I often come across problems with overdispersed poisson-distributed data. For example time series of counts of animals in a given area, e.g. one count per year over 30 years. In these situations it makes sense to me to model these using a gaussian observation level error, a logarithmical link functi…

If you can write your model in equations, it might make it easier for us to see what can be done. There might be a closed form solution lurking about, but for me at least its hard to gauge at the moment.

if you can write us a theoretical equation to see better nothing is better than a mathematical equation to solve a problem with an equation in front of us we can play with the flexibility of mathematics

This is the basic model: y~poisson(exp(linearPredictor+e)) e~normal(0,sd) where: linearPredictor: vector, representing the combined effect of all predictors y: vector, data to predict, e.g. numberOfBirds counted e: vector, latent observation level error representing e.g. effect of weather s…

Looks very similar to the models discussed in [image] Preprint on HMC using an embedded Laplace approximation Publicity @avehtari , @anon75146577 , Raj Agrawal and I posted a preprint on the coupling of Hamiltonian Monte Carlo with a Laplace approximation. Note that sever…

Not sure if you’ve already mentioned it, but for your model: y~poisson(exp(linearPredictor+e)) If you assume that e is Gamma-distributed with shape and scale parameters \frac{1}{\phi}: y \sim Poisson(\exp(\mu + e)) \\ e \sim Gamma(\frac{1}{\phi},\frac{1}{\phi}) then this reduces to a negative-b…

That works well if sd (in my formula) is small, but as sd becomes larger than 1 the negative binomial is quite different from lognormal+poisson. At large sd values the shape of the distribution is dominated by the lognormal, thats why I started to experiment with mixtures of negative-binomial and l…

Right, I poked around a bit but I think closed-form marginalisation is out of reach. Nevertheless, we can do a few calculations to help us understand the situation a little bit better. Consider the following hierarchical model: \begin{align*} W &\sim \mathcal{P}(\lambda), \\ \lambda &= \exp(\mu…

[image] maxbiostat: No wonder things go awry when the normal random effect’s variance grows, look at what happens to the variance of WW when σ2\sigma^2 grows. I don’t quite know what do to from here other than maybe fix the linear predictor ( μ\mu in the calculations above) and see what the indu…

I’ve only had a quick scheme and I’ll take a deeper look at the conversation. In the meantime a few comments. As @nhuurre pointed out, we studied a similar model when prototyping HMC using an embedded Laplace approximation. The idea here is to do an approximate marginalization, although with a Poi…

Efficient modeling of poisson likelihoods with gaussian observation level errors

Modeling

nhuurre February 20, 2021, 7:45am 5

Looks very similar to the models discussed in

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Efficient modeling of poisson likelihoods with gaussian observation level errors

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