A simple probabilistic model that calculates a website conversion rate given two params (number of total visitors and number of conversions). The output measures uncertainty about the true value of conversion rate
from iframer import *
iframer('https://statsim.com/app/?m=conversion-rate&preview=1')
What is Conversion Rate?¶
Conversion rate measures how many users complete a desired goal (a conversion) compared to the total number of users. It's usually calculated as a fraction $n/N$ where $n$ is number of conversions and $N$ - total number of visitors. The output of such model is deterministic and shows only what it calculates - the proportion of visitors during specific period. On the contrary, a probabilistic model encorporates uncertainty about true conversion rate.
Model¶
$$ \begin{align} Rate \sim \text{Uniform(0,1)} \\ Conversions \sim \text{Binomial(Rate, N)} \\ p(Rate|Conversions, N) \varpropto p(Conversions|Rate, N) p(Rate) \\ \end{align} $$Model contains an uninformative uniform prior and a binomial distribution to evaluate log-likelihood of provided data (Number of trials, Conversions)