How to predict when the next event occurs, with random data

I am working on an academic project, I'd like to know what is the best approach to build a predictive model to predict when the next event occurs.

I am working on predicting a specific kind of "crimes", it's a random event that occur in different times of the day, by different types of people.

Usually, prediction is discussing the ability to statistically foretell the occurrence of future events in the aggregate data on how those populations behaved in the past, you can predict their behaviors with a reasonable degree of confidence.

The problem with "random events" is that we can't build patterns based on the past data, so it's challenging a little bit to find a good approach to tell when the next event will happen.

I'd like to know what's the best approach to tackle this problem. I found different suggestions in the website, but don't know if it fits the "random" events:

• Power low (Duane) model
• Poisson Model
• Poisson point process model
• Hidden Markov Model
• inhomogeneous Poisson process

from what I know, the crucial assumption in the Poisson process is that what happens now is independent of what happened a moment ago or what will happen in the next moment (or at any other moment, for that matter). Therefore the distribution of events during any (measurable) period of time depends only on the length of time, not on how it is broken up.

When it comes to "crimes", the events are independent. In this case, should I use Poisson model to predict "crimes". I think it's the same also for earth-quacks. Is there any better solution as I don't have a lot of (positive data). what I mean is, In places where crimes never happened, how can I use poisson in this case, it's already no-event.

Can anyone explain an effective approach to tackle this problem ?

• I don't have an answer, but computational mechanics deals with exactly these kinds of questions. See, for example, Crutchfield, J. P. and Feldman, D. P. (2003). Regularities unseen, randomness observed: Levels of entropy convergence. Chaos, 13(1):25–54. – Alexis Apr 25 '14 at 15:42
• @Alexis : Thanks. Should I project that on prediction earthquack ? – user3378649 Apr 26 '14 at 10:15
• Given that you said "from what I know..." about a poisson process, it sounds like you need to hit the books to learn about each of the models you mention. – JenSCDC Jul 4 '14 at 20:56