# Find the most frequent timespan of event occurrence

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!

Example 1

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.

Example 2

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).

Basically, here is what I get with 2 events :

Note :

• 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 !

Questions

1. Should I put some stronger regularisation ?
2. 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.

• Yep - this is called aoristic analysis. I've seen presentations (by Mike Porter) where he spreads the distribution out to places with known times of occurrence - but he has not published that work yet. – Andy W May 18 '16 at 12:05
• I don't think the 1/2 (1 event over 2 hours) addition between 3 and 5 is too big a distortion on your 3/4 (9 events over 12 hours) base. It would be nice to have a better model of when it happens within, but without hard data, I think uniform is really all you can do. It would be really nice if you knew how many bikes in the area were unattended over the time as well, as this would be a good scaling factor as well. My guess is that crooks are creatures of habit like all of us, and there probably really is some good periodicity to this! – MikeP May 18 '16 at 17:50
• I'm not sure I got your first sentence right, but in overall I must agree with your statement "uniform is really all you can do". This is what i will do. For now. – gowithefloww May 24 '16 at 14:21