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# Copyright 2017-2020 Spotify AB 

# 

# Licensed under the Apache License, Version 2.0 (the "License"); 

# you may not use this file except in compliance with the License. 

# You may obtain a copy of the License at 

# 

# http://www.apache.org/licenses/LICENSE-2.0 

# 

# Unless required by applicable law or agreed to in writing, software 

# distributed under the License is distributed on an "AS IS" BASIS, 

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 

# See the License for the specific language governing permissions and 

# limitations under the License. 

 

from collections import OrderedDict 

 

import chartify 

import numpy as np 

import pandas as pd 

from scipy.stats import beta 

 

from spotify_confidence.analysis.bayesian.bayesian_base import BaseTest, \ 

randomization_warning_decorator, axis_format_precision 

 

 

class BetaBinomial(BaseTest): 

def __init__(self, 

data_frame, 

numerator_column, 

denominator_column, 

categorical_group_columns=None, 

ordinal_group_column=None, 

prior_alpha_column=None, 

prior_beta_column=None, 

interval_size=0.95): 

""" 

Bayesian BetaBinomial model. 

 

See: https://en.wikipedia.org/wiki/Beta-binomial_distribution 

 

data_frame (pd.DataFrame): DataFrame 

numerator_column (str): Column name for numerator column. 

denominator_column (str): Column name for denominator column. 

categorical_group_columns (str or list): Column names 

for categorical groupings. 

ordinal_group_column (str): Column name for ordinal 

grouping (e.g. numeric or date values). 

prior_alpha_column (str): Column name to use for prior alpha. 

prior_beta_column (str): Column name to use for prior beta. 

interval_size (float): Size of credible intervals. Default 0.95 

""" 

super().__init__(data_frame, categorical_group_columns, 

ordinal_group_column, 

numerator_column, 

denominator_column, 

interval_size) 

 

self._monte_carlo_sample_size = 500000 

 

# Initialize priors. 

if prior_alpha_column is None or prior_beta_column is None: 

self._alpha_prior, self._beta_prior = (0.5, 0.5) 

else: 

self._alpha_prior = data_frame[prior_alpha_column] 

self._beta_prior = data_frame[prior_beta_column] 

 

def _interval(self, row): 

interval = beta.interval( 

self._interval_size, 

row[self._numerator_column] + self._alpha_prior, 

row[self._denominator_column] - row[self._numerator_column] + 

self._beta_prior) 

return interval 

 

def _posterior_parameters(self, group_df): 

"""Calculate parameters of posterior distribution. 

 

Returns: 

tuple of floats: posterior_alpha, posterior_beta""" 

numerator = group_df[self._numerator_column].values[0] 

denominator = group_df[self._denominator_column].values[0] 

posterior_alpha = numerator + self._alpha_prior 

posterior_beta = denominator - numerator + self._beta_prior 

return posterior_alpha, posterior_beta 

 

def _beta_pdf(self, group_df): 

"""Beta pdfs for the given dataframe""" 

posterior_alpha, posterior_beta = self._posterior_parameters(group_df) 

epsilon = .001 

lower_range = beta.isf(1.0 - epsilon, posterior_alpha, posterior_beta) 

upper_range = beta.isf(epsilon, posterior_alpha, posterior_beta) 

x_range = np.linspace(lower_range, upper_range, 1000) 

beta_pdf = [ 

beta.pdf(x, posterior_alpha, posterior_beta) for x in x_range 

] 

beta_dist = pd.DataFrame({'x': x_range, 'y': beta_pdf}) 

return beta_dist 

 

def _sample_posterior(self, group_df, posterior_sample_size=None): 

"""MCMC sampling of posterior distribution. 

Used to calculate the posterior distribution of 

the difference in Beta RVs. 

 

Arguments: 

- seed (int): Seed for random number generator. 

Set it to make the posteriors deterministic. 

