pymc.find_constrained_prior#

pymc.find_constrained_prior(distribution,lower,upper,init_guess,mass=0.95,fixed_params=None,mass_below_lower=None,**kwargs)[source]#

Find optimal parameters to getmass % of probability of a distribution betweenlower andupper.

Note: only works for one- and two-parameter distributions, as thereare exactly two constraints. Fix some combination of parametersif you want to use it on >=3-parameter distributions.

Parameters:

distributionDistribution

PyMC distribution you want to set a prior on.Needs to have alogcdf method implemented in PyMC.

lowerfloat

Lower bound to getmass % of probability ofpm_dist.

upperfloat

Upper bound to getmass % of probability ofpm_dist.

init_guessdict of {strfloat}

Initial guess forscipy.optimize.least_squares to find theoptimal parameters ofpm_dist fitting the interval constraint.Must be a dictionary with the name of the PyMC distribution’sparameter as keys and the initial guess as values.

massfloat, default 0.95

Share of the probability mass we want betweenlower andupper.Defaults to 95%.

fixed_paramsstr orfloat, optional, defaultNone

Only used whenpm_dist has at least three parameters.Dictionary of fixed parameters, so that there are only 2 to optimize.For instance, for a StudentT, you fix nu to a constant and get the optimizedmu and sigma.

mass_below_lowerfloat, optional, defaultNone

The probability mass below thelower bound. IfNone,defaults to(1-mass)/2, which implies that the probabilitymass below thelower value will be equal to the probabilitymass above theupper value.

Returns:

opt_paramsdict

The optimized distribution parameters as a dictionary.Dictionary keys are the parameter names anddictionary values are the optimized parameter values.

Notes

Optional keyword arguments can be passed tofind_constrained_prior. These will bedelivered to the underlying call toscipy.optimize.minimize().

Examples

# get parameters obeying constraintsopt_params=pm.find_constrained_prior(pm.Gamma,lower=0.1,upper=0.4,mass=0.75,init_guess={"alpha":1,"beta":10})# use these parameters to draw random samplessamples=pm.Gamma.dist(**opt_params,size=100).eval()# use these parameters in a modelwithpm.Model():x=pm.Gamma("x",**opt_params)# specify fixed values before optimizationopt_params=pm.find_constrained_prior(pm.StudentT,lower=0,upper=1,init_guess={"mu":5,"sigma":2},fixed_params={"nu":7},)

Under some circumstances, you might not want to have the same cumulativeprobability below thelower threshold and above theupper threshold.For example, you might want to constrain an Exponential distribution tofind the parameter that yields 90% of the mass below theupper bound,and have zero mass belowlower. You can do that with the following calltofind_constrained_prior

opt_params=pm.find_constrained_prior(pm.Exponential,lower=0,upper=3.0,mass=0.9,init_guess={"lam":1},mass_below_lower=0,)