Hi,

I’m trying to fit a GEV with the following data, taking from the annual maxima (block maxima approach):

```
array([ 3.698211 , 12.084102 , 15.341089 , 9.201157 , 7.0970197,
13.50453 , 26.924686 , 16.444876 , 9.672132 , 8.024217 ,
22.364328 , 16.575699 , 6.1274405, 8.381071 , 16.532887 ,
14.530084 , 5.5311694, 8.343545 , 13.957676 , 5.140601 ,
23.630177 ], dtype=float32)
```

Very few data, I know. Another option would be to use Peak Over Threshold instead of Block Maxima, and I think that would add more data, but Peak Over Threshold needs a Generalized Pareto Distribution, and I can’t find that distribution in PyMC right now.

I did, following Generalized Extreme Value Distribution — PyMC example gallery :

```
import pymc as pm
import numpy as np
import pymc_experimental.distributions as pmx
# Consider return period of 5 years (p=1/5)
p = 1/5
with pm.Model() as model:
# Priors
μ = pm.Normal("μ", mu=2, sigma=2)
σ = pm.HalfNormal("σ", sigma=2)
ξ = pm.Normal("ξ", mu=1, sigma=1.5)
# Estimation
gev = pmx.GenExtreme("gev", mu=μ, sigma=σ, xi=ξ, observed=data)
# Return level
z_p = pm.Deterministic("z_p", μ - (σ / ξ) * (1 - (-np.log(1 - p)) ** (-ξ)))
# The inference
with model:
trace = pm.sample(
5000,
#cores=4,
chains=4,
tune=1000,
#initvals={"μ": 2, "σ": 1.0, "ξ": 1},
target_accept=0.98,
)
# add trace to existing idata object
idata.extend(trace)
```

I have done many tests changing the priors, the initialization of the priors and I have standardized the data, but I can’t get rid of the so many divergences. Sometimes even the NUTS stops because the initialization doesn’t work.

I could perform a frequentist analysis with “PyExtremes”, so I’d say there should be some combination of parameters allowing also a Bayesian analysis. Any help would be very much appreciated. Thx.