- posterior_sample_size (int): Number of posterior 

samples (affects precision) 

""" 

if posterior_sample_size is None: 

posterior_sample_size = self._monte_carlo_sample_size 

posterior_alpha, posterior_beta = self._posterior_parameters(group_df) 

posterior_samples = np.random.beta( 

posterior_alpha, posterior_beta, size=posterior_sample_size) 

return posterior_samples 

 

def _categorical_summary_plot(self, level_name, level_df, remaining_groups, 

groupby): 

 

if not remaining_groups: 

remaining_groups = groupby 

grouped_df = level_df.groupby(remaining_groups) 

 

distributions = pd.DataFrame() 

for group_name, group_df in grouped_df: 

beta_dist = self._beta_pdf(group_df) 

beta_dist['group'] = str(group_name) 

distributions = pd.concat([distributions, beta_dist], axis=0) 

 

# Filter out the long tails of the distributions 

filtered_xs = distributions.groupby('x')['y'].max().reset_index().loc[ 

lambda x: x['y'] > .01] 

distributions = distributions[distributions['x'].isin( 

filtered_xs['x'])] 

 

# Remove legend if only one color 

color_column = 'group' if len(grouped_df) > 1 else None 

 

ch = chartify.Chart() 

ch.plot.area( 

distributions, 

'x', 

'y', 

color_column=color_column, 

stacked=False, 

color_order=[str(x) for x in list(grouped_df.groups.keys())]) 

ch.set_title("Estimate of {} / {}".format(self._numerator_column, 

self._denominator_column)) 

 

if groupby: 

ch.set_subtitle("{}: {}".format(groupby, level_name)) 

else: 

ch.set_subtitle("") 

ch.axes.set_xaxis_label("{} / {}".format(self._numerator_column, 

self._denominator_column)) 

ch.axes.set_yaxis_label("Probability Density") 

ch.set_source_label("") 

ch.axes.set_yaxis_range(0) 

axis_format = axis_format_precision(distributions['x'].min(), 

distributions['x'].max(), 

absolute=True) 

ch.axes.set_xaxis_tick_format(axis_format) 

 

ch.style.color_palette.reset_palette_order() 

 

# Plot callouts for the means 

for group_name, group_df in grouped_df: 

posterior_alpha, posterior_beta = self._posterior_parameters( 

group_df) 

posterior_mean = posterior_alpha / ( 

posterior_alpha + posterior_beta) 

density = beta.pdf(posterior_mean, posterior_alpha, posterior_beta) 

ch.callout.line( 

posterior_mean, 

orientation='height', 

line_color=ch.style.color_palette.next_color(), 

line_dash='dashed') 

ch.callout.text('{0:.1f}%'.format(posterior_mean * 100), 

posterior_mean, density) 

 

ch.axes.hide_yaxis() 

if color_column: 

ch.set_legend_location('outside_bottom') 

return ch 

 

def _difference_posteriors(self, data, level_1, level_2, absolute=True): 

 

posterior_1 = self._sample_posterior(data.get_group(level_1)) 

posterior_2 = self._sample_posterior(data.get_group(level_2)) 

 

if absolute: 

difference_posterior = posterior_2 - posterior_1 

else: 

difference_posterior = posterior_2 / posterior_1 - 1. 

 

return difference_posterior 

 

def _differences(self, difference_posterior, level_1, level_2, absolute): 

# 95% credible interval for posterior 

credible_interval = (pd.Series(difference_posterior).quantile( 

(1. - self._interval_size) / 2), 

pd.Series(difference_posterior).quantile( 

(1. - self._interval_size) / 2 + self._interval_size)) 

 

# Probability that posterior is greater 

# than zero (count occurences in the MC sample) 

p_gt_zero = (difference_posterior > 0).mean() 

 

expected_loss_v2 = ( 

difference_posterior[difference_posterior < 0].sum() / 

len(difference_posterior)) 

if (difference_posterior > 0).sum() == 0: 

expected_gain_v2 = 0 

else: 

expected_gain_v2 = ( 

difference_posterior[difference_posterior > 0].sum() / 

len(difference_posterior)) 

 

expected_loss_v1 = ( 

(difference_posterior[difference_posterior * -1.0 < 0] * 

-1.0).sum() / len(difference_posterior)) 

