Apologies, I feel that this is a fairly basic question, however, after searching high and low I can find no answer. There is a similar post here , however, it doesn’t seem to answer my question. This stems from trying to find bayesian point estimates from a poisson regression model where some of th…

Just to add more context, similar discussion has been held at Pystan log-probability confusing! and How exactly is lp__ being calculated which could shed more details on why all this stuff happens :-)

What you are describing seems right to me, unless I’m missing something MAP should be nothing more than the mode of the posterior, i.e. the highest lp__ in the chain. Except for a bug (or something I could be missing) there is no reason it shouldn’t be. The problem, however, may be as simple as a f…

Unless I’m missing something (always possible), in your example `x = c(8, 10)` `sum(x)/n = (8+10)/2 = 9.5` The MLE and MAP (with a flat prior) are both 9.5.

Did you include a typo in the above? MLE = (10 + 8)/2 = 9.0

I’m almost certain that seed is not the problem. While the sampling is random and may be impacted by the seed the point where lp__ is maximum will be the same as long as the relevant domain is covered by that sampling. I also don’t think is a bug but a gap in my understanding. I have added to the…

A few things to note here. Firstly, the ~ syntax drops any normalising constants from the log-probability calculations, so you should use the: target += poisson_lpmf(x | lambda) format instead if you’re interested in inference with the lp__ value. Additionally, the use of the lower bound on the ra…

In addition to my post I have slightly restated my model as follows: poisson_model <- "data{ int<lower=1> n; int<lower=0> x[n]; } parameters{ real log_lambda; } transformed parameters{ real<lower=0> lambda = exp(log_lambda); } model{ x ~ poisson(lambda); }" When I run this new mod…

I don’t see a gap in you understanding of the concepts you describe, which seems correct to me I’m not sure I understand how what @andrjohns describes would affect what the MAP estimate is, but that is something on the implementation side and treatment of the log-probability, not the basic concept.…

A reason why the restated model would be consistent but not the original would possibly be cause the sampled parameter log_lambda no longer has a lower-bound, and so no correction to the log-probability is being made while sampling

Hi, thanks for your help, you were right in that the issue was to do with the fact that lambda is constrained. I have now managed to get the behaviour that I expected by adding the log of the Jacobian (i.e. log(1 / lambda) to lp__. This adjusted value is now maximum at the MLE or MAP and agrees wi…

Trying to understand lp__ as it is not producing the results that I expect when modelling count data using poisson distribution

Modeling

maxwellsmart September 6, 2020, 10:13pm 13

Thanks - this is very helpful and supports my understanding. Would definitely vote for Bob to be king of Stan.

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Trying to understand lp__ as it is not producing the results that I expect when modelling count data using poisson distribution

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