meridian.model.adstock_hill.transform_non_negative_reals_distribution

Transforms a distribution with support on [0, infinity) to (0, 1].

meridian.model.adstock_hill.transform_non_negative_reals_distribution(
    distribution: backend.tfd.Distribution
) -> backend.tfd.TransformedDistribution

This allows for defining a prior on alpha_*, the exponent of the binomial Adstock decay function, directly, and then translating it to a distribution defined on the unit interval as Meridian expects. This transformation (x -> 1 / (1 + x)) is the inverse of the interval mapping the Meridian performs (x -> 1 / x - 1) on alpha to define the binomial Adstock decay function's exponent.

For example, to define a LogNormal(0.2, 0.9) prior on alpha_*:

from meridian import backend
alpha_star_prior = backend.tfd.LogNormal(0.2, 0.9)
alpha_prior = transform_non_negative_reals_distribution(alpha_star_prior)
prior = prior_distribution.PriorDistribution(
    alpha_m=alpha_prior,
    ...
)

distribution A Tensorflow Probability distribution with support on [0, infinity).

A Tensorflow Probability TransformedDistribution with support on (0, 1], such that the resultant prior on alpha_* is the input distribution.