 

if (difference_posterior * -1.0 > 0).sum() == 0: 

expected_gain_v1 = 0 

else: 

expected_gain_v1 = ( 

(difference_posterior[difference_posterior * -1.0 > 0] * 

-1.0).sum() / len(difference_posterior)) 

 

return pd.DataFrame( 

OrderedDict( 

[('level_1', str(level_1)), ('level_2', str(level_2)), 

('absolute_difference', 

absolute), ('difference', difference_posterior.mean()), 

('ci_lower', [credible_interval[0]]), ('ci_upper', [ 

credible_interval[1] 

]), ('P(level_2 > level_1)', p_gt_zero), 

('level_1 potential loss', 

expected_loss_v1), ('level_1 potential gain', 

expected_gain_v1), 

('level_2 potential loss', 

expected_loss_v2), ('level_2 potential gain', 

expected_gain_v2)])) 

 

def _difference(self, level_name, level_df, remaining_groups, groupby, 

level_1, level_2, absolute): 

 

difference_df, _ = self._difference_and_difference_posterior( 

level_df, 

remaining_groups, 

level_2, 

level_1, 

absolute) 

 

self._add_group_by_columns(difference_df, groupby, level_name) 

 

return difference_df 

 

def _difference_and_difference_posterior(self, level_df, remaining_groups, 

level_2, level_1, absolute): 

self._validate_levels(level_df, remaining_groups, level_1) 

self._validate_levels(level_df, remaining_groups, level_2) 

# difference is posterior_2 - posterior_1 

difference_posterior = self._difference_posteriors( 

level_df.groupby(remaining_groups), level_1, level_2, absolute) 

difference_df = self._differences(difference_posterior, level_1, 

level_2, absolute) 

return difference_df, difference_posterior 

 

@randomization_warning_decorator 

def difference(self, level_1, level_2, absolute=True, groupby=None): 

"""Return DataFrame with summary statistics of the difference between 

level 1 and level 2. 

 

Args: 

level_1 (str, tuple of str): Name of first level. 

level_2 (str, tuple of str): Name of second level. 

absolute (bool): If True then return the 

absolute difference (level2 - level1) 

otherwise return the relative difference (level2 / level1 - 1) 

groupby (str): Name of column. 

If specified, will return the difference for each level 

of the grouped dimension. 

 

Returns: 

Pandas DataFrame with the following columns: 

- level_1: Name of level 1. 

- level_2: Name of level 2. 

- absolute_difference: True if absolute. 

Absolute: level2 - level1 

Relative: level2 / level1 - 1 

- difference: Best estimate of the difference between level 2 and 1. 

Posterior mean of the difference between level 1 and level 2. 

https://en.wikipedia.org/wiki/Bayes_estimator 

- ci_lower: Lower credible interval bound of the difference. 

- ci_upper: Upper credible interval bound of the difference. 

- P(level_2 > level_1): Probability that the level 2 > level 1. 

- level_1 potential loss: The expected loss if we 

switch to level 1, but level 2 is actually better. 

- level_1 potential gain: The expected gain if we 

switch to level 1, and level 1 is actually better. 

- level_2 potential loss: The expected loss if we 

switch to level 2, but level 1 is actually better. 

- level_2 potential gain: The expected gain if we 

switch to level 2, and level 2 is actually better. 

""" 

 

results_df = self._iterate_groupby_to_dataframe( 

self._difference, 

groupby=groupby, 

level_1=level_1, 

level_2=level_2, 

absolute=absolute) 

 

return results_df 

 

@randomization_warning_decorator 

def _categorical_difference_plot(self, level_1, level_2, absolute, groupby): 

chart_grid = self._iterate_groupby_to_chartgrid( 

self._categorical_difference_plot_, 

groupby=groupby, 

level_1=level_1, 

level_2=level_2, 

absolute=absolute) 

