BetaGeoBetaBinomModel

class pymc_marketing.clv.models.beta_geo_beta_binom.BetaGeoBetaBinomModel(data=None, *, model_config=None, sampler_config=None)

Beta-Geometric/Beta-Binomial Model (BG/BB).

CLV model for non-contractual, discrete purchase opportunities, introduced by Fadel et al. [1].

The BG/BB model assumes the probability a customer will become inactive follows a Beta distribution, and the probability of making a purchase is also Beta-distributed while customers are still active.

This model requires data to be summarized by recency, frequency, and T for each customer. T should be the same value across all customers.

Parameters:

dataDataFrame

DataFrame containing the following columns:

• customer_id: Unique customer identifier

• frequency: Number of repeat purchases

• recency: Purchase opportunities between the first and the last purchase

• T: Total purchase opportunities. Model assumptions require T >= recency and all customers share the same value for *T.

model_configdict, optional

Dictionary containing model parameters:

• alpha: Shape parameter of purchase process; defaults to phi_purchase * kappa_purchase

• beta: Shape parameter of purchase process; defaults to 1-phi_purchase * kappa_purchase

• gamma: Shape parameter of dropout process; defaults to phi_purchase * kappa_purchase

• delta: Shape parameter of dropout process; defaults to 1-phi_dropout * kappa_dropout

• phi_purchase: Nested prior for alpha and beta priors; defaults to Prior("Uniform", lower=0, upper=1)

• kappa_purchase: Nested prior for alpha and beta priors; defaults to Prior("Pareto", alpha=1, m=1)

• phi_dropout: Nested prior for gamma and delta priors; defaults to Prior("Uniform", lower=0, upper=1)

• kappa_dropout: Nested prior for gamma and delta priors; defaults to Prior("Pareto", alpha=1, m=1)

If not provided, the model will use default priors specified in the default_model_config class attribute.

sampler_configdict, optional

Dictionary of sampler parameters. Defaults to None.

References

[1]

Peter Fader, Bruce Hardie, and Jen Shang. “Customer-Base Analysis in a Discrete-Time Noncontractual Setting”. Marketing Science, Vol. 29, No. 6 (Nov-Dec, 2010), pp. 1086-1108. https://www.brucehardie.com/papers/020/fader_et_al_mksc_10.pdf

Examples

import pymc as pm

from pymc_extras.prior import Prior
from pymc_marketing.clv import BetaGeoBetaBinomModel

rfm_df = rfm_summary(raw_data, "id_col_name", "date_col_name")

# Initialize model with customer data; `model_config` parameter is optional
model = BetaGeoBetaBinomModel(
    model_config={
        "alpha": Prior("HalfFlat"),
        "beta": Prior("HalfFlat"),
        "gamma": Prior("HalfFlat"),
        "delta": Prior("HalfFlat"),
    },
)

# Fit model quickly to large datasets via Maximum a Posteriori
model.fit(data=rfm_df, fit_method="map")
print(model.fit_summary())

# Fit with the default 'mcmc' for more informative predictions and reliable performance on smaller datasets
model.fit(fit_method="mcmc")
print(model.fit_summary())

# Predict number of purchases for customers over the next 10 time periods
expected_purchases = model.expected_purchases(
    data=rfm_df,
    future_t=10,
)

# Predict probability of customer making 'n' purchases over 't' time periods
# Data parameter is omitted here because predictions are ran on original dataset
expected_num_purchases = model.expected_purchase_probability(
    n=[0, 1, 2, 3],
    future_t=[10, 20, 30, 40],
)

new_data = pd.DataFrame(
    data={
        "customer_id": [0, 1, 2, 3],
        "frequency": [5, 2, 1, 8],
        "recency": [7, 4, 2.5, 11],
        "T": [10, 8, 10, 22],
    }
)

# Predict probability customers will still be active in 'future_t' time periods
probability_alive = model.expected_probability_alive(
    data=new_data,
    future_t=[0, 3, 6, 9],
)

# Predict number of purchases for a new customer over 't' time periods.
expected_purchases_new_customer = model.expected_purchases_new_customer(
    t=[2, 5, 7, 10],
)

Methods

BetaGeoBetaBinomModel.__init__([data, ...])	Initialize model configuration and sampler configuration for the model.
BetaGeoBetaBinomModel.attrs_to_init_kwargs(attrs)	Convert the model configuration and sampler configuration from the attributes to keyword arguments.
BetaGeoBetaBinomModel.build_from_idata(idata)	Build the model from the InferenceData object.
BetaGeoBetaBinomModel.build_model([data])	Build the model.
BetaGeoBetaBinomModel.create_idata_attrs()	Create attributes for the inference data.
BetaGeoBetaBinomModel.distribution_new_customer_dropout([...])	Sample from the Beta distribution representing dropout probabilities for new customers.
BetaGeoBetaBinomModel.distribution_new_customer_purchase_rate([...])	Sample from the Beta distribution representing purchase probabilities for new customers.
BetaGeoBetaBinomModel.distribution_new_customer_recency_frequency([...])	BG/BB process representing purchases across the customer population.
BetaGeoBetaBinomModel.expected_probability_alive([...])	Predict expected probability of being alive.
BetaGeoBetaBinomModel.expected_purchases([...])	Predict expected number of future purchases.
BetaGeoBetaBinomModel.expected_purchases_new_customer([...])	Predict the expected number of purchases for a new customer across t time periods.
BetaGeoBetaBinomModel.fit([data, method, ...])	Infer model posterior.
BetaGeoBetaBinomModel.fit_summary(**kwargs)	Compute the summary of the fit result.
BetaGeoBetaBinomModel.graphviz(**kwargs)	Get the graphviz representation of the model.
BetaGeoBetaBinomModel.idata_to_init_kwargs(idata)	Create the initialization kwargs from an InferenceData object.
BetaGeoBetaBinomModel.load(fname[, check])	Create a ModelBuilder instance from a file.
BetaGeoBetaBinomModel.load_from_idata(idata)	Create a ModelBuilder instance from an InferenceData object.
BetaGeoBetaBinomModel.save(fname, **kwargs)	Save the model's inference data to a file.
BetaGeoBetaBinomModel.set_idata_attrs([idata])	Set attributes on an InferenceData object.
BetaGeoBetaBinomModel.table(**model_table_kwargs)	Get the summary table of the model.
BetaGeoBetaBinomModel.thin_fit_result(keep_every)	Return a copy of the model with a thinned fit result.

Attributes

default_model_config	Default model configuration.
default_sampler_config	Default sampler configuration.
fit_result	Get the posterior fit_result.
id	Generate a unique hash value for the model.
posterior
posterior_predictive
predictions
prior
prior_predictive
version
idata
sampler_config
model_config