Decision analysis

Bayesian Data Analysis in Python

Michal Oleszak

Machine Learning Engineer

Decision analysis

Decision-makers care about maximizing profit, reducing costs, saving lives, etc.

A syringe next to three bank notes and a digit 99%. An arrow points from it to a single person icon.

Decision analysis

Decision-makers care about maximizing profit, reducing costs, saving lives, etc.

A syringe next to a single bank note and a digit 98%. An arrow points from it to a group of people.

Decision analysis → translating parameters to relevant metrics to inform decision-making

From posteriors to decisions

To make strategic decisions, one should know the probabilities of different scenarios.
Bayesian methods allow us to translate parameters into relevant metrics easily.

A icon representing a click rate distribution.

From posteriors to decisions

To make strategic decisions, one should know the probabilities of different scenarios.
Bayesian methods allow us to translate parameters into relevant metrics easily.

A icon representing a click rate distribution multiplied with "impressions".

From posteriors to decisions

To make strategic decisions, one should know the probabilities of different scenarios.
Bayesian methods allow us to translate parameters into relevant metrics easily.

A icon representing a click rate distribution multiplied with "impressions", multiplied with "revenue per click".

From posteriors to decisions

To make strategic decisions, one should know the probabilities of different scenarios.
Bayesian methods allow us to translate parameters into relevant metrics easily.

A icon representing a click rate distribution multiplied with "impressions", multiplied with "revenue per click", equals an icon representing a revenue distribution.

Posterior revenue

# Different revenue per click
num_impressions = 1000
rev_per_click_A = 3.6
rev_per_click_B = 3


# Compute number of clicks
num_clicks_A = A_posterior * num_impressions
num_clicks_B = B_posterior * num_impressions


# Compute posterior revenue
rev_A = num_clicks_A * rev_per_click_A
rev_B = num_clicks_B * rev_per_click_B

Two density plots slightly overlapping.

Two density plots overlapping to a large extent.

Forest plot

import pymc3 as pm


# Collect posterior draws in a dictionary
revenue = {"A": rev_A, "B": rev_B}


# Draw the forest plot
pm.forestplot(revenue)

A plot showing two lines, each of them denoting one distribution. The length of each line represents the 94% credible interval.

Forest plot

import pymc3 as pm

# Collect posterior draws in a dictionary
revenue = {"A": rev_A, "B": rev_B}

# Draw the forest plot
pm.forestplot(revenue, hdi_prob=0.99)

A plot showing two lines, each of them denoting one distribution. The length of each line represents the 99% credible interval.

Let's analyze decisions!

Bayesian Data Analysis in Python