 

return chart_grid 

 

def _categorical_difference_plot_(self, level_name, level_df, 

remaining_groups, groupby, 

level_1, level_2, absolute): 

difference_df, difference_posterior = \ 

self._difference_and_difference_posterior(level_df, 

remaining_groups, 

level_2, 

level_1, 

absolute) 

 

posterior_mean = difference_df['difference'][0] 

# potential_loss = difference_df['{} potential loss'.format(level_2)][0] 

 

# Take the difference posterior and create a chart 

df = pd.DataFrame({'values': difference_posterior}) 

 

ch = chartify.Chart(y_axis_type='density', x_axis_type='linear') 

 

ch.plot.kde(df, 'values') 

 

ch.set_title("Change from {} to {}".format(level_1, level_2)) 

 

subtitle = "" if not groupby else "{}: {}".format(groupby, level_name) 

ch.set_subtitle(subtitle) 

 

# Line at no difference 

ch.callout.line(0, 

orientation='height', 

line_color='black', 

line_dash='dashed') 

# ch.callout.text('No change', 0, .5, angle=90) 

 

# Plot callout for the mean 

ch.callout.line( 

posterior_mean, 

orientation='height', 

line_color=ch.style.color_palette._colors[0], 

line_dash='dashed') 

# ch.callout.text( 

# '{0:.2f}%'.format(posterior_mean * 100), posterior_mean, 0) 

ch.callout.text( 

'Expected change: {0:.2f}%'.format(posterior_mean * 100), 

posterior_mean, 

0, 

angle=90) 

 

# ch.callout.line( 

# potential_loss, 

# orientation='height', 

# line_color=ch.style.color_palette._colors[1]) 

# ch.callout.text( 

# 'Potential Loss: {0:.2f}%'.format(potential_loss * 100), 

# potential_loss, 

# 1.5, 

# angle=90) 

# ch.callout.text( 

# '{0:.2f}%'.format(potential_loss * 100), potential_loss, 1.) 

 

ch.set_source_label("") 

ch.axes.set_yaxis_range(0) 

ch.axes.set_xaxis_label(self.get_difference_plot_label(absolute)) 

ch.axes.set_yaxis_label("Probability Density") 

ch.axes.hide_yaxis() 

axis_format = axis_format_precision(df['values'].max() * 10, 

df['values'].min() * 10, 

absolute) 

ch.axes.set_xaxis_tick_format(axis_format) 

 

return ch 

 

def _multiple_difference_joint_dataframe(self, *args, **kwargs): 

 

return self._multiple_difference_joint_base(*args, **kwargs)[0] 

 

def _multiple_difference_joint_base(self, 

level_name, 

level_df, 

remaining_groups, 

groupby, 

level, 

absolute): 

 

grouped_df = level_df.groupby(remaining_groups) 

 

grouped_df_keys = tuple(grouped_df.groups.keys()) 

 

self._validate_levels(level_df, remaining_groups, level) 

 

posteriors = [ 

self._sample_posterior(grouped_df.get_group(level)) 

for level in grouped_df_keys 

] 

 

var_indx = grouped_df_keys.index(level) 

other_indx = [ 

i for i, value in enumerate(grouped_df_keys) if value != level 

] 

 

posterior_matrix = np.vstack(posteriors) 

 

ge_bool_matrix = posterior_matrix[var_indx, :] >= posterior_matrix[:, :] 

 

best_arr = ge_bool_matrix.all(axis=0) 

 

p_ge_all = best_arr.mean() 

 

end_value = posterior_matrix[var_indx] 

start_value = posterior_matrix[other_indx].max(axis=0) 

 

if absolute: 

difference_posterior = end_value - start_value 

else: 

difference_posterior = end_value / start_value - 1 

 

# E(level - best level | level != best) 

if not (~best_arr).sum(): 

expected_loss = 0 

else: 

expected_loss = difference_posterior[~best_arr].mean() 

 

# E(level - median level | level = best) 

if not (best_arr).sum(): 

expected_gain = 0 

else: 

expected_gain = difference_posterior[best_arr].mean() 

