R/sample_total_cm.R

In grizbayr: Bayesian Inference for A|B and Bandit Marketing Tests

#' Sample Total CM (Given Impression Count)
#'
#' @description
#' Adds 4 new nested columns to the input_df: `beta_params_ctr`,
#' `beta_params_conv`,`gamma_params_rev`, `gamma_params_cost`
#' and `samples`.
#'
#' @details
#'`beta_params` and `gamma_params` in each row should be a tibble of length 2
#' (\eqn{\alpha} and \eqn{\beta} params and \eqn{k} and \eqn{\theta} params).
#'`samples` in each row should be a tibble of length `n_samples`.
#'
#' One assumption in this model is that sum_impressions is not stochastic.
#' This assumes that Clicks are stochastically generated from a set number
#' of Impressions. It does not require that the number of impressions are
#' equal on either side. Generally this assumption holds true in marketing
#' tests where traffic is split 50/50 and very little variance is observed
#' in the number of impressions on either side.
#'
#'
#' See update_rules vignette for a mathematical representation.
#'
#' \deqn{TotalCM = Impr * ExpectedCTR * (RevPerOrder * OrdersPerClick - ExpectedCPC)}
#'
#'
#' @param input_df Dataframe containing option_name (str),
#'     sum_conversions (dbl), sum_revenue (dbl), and sum_clicks (dbl).
#' @param priors Optional list of priors {alpha0, beta0} for Beta,
#'     {k0, theta0} for Gamma Inverse Revenue, and {k01, theta01} for
#'     Gamma Cost (uses alternate priors so they can be different from Revenue).
#'     Default \eqn{Beta(1,1)} and \eqn{Gamma(1, 250)} will be use otherwise.
#' @param n_samples Optional integer value. Defaults to 50,000 samples.
#'
#' @importFrom purrr pmap map2
#' @importFrom dplyr mutate select %>%
#' @importFrom stats rgamma rbeta
#' @importFrom rlang .data
#'
#' @return input_df with 5 new nested columns `beta_params_conv`,
#'     `beta_params_ctr`, `gamma_params_rev`,`gamma_params_cost`,
#'     and `samples`
#'
sample_total_cm <- function(input_df, priors, n_samples = 5e4){
  input_df %>%
    dplyr::mutate(
      beta_params_conv = purrr::map2(.x = .data$sum_conversions,
                                     .y = .data$sum_clicks,
                                     ~ update_beta(alpha = .x,
                                                   beta = .y - .x,
                                                   priors = priors)
      ),
      beta_params_ctr = purrr::map2(.x = .data$sum_clicks,
                                    .y = .data$sum_impressions,
                                    ~ update_beta(alpha = .x,
                                                  beta = .y - .x,
                                                  priors = priors)
      ),
      gamma_params_rev = purrr::map2(.x = .data$sum_conversions,
                                     .y = .data$sum_revenue,
                                     ~ update_gamma(k = .x,
                                                    theta = .y,
                                                    priors = priors)
      ),
      gamma_params_cost = purrr::map2(.x = .data$sum_clicks,
                                      .y = .data$sum_cost,
                                      ~ update_gamma(k = .x,
                                                     theta = .y,
                                                     priors = priors,
                                                     alternate_priors = TRUE)
      ),
      rev_per_click_samples = purrr::map2(.x = .data$beta_params_conv,
                                          .y = .data$gamma_params_rev,
                                          ~ stats::rbeta(n_samples,
                                                         shape1 = .x$alpha,
                                                         shape2 = .x$beta) /
                                            stats::rgamma(n_samples,
                                                          shape = .y$k,
                                                          scale = .y$theta)
      ),
      cost_per_click_samples = purrr::map(.x = .data$gamma_params_cost,
                                          ~ 1 / stats::rgamma(n_samples,
                                                              shape = .x$k,
                                                              scale = .x$theta)
      ),
      expected_clicks_rates = purrr::map(.x = .data$beta_params_ctr,
                                            ~ stats::rbeta(n_samples,
                                                           shape1 = .x$alpha,
                                                           shape2 = .x$beta)
      ),
      # Expected CTR samples Times Fixed Impressions
      expected_clicks_samples = purrr::map2(.x = .data$expected_clicks_rates,
                                            .y = .data$sum_impressions,
                                             ~ .x * .y),
      samples = purrr::pmap(list(rev_per_click = .data$rev_per_click_samples,
                                 cost_per_click = .data$cost_per_click_samples,
                                 expected_clicks = .data$expected_clicks_samples),
                            ~ calculate_total_cm(...)
      )
    ) %>%
    dplyr::select(
      -"rev_per_click_samples",
      -"cost_per_click_samples",
      -"expected_clicks_rates",
      -"expected_clicks_samples",
      )
}