist, PDF):
dist_gen = getattr(dist.rv, 'dist', None)
if isinstance(dist.rv, stats.rv_continuous):
dist_gen = dist.rv
if isinstance(dist_gen, type(stats.uniform)):
if hasattr(dist.rv, 'args'):
p = pm.Uniform(name, dist.rv.args[0],
dist.rv.args[1] + dist.rv.args[0])
else:
p = pm.Uniform(name, 0, 1)
return p
# norm from scipy.stats
if isinstance(dist_gen, type(stats.norm)):
if hasattr(dist.rv, 'args'):
p = pm.Normal(name, mu=dist.rv.args[0], sd=dist.rv.args[1])
else:
p = pm.Normal(name, mu=0, sd=1)
return p
# not open, uniform, or normal, so fall back to DensityDist.
d = as_op(itypes=[T.dscalar], otypes=[T.dscalar])(dist.logp)
r = as_op(itypes=[T.dscalar], otypes=[T.dscalar])(dist.rvs)
p = pm.DensityDist(name, d, random=r)
return p