 

expectation = difference_posterior.mean() 

ci_l_expectation = pd.Series(difference_posterior).quantile( 

(1. - self._interval_size) / 2) 

ci_u_expectation = pd.Series(difference_posterior).quantile( 

(1. - self._interval_size) / 2 + self._interval_size) 

 

difference_df = pd.DataFrame( 

OrderedDict([ 

('level', [str(level)]), 

('absolute_difference', absolute), 

('difference', expectation), 

('ci_lower', ci_l_expectation), 

('ci_upper', ci_u_expectation), 

('P({} >= all)'.format(level), p_ge_all), 

('{} potential loss'.format(level), expected_loss), 

('{} potential gain'.format(level), expected_gain), 

])) 

self._add_group_by_columns(difference_df, groupby, level_name) 

 

return (difference_df, difference_posterior) 

 

@randomization_warning_decorator 

def multiple_difference_joint(self, 

level, 

absolute=True, 

groupby=None): 

"""Calculate the joint probability that the given level is greater 

than all other levels in the test. 

 

Args: 

level (str, tuple of str): Name of level. 

absolute (bool): If True then return the absolute difference 

otherwise return the relative difference. 

groupby (str): Name of column. 

If specified, will return an interval for each level 

of the grouped dimension. 

 

Returns: 

Pandas DataFrame with the following columns: 

- level: Name of level 

- absolute_difference: True if absolute. 

Absolute: level2 - level1 

Relative: level2 / level1 - 1 

- difference: Difference between the level and the best performing 

among the other levels. 

- ci_lower: Lower credible interval bound of the difference. 

- ci_upper: Upper credible interval bound of the difference. 

- P(level > all): Probability that the level > all other levels. 

- potential loss: The expected loss if we 

switch to level, but some other level is actually better. 

- potential gain: The expected gain if we 

switch to level, and it is actually the best. 

""" 

 

results_df = self._iterate_groupby_to_dataframe( 

self._multiple_difference_joint_dataframe, 

groupby=groupby, 

level=level, 

absolute=absolute 

) 

 

return results_df 

 

def _multiple_difference_joint_plot(self, 

level_name, 

level_df, 

remaining_groups, 

groupby, 

level, 

absolute): 

 

self._validate_levels(level_df, remaining_groups, level) 

 

difference_df, difference_posterior = \ 

self._multiple_difference_joint_base(level_name, 

level_df, 

remaining_groups, 

groupby, 

level, 

absolute) 

 

posterior_mean = difference_df.loc[:, 'difference'].values[0] 

 

# potential_loss = difference_df.loc[:, '{} potential loss'.format( 

# level)].values[0] 

 

# Take the difference posterior and create a chart 

df = pd.DataFrame({'values': difference_posterior}) 

 

ch = chartify.Chart(y_axis_type='density', x_axis_type='linear') 

 

ch.plot.kde(df, 'values') 

 

ch.set_title("Comparison to {}".format(level)) 

 

subtitle = "" if not groupby else "{}: {}".format(groupby, level_name) 

ch.set_subtitle(subtitle) 

 

# Line at no difference 

ch.callout.line(0, orientation='height', line_color='black') 

 

# Plot callout for the mean 

ch.callout.line( 

posterior_mean, 

orientation='height', 

line_color=ch.style.color_palette._colors[0]) 

 

ch.callout.text( 

'Expected change: {0:.2f}%'.format(posterior_mean * 100), 

posterior_mean, 

0, 

angle=90) 

 

ch.set_source_label("") 

ch.axes.set_yaxis_range(0) 

ch.axes.set_xaxis_label(self.get_difference_plot_label(absolute)) 

ch.axes.set_yaxis_label("Probability Density") 

ch.axes.hide_yaxis() 

 

axis_format = axis_format_precision(df['values'].max() * 10, 

df['values'].min() * 10, 

absolute) 

ch.axes.set_xaxis_tick_format(axis_format) 

return ch 

 

@randomization_warning_decorator 

def multiple_difference_joint_plot(self, 

level, 

absolute=True, 

groupby=None): 

"""Calculate the joint probability that the given level is greater 

than all other levels in the test. 

