It is generally known that 'jumps' in frequency data are difficult to estimate. In the current literature, many different techniques for estimating such jumps have been tested and often with satisfactory results. A summarizing paper about some of these techniques would be, for example, Riley, 2008.
However, all these techniques are concerning frequency data that 'floats', in the sense that the data returns to a mean $\alpha>0$. I'm interested in detecting outbreaks for frequency data where $\alpha = 0$.
A visualisation of this type of frequency data (graph from Brookmeyer & Stroup, 2003) would be:
Now I found that this sort of data is often considered in 'disease outbreak detection' literature. But I am not able to find good transformations, algorithms or estimation procedures at all.
This might be due to the fact that I am unsure about the name of this sort of frequency data.
The graph I showed above of Brookmeyer & Stroup is a CUSUM plot of 'floating' frequency data, so it's not the data itself. They state that if the CUSUM plot exceeds $h\sigma$, an alert is declared. This makes sense as the CUSUM is a transformation of the deviations from the mean. But in the case of $\alpha=0$ type frequency data, this technique can't be applied.
So, I have two questions:
- What are known transformations (such as CUSUM for 'floating' frequency data) for this type?
- What are well known and widely used detection algorithms for this type?
Any insights are highly appreciated.
Edit (some intuition)
Simple algorithms that work well in real-time might be some type of transformation that takes into account the mean or stdev. of the data. Even though such a transformations are easy to construct, it might be very difficult to separate 'real outbreaks' from normal observations. This because the mean and stdev. both tend to zero when taken over a certain window. E.g. a threshold such as $k \sigma$ or $k \mu$ will not be robust.