HillSaturation#

class pymc_marketing.mmm.components.saturation.HillSaturation(priors=None, prefix=None)[source]#

Wrapper around Hill saturation function.

Multiplies pymc_marketing.mmm.transformers.hill_function() by an extra scaling parameter beta so the curve can reach an asymptote other than 1.

Parameters:

slopetensor

Slope of the Hill curve, controlling its steepness. Default prior: Prior("HalfNormal", sigma=1.5).

kappatensor

Half-saturation point where the response equals half its asymptote. Default prior: Prior("HalfNormal", sigma=1.5).

betatensor

Asymptote that the saturated response approaches as the input grows. Default prior: Prior("HalfNormal", sigma=1.5).

.. plot::

context:: close-figs

import matplotlib.pyplot as plt import numpy as np from pymc_marketing.mmm import HillSaturation

rng = np.random.default_rng(0)

adstock = HillSaturation() prior = adstock.sample_prior(random_seed=rng) curve = adstock.sample_curve(prior) adstock.plot_curve(curve, random_seed=rng) plt.show()

Methods

`HillSaturation.__init__`([priors, prefix])
`HillSaturation.apply`(x, *[, core_dim, idx])	Call within a model context.
`HillSaturation.from_dict`(data)	Reconstruct a transformation from a dict.
`HillSaturation.function`(x, slope, kappa, beta, *)	Hill saturation function.
`HillSaturation.plot_curve`(curve[, ...])	Plot curve HDI and samples.
`HillSaturation.plot_curve_hdi`(curve[, ...])	Plot the HDI of the curve.
`HillSaturation.plot_curve_samples`(curve[, ...])	Plot samples from the curve.
`HillSaturation.sample_curve`([parameters, ...])	Sample the curve of the saturation transformation given parameters.
`HillSaturation.sample_prior`([coords])	Sample the priors for the transformation.
`HillSaturation.set_dims_for_all_priors`(dims)	Set the dims for all priors.
`HillSaturation.to_dict`([_orig])	Convert the transformation to a dictionary.
`HillSaturation.update_priors`(priors)	Update the priors for a function after initialization.
`HillSaturation.with_default_prior_dims`(dims)	Return a copy with default prior dims (dims=None) set to `dims` instead.
`HillSaturation.with_updated_priors`(priors)	Return a copy with updated priors.

Attributes

`HillSaturation.combined_dims`	Get the combined dims for all the parameters.
`HillSaturation.default_priors`
`HillSaturation.function_priors`	Get the priors for the function.
`HillSaturation.model_config`	Mapping from variable name to prior for the model.
`HillSaturation.prefix`
`HillSaturation.priors`	Get the priors for the function.
`HillSaturation.requires_unscaled_input`	Whether the saturation must receive raw (unscaled) channel inputs.
`HillSaturation.variable_mapping`	Mapping from parameter name to variable name in the model.