 

Args: 

level (str, tuple of str): Name of level. 

absolute (bool): If True then return the absolute difference 

otherwise return the relative difference. 

groupby (str): Name of column. 

If specified, will return an interval for each level 

of the grouped dimension. 

 

Returns: 

GroupedChart object. 

""" 

 

results_df = self._iterate_groupby_to_chartgrid( 

self._multiple_difference_joint_plot, 

groupby=groupby, 

level=level, 

absolute=absolute 

) 

 

return results_df 

 

def _multiple_difference(self, level_name, level_df, remaining_groups, 

groupby, level, absolute, level_as_reference): 

 

grouped_df = level_df.groupby(remaining_groups) 

 

grouped_df_keys = tuple(grouped_df.groups.keys()) 

 

other_keys = [ 

value for i, value in enumerate(grouped_df_keys) if value != level 

] 

 

for key in other_keys: 

 

# Switch the subtraction order as specified. 

start_value, end_value = level, key 

if not level_as_reference: 

start_value, end_value = end_value, start_value 

 

difference_df = self._difference( 

level_name, 

level_df, 

remaining_groups, 

groupby, 

start_value, 

end_value, 

absolute=absolute) 

 

yield difference_df 

 

@randomization_warning_decorator 

def multiple_difference(self, 

level, 

absolute=True, 

groupby=None, 

level_as_reference=False): 

"""Pairwise comparison of the given level to all others. 

 

Args: 

level (str, tuple of str): Name of level. 

absolute (bool): If True then return the absolute difference 

otherwise return the relative difference. 

groupby (str): Name of column. 

If specified, will return an interval for each level 

of the grouped dimension. 

level_as_reference (bool): If True, the given level is the reference 

value for the change. (level1) 

 

Returns: 

Pandas DataFrame with the following columns: 

- groupby (If groupby is not None): Grouped dimension 

- level_1: Name of level 1. 

- level_2: Name of level 2. 

- absolute_difference: True if absolute. 

Absolute: level2 - level1 

Relative: level2 / level1 - 1 

- difference: Best estimate of the difference between level 2 and 1. 

Posterior mean of the difference between level 1 and level 2. 

https://en.wikipedia.org/wiki/Bayes_estimator 

- ci_lower: Lower credible interval bound of the difference. 

- ci_upper: Upper credible interval bound of the difference. 

- P(level_2 > level_1): Probability that the level 2 > level 1. 

- level_1 potential loss: The expected loss if we 

switch to level 1, but level 2 is actually better. 

- level_1 potential gain: The expected gain if we 

switch to level 1, and level 1 is actually better. 

- level_2 potential loss: The expected loss if we 

switch to level 2, but level 1 is actually better. 

- level_2 potential gain: The expected gain if we 

switch to level 2, and level 2 is actually better. 

""" 

 

results_df = self._iterate_groupby_to_dataframe( 

self._multiple_difference, 

groupby=groupby, 

level=level, 

absolute=absolute, 

level_as_reference=level_as_reference) 

 

results_df = results_df.reset_index(drop=True) 

 

return results_df 

 

def _categorical_multiple_difference_chart(self, level_name, level_df, 

remaining_groups, groupby, level, 

absolute, level_as_reference): 

 

grouped_df = level_df.groupby(remaining_groups) 

 

grouped_df_keys = tuple(grouped_df.groups.keys()) 

 

self._validate_levels(level_df, remaining_groups, level) 

 

posteriors = [ 

self._sample_posterior(grouped_df.get_group(level)) 

for level in grouped_df_keys 

] 

 

var_indx = grouped_df_keys.index(level) 

 

other_indx = [ 

i for i, value in enumerate(grouped_df_keys) if value != level 

] 

 

posterior_matrix = np.vstack(posteriors) 

