[Question]: LGCP/Point process forecasting methodology?
Anyone worked on forecasting point processes before? Just a bit stuck if this is the best way for me to do it with the tools I am using.
Currently as my estimation procedure is not likelihood based for an LGCP(stopp package in R), there is no easily available posterior so I can't draw parameters from there. It does have functions to fit the model with covariates and simulate from a Log gaussian cox process(LGCP) using covariates though.
My current idea is parametric bootstrapping:
fit my model to my original data
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use fitted parameters to estimate new data and refit the model
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repeat this and store the param estimates
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simulate from the assumed log Gaussian Cox process(LGCP) using the list of param estimates and store the points
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Grid/Voxelize my domain over the temporal and spatial forecast window and count whenever a simulation has a point in that grid, basically an indicator variable if that simulation has a point present in that grid.
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Grab the "HPD" region, so the regions sorted by the mean count of presence of events in that region across simulations, as many simulations might have 0 events it will below 1 and can be interpreted as a predicted probability, collect these grids until the regions add up to or above the considered prob threshold.
Maybe I am overlooking something, so any guidance would be helpful.
For those still reading the goal is to use lightning strike event data and predict the next most likely region in time and space for activity in a chosen forecast window(A country and within 6-24h). LGCP was chosen due to it being a model that can capture the clustering behavior of lightning. I have also found self-exciting models such as Hawkes-processes as a good contender capturing the same clustering behavior that I will explore further.