During the last days I was learning about bayesian inference, and am now wondering if this could be of any practical use for a food stand I own. Here is the problem:
I own a food stand and sell sausages before football matches. Before every match, I have to decide how many buns and sausages I have to buy / how many sells I expect. This depends mostly on the condition, of how many tickets have been sold for the match.
This condition can change quite dynamically from match to match. So although I can make quite an educated guess out of the years of experience, I still end up throwing away many buns and sausages after each match. So the problem I am thinking about can be summarized as:
Given the number of sells I've made in the past for number of tickets T, how many buns and sausages shall I buy for todays match, when the sold tickets are T_today.
Even if the following approach is of no practical use, I am still curious in terms of it being an academic exercise. So my idea is the following:
Describe the guessed number of sells for the next match using a normal distribution, with mean and variance being an educated guess.
Measure the number of tickets that have been sold, and the number of sells I have made.
Before the next matchday, look at the numbers of tickets that have been sold and update the normal distribution, given this number of tickets and the experience of the last match.
Now, its quite straightforward how you update a normal distribution using bayesian inference. You measure a dataset, compute its variance and mean and you are then able to compute the updated normal distributions mean, variance etc. However, in this case, the measurement I do is the number of sells I've made and tickets sold. This I can measure with 100% accuracy, so there is no variance. How can I perform bayesian inference in this case?