Poisson process for the spatial analysis of accidents I have a large dataset consisting of the geographic location, company, and date of accident.  I also have a grid with a cell size that is 6 miles x 6 miles to disaggregate the data, since the dataset is much larger than the one shown (>1 million location points over a provincial scale).  I am trying to calculate the probability of a k-number of accidents in each grid cell based on the data points.
The accidents have the following characteristics:

*

*Accidents can randomly occur at any location within each grid cell.

*Two accidents can occur at the same time in each grid cell.

*Accidents can be counted 1, 2, 3, ... , n.

*Accidents are independent of each other.

*The average rate of accident can be calculated for each grid cell.

Everything seems to almost fit the criteria for a Poisson Process; however, two accident events can occur at the same time in each grid cell.  I have calculated the Poisson probability CDF of each grid cell for a k-number of accidents, but not comfortable with the results because of the fact that two accidents can occur at the same time within a single grid cell.
Is the Poisson distribution robust enough to handle the fact that two accidents can occur at the same time within a grid cell.
Also, is there a better way to deal with this sort of problem, since I fully expect the results of this probability analysis to have a spatial scale dependence.


I think your approach is reasonable. You presume a different Poisson process for each cell, which lets you predict the accident rate with a larger resolution. The cells are not too small, so there is still enough data for each cell. You also presume that the rate doesn't change with time, which seems to be OK, too.
You don't have to worry about accidents happening at the same time. You can adopt the viewpoint that none of your accidents will ever happen at the same time, the probability for this is zero, and the fact that the clocks used to measure the time of the accident are not precise enough to show this doesn't have a bearing on the usability of the Poisson distribution. Relevant is the independence between the accidents and the time independence of the rate of the process.