 

start_value = posterior_matrix[var_indx] 

end_value = posterior_matrix 

if not level_as_reference: 

start_value, end_value = end_value, start_value 

 

if absolute: 

difference_posterior = end_value - start_value 

else: 

difference_posterior = end_value / start_value - 1 

 

df = pd.DataFrame() 

for group in other_indx: 

df = pd.concat([df, 

pd.DataFrame({'values': difference_posterior[group], 

'group': str(grouped_df_keys[group]) 

})], 

axis=0) 

 

# Take the difference posterior and create a chart 

# df = pd.DataFrame({'values': difference_posterior}) 

 

ch = chartify.Chart(y_axis_type='density', x_axis_type='linear') 

 

ch.plot.kde(df, 'values', color_column='group') 

 

title_change_label = 'from' if level_as_reference else 'to' 

ch.set_title("Change {} {}".format(title_change_label, level)) 

 

subtitle = "" if not groupby else "{}: {}".format(groupby, level_name) 

ch.set_subtitle(subtitle) 

 

# Line at no difference 

ch.callout.line(0, 

orientation='height', 

line_color='black', 

line_dash='dashed') 

# ch.callout.text('No change', 0, .5, angle=90) 

ch.style.color_palette.reset_palette_order() 

 

for group in other_indx: 

posterior_mean = difference_posterior[group].mean() 

# Plot callout for the mean 

ch.callout.line( 

posterior_mean, 

orientation='height', 

line_color=ch.style.color_palette.next_color(), 

line_dash='dashed') 

 

ch.callout.text( 

'Expected change: {0:.2f}%'.format(posterior_mean * 100), 

posterior_mean, 

0, 

angle=90) 

 

# ch.callout.line( 

# potential_loss, 

# orientation='height', 

# line_color=ch.style.color_palette._colors[1]) 

# ch.callout.text( 

# 'Potential Loss: {0:.2f}%'.format(potential_loss * 100), 

# potential_loss, 

# 1.5, 

# angle=90) 

# ch.callout.text( 

# '{0:.2f}%'.format(potential_loss * 100), potential_loss, 1.) 

 

ch.set_source_label("") 

ch.axes.set_yaxis_range(0) 

ch.axes.set_xaxis_label(self.get_difference_plot_label(absolute)) 

ch.axes.set_yaxis_label("Probability Density") 

ch.axes.hide_yaxis() 

axis_format = axis_format_precision(df['values'].max() * 10, 

df['values'].min() * 10, 

absolute) 

ch.axes.set_xaxis_tick_format(axis_format) 

 

return ch 

 

@randomization_warning_decorator 

def _categorical_multiple_difference_plot(self, level, absolute, groupby, 

level_as_reference): 

"""Pairwise comparison of the given level to all others. 

 

Args: 

level (str, tuple of str): Name of level. 

absolute (bool): If True then return the absolute difference 

otherwise return the relative difference. 

groupby (str): Name of column. 

If specified, will return an interval for each level 

of the grouped dimension. 

level_as_reference (bool): If True, the given level is the reference 

value for the change. (level1) 

 

Returns: 

GroupedChart object. 

""" 

 

results_df = self._iterate_groupby_to_chartgrid( 

self._categorical_multiple_difference_chart, 

groupby=groupby, 

level=level, 

absolute=absolute, 

level_as_reference=level_as_reference 

) 

 

return results_df 

 

# class GammaPoisson(PoissonResponse): 

# pass 

 

 

# class DirichetMultinomial(MultinomialResponse): 

# def __init__(self, 

# data_frame, 

# group_columns, 

# category_column, 

# value_column, 

# prior_value_column=None): 

 

# super().__init__(data_frame, group_columns, category_column, 

# value_column) 

 

 

# class Gaussian(GaussianResponse): 

# def __init__(self, 

# data_frame, 

# groupings, 

# mean_col, 

# std_col, 

# n_col, 

# time_grouping=None, 

# prior_columns=None): 

# self.prior_lambda_column = prior_lambda_column 

# super(BaseGaussianResponse, self).__init__( 

# data_frame, groups, mean_col, std_col, n_col, time_grouping) 

# raise (NotImplementedError) 

 

 

# class DirichetCategorical(CategoricalResponse): 

# pass