I’d like to use a Poisson distribution and it’s conjugate prior Gamma…

But I’m having problem to understand a basic example.

This is the sampling of ‘mu’ for a Poisson distribution with one observed value = 1.

```
with pm.Model() as model:
mu = pm.HalfFlat('mu')
p_obs = pm.Poisson('p_obs',mu=mu,observed=[1])
trace = pm.sample()#tune=2000,draws=10000,target_accept=0.9)
pm.traceplot(trace)
```

This is what I get :

And

`trace['mu'].mean() = 1.993718...`

First surprise : I expected the mean to be around 1, not 2… !?

Then I try this other way to sample mu with the same data (observed value =1 , seen once) directly with a Gamma which is the Poisson conjugate prior.

```
with pm.Model() as model:
mu = pm.Gamma('mu',alpha=1,beta=1)
trace = pm.sample() #tune=2000,draws=10000)#,target_accept=0.9)
pm.traceplot(trace)
```

Which shows this posterior :

This does not correspond to the previous curve !! I don’t understand why…

And when it comes to the mean of the samples:

`trace['mu'].mean() = 1.0148405502...`

Which is totally different from the previous model !

It’s closer to what I think it should be (regarding the observed data), but I don’t understand why this two models give far different results…

I don’t know which model is wrong, and why.

Any help will be appreciated.