This number, divided by the count of all arcs outgoing of the given node, represents the probability of transition between the graph nodes: These paths can be presented as the following graph:įor better readability, instead of multiple arrows, we will use single arrows (arcs) labelled with the number of conversion paths included in the given arc. Conversion rate is therefore 50% (yes, it is high, but on such numbers it will be easier to understand the calculations). Imagine that we have only four paths, two of which are converting. How can we use Markov chains to analyse multi-channel conversion paths? It explains why I return home with a leg in a cast every 5-6 years if I travel three times a year. The total probability of an accident is thus: In this process, there is no other way to have an accident. The likelihood that the given holiday I will spend on the beach AND I will have an accident there (i.e, START > Beach > Sport > Injury) is: The probability that during given vacation I will go to the mountains AND I will have an accident there (i.e. The graph shows that an accident can happen when going to the beach as well as and in the mountains. The risk of injury during relaxation is negligible, while sport involves 1/10 probability of an accident:

The likelihood whether I will do sport or just relax there, depends on where I spend my vacation (mountains or beach). The Markov chain is a model describing a sequence of possible events in which the probability of each event depends only on the current state.Īn example of a Markov chain may be the following process: Markov chains, alongside Shapley value, are one of the most common methods used in algorithmic attribution modeling.

Markov chain model