I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery.
Most of time, the robbery does not occur when the owner is watching => the declared timespan can be very large!
Jack comes back from work at 8pm, park his bike and go home. In the morning, Jack leave his home at 8 am to go to work and realised that his bike has been stolen ! => Declared timespan = 12 hours.
Emily parks her bike to get some cigarettes, when she gets back 5 minutes after it has been stolen. => Declared timespan = 5 minutes.
Here are timespans' distributions :
My first approach was to assume that there is the same probability of event-occurence all along its timespan. I also normalised by the length of each timespan to give a higher weight to shorter timespan (more precised).
t(t, t+n) > 1 if the event occur in a timespan > 24h
y(t, t+n) = 1 if the event occured in [t, t+n]
y(t, t+n) = 0 if the event did not occur not in [t, t+n]
With normalisation, we take instead y(t, t+n)/n
But there is a "problem" with this approach. I'll try to illustrate it with an example:
Let's imagine 10 robberies.
- 9 of them occured between 8pm and 8am
- the last one occured between 3am and 5am
we will then get a pike between 3am and 5am but it does not mean that there is a higher chance that an event occurs between this timespan !
- Should I put some stronger regularisation ?
- Is my hypothesis about having the same probability of occurence all along the timespan seems correct ? Or should I add some a priori information (known distribution, ...) ?
The aim of this approach is to give an idea of when people should look out the window to check if their bike is safe.