For the sake of simplicity, we can assume that the most successful campaign is the one that results in the highest click-through rate: the ads that are most likely to be clicked if shown.We introduce a new campaign called "facebook-yellow-dress," a campaign presented to Facebook users featuring a yellow dress.We'll focus on Bayesian concepts that are foreign to traditional frequentist approaches and are actually used in applied work, specifically the prior and posterior distributions.Consider Bayes' theorem: Think of asks, "What is the probability that it rained given that it is wet outside?

We would like to estimate the probability that the next user will click on the ad.Let's overlay this likelihood function with the distribution of click-through rates from our previous 100 campaigns: Params['figure.figsize'] = (16, 7) import numpy as np import pandas as pd true_a = 11.5 true_b = 48.5 #number of marketing campaigns N = 100#randomly generate "true" click through rate for each campaign p = np.random.beta(true_a,true_b, size=N) #randomly pick the number of impressions for each campaign impressions = np.random.randint(1, 10000, size=N) #sample number of clicks for each campaign clicks = np.random.binomial(impressions, p).astype(float) click_through_rates = clicks / impressions #plot the histogram of previous click through rates with the evidence#of the new campaign f, ax = plt.subplots(1) ax.axvline(mle, linestyle = "--") ax.plot(possible_theta_values, likelihoods) zero_to_one = [j/100.for j in xrange(100)] counts, bins = np.histogram(click_through_rates , bins=zero_to_one) counts = counts / 100.These campaigns feature various ad images and captions, and are presented on a number of social networking websites.We want to present the ads that are the most successful.To unpack what that means and how to leverage these concepts for actual analysis, let's consider the example of evaluating new marketing campaigns.Assume that we run an ecommerce platform for clothing and in order to bring people to our site, we deploy several digital marketing campaigns.Alternatively, this campaign could be truly outperforming all previous campaigns. Ideally, we would rely on other campaigns' history if we had no data from our new campaign.And as we got more and more data, we would allow the new campaign data to speak for itself.This can be confusing, as the lines drawn between the two approaches are blurry.The true Bayesian and frequentist distinction is that of philosophical differences between how people interpret what probability is.

Bayesian inference is an approach to statistics in which all forms of uncertainty are expressed in terms of probability. A Bayesian approach to a problem starts.

The underlying difference between the Bayesian and frequentist approaches to statistical inference is in the definition of probability. A frequentist views.

Dec 12, 2016. In his overview of Bayesian inference, Data Scientist Aaron Kramer walks. To see why, let's return to the definition of the posterior distribution.

Expert judgment and Bayesian updating. L9. Used to derive PDFs by asking experts to define bounds and express relative likelihoods. – What is the largest.

We are defining probability by imagining a series of hypothetical experiments repeatedly sampling the population, which have not actually taken place.