Adds 3 new nested columns to the input_df: `beta_params`, `gamma_params`, and `samples` `beta_params` and `gamma_params` in each row should be a tibble of length 2 (\(\alpha\) and \(\beta\) parameters and \(k\) and \(\theta\) parameters) `samples` in each row should be a tibble of length `n_samples`
sample_cpa(input_df, priors, n_samples = 50000)input_df with 3 new nested columns `beta_params`, `gamma_params`, and `samples`
Dataframe containing option_name (str), sum_conversions (dbl), sum_cost (dbl), and sum_clicks (dbl).
Optional list of priors alpha0, beta0 for Beta and k0, theta0 for Gamma. Default \(Beta(1,1)\) and \(Gamma(1, 250)\) will be use otherwise.
Optional integer value. Defaults to 50,000 samples.
See update_rules vignette for a mathematical representation. This is a combination of a Beta-Bernoulli update and a Gamma-Exponential update.
$$conversion_i ~ Bernoulli(\phi)$$ $$cpc_i ~ Exponential(\lambda)$$ $$\phi ~ Beta(\alpha, \beta)$$ $$\lambda ~ Gamma(k, \theta)$$
$$cpa_i ~ 1/ (Bernoulli(\phi) * Exponential(\lambda))$$ $$averageCPA ~ 1/(\phi\lambda)$$
Conversion Rate is sampled from a Beta distribution with a Binomial likelihood of an individual converting.
Average CPC is sampled from a Gamma distribution with an Exponential likelihood of an individual cost.