Month: September 2017

Kennie Nybo Pontoppidan has just completed a course on Bayesian statistics:

Last month I finished a four-week course on Bayesian statistics. I have always wondered why people deemed it hard, and why I heard that the computations quickly became complicated. The course wasn’t that hard, and it gave a nice introduction to prior/posterior distributions and I many cases also how to interpret the parameters in the prior distribution as extra data points.

An interesting aspect of Bayesian statistics is that it is a mathematically rigorous model, with no magic numbers such as the 5% threshold for p-values. And I like the way it naturally caters sequential hypothesis testing with where the sample size of each iteration is not fixed in advance. Instead data are evaluated and used to update the model as they are collected.

Check out Kennie’s explanation as well as the course.  I also went through Bayes’ Theorem not too long ago, which is a good introduction to the topic if you’re unfamiliar with Bayes’s Law.

Lingrui Gan explains how to model for parameters whose effects change over time:

We can frame conversion prediction as a binary classification problem, with outcome “1” when the visitor converts, and outcome “0” when they do not. Suppose we build a model to predict conversion using site visitor features. Some examples of relevant features are: time of day, geographical features based on a visitor’s IP address, their device type, such as “iPhone”, and features extracted from paid ads the visitor interacted with online.

A static classification model, such as logistic regression, assumes the influence of all features is stable over time, in other words, the coefficients in the model are constants. For many applications, this assumption is reasonable—we wouldn’t expect huge variations in the effect of a visitor’s device type. In other situations, we may want to allow for coefficients that change over time—as we better optimize our paid ad channel, we expect features extracted from ad interactions to be more influential in our prediction model.

Read on for more.

Eleni Markou shows one method of analyzing clickstream data:

We chose to use the third-order Markov Chain on the above-produced data, as:

• The number of parameters needed for the chain’s representation remains manageable. As the order increases, the parameters necessary for the representation increase exponentially and thus managing them requires significant computational power.
• As a rule of thumb, we would like at least half of the clickstreams to consist of as many clicks as the order of the Markov Chain that should be fitted. There is no point in selecting a third-order chain if the majority of the clickstream consists of two states and so there is no state three steps behind to take into consideration.

Fitting the Markov Chain model gives us transition probabilities matrices and the lambda parameters of the chain for each one of the three lags, along with the start and end probabilities.

This particular analysis is trying to understand which page (if any) a user will go to next when on a particular page.  Eleni uses additional techniques like k-means clustering to segment out particular groups of users.  Very interesting analysis.