# GEV responses

In this tutorial, we illustrate how to set up a distributional
regression model with the generalized extreme value distribution as a
response distribution. First, we simulate some data in R:

- The location parameter ($\mu$) is a function of an intercept and a
  non-linear covariate effect.
- The scale parameter ($\sigma$) is a function of an intercept and a
  linear effect and uses a log-link.
- The shape or concentration parameter ($\xi$) is a function of an
  intercept and a linear effect.

After simulating the data, we can configure the model with a single call
to the `rliesel::liesel()` function.

``` r
library(rliesel)
```

    Please make sure you are using a virtual or conda environment with Liesel installed, e.g. using `reticulate::use_virtualenv()` or `reticulate::use_condaenv()`. See `vignette("versions", "reticulate")`.

    After setting the environment, check if the installed versions of RLiesel and Liesel are compatible with `check_liesel_version()`.

``` r
library(VGAM)
```

    Loading required package: stats4

    Loading required package: splines

``` r
set.seed(1337)

n <- 1000

x0 <- runif(n)
x1 <- runif(n)
x2 <- runif(n)

y <- rgev(
  n,
  location = 0 + sin(2 * pi * x0),
  scale = exp(-3 + x1),
  shape = 0.1 + x2
)

plot(y)
```

![](03-gev_files/figure-commonmark/model-1.png)

``` r
model <- liesel(
  response = y,
  distribution = "GeneralizedExtremeValue",
  predictors = list(
    loc = predictor(~ s(x0)),
    scale = predictor(~ x1, inverse_link = "Exp"),
    concentration = predictor(~ x2)
  )
)
```

    Installed Liesel version 0.2.5 is compatible, continuing to set up model

Now, we can continue in Python and use the `lsl.dist_reg_mcmc()`
function to set up a sampling algorithm with IWLS kernels for the
regression coefficients ($\boldsymbol{\beta}$) and a Gibbs kernel for
the smoothing parameter ($\tau^2$) of the spline. Note that we need to
set $\beta_0$ for $\xi$ to 0.1 manually, because $\xi = 0$ breaks the
sampler.

``` python
import liesel.model as lsl
import jax.numpy as jnp

model = r.model

# concentration == 0.0 seems to break the sampler
model.vars["concentration_p0_beta"].value = jnp.array([0.1, 0.0])

builder = lsl.dist_reg_mcmc(model, seed=42, num_chains=4)
builder.set_duration(warmup_duration=1000, posterior_duration=1000)

engine = builder.build()
```

    liesel.goose.engine - INFO - Initializing kernels...
    liesel.goose.engine - INFO - Done

``` python
engine.sample_all_epochs()
```

    liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 75 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 75, 75, 75, 75 / 75 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 75, 75, 75, 75 / 75 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 75, 75, 75, 75 / 75 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 75, 75, 75, 75 / 75 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 25 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 25, 25, 25, 25 / 25 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 25, 25, 25, 25 / 25 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 25, 25, 25, 25 / 25 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 25, 25, 25, 25 / 25 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 50 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 100 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 100, 100, 100, 100 / 100 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 100, 100, 100, 100 / 100 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 100, 100, 100, 100 / 100 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 100, 100, 100, 100 / 100 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 200 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 200, 200, 200, 200 / 200 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 200, 200, 200, 200 / 200 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 200, 200, 200, 200 / 200 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 200, 200, 200, 200 / 200 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 500 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 500, 500, 500, 500 / 500 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 500, 500, 500, 500 / 500 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 500, 500, 500, 500 / 500 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 500, 500, 500, 500 / 500 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 50 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 50, 50, 50, 50 / 50 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Finished warmup
    liesel.goose.engine - INFO - Starting epoch: POSTERIOR, 1000 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1000, 1000, 1000, 1000 / 1000 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_01: 1000, 1000, 1000, 1000 / 1000 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_03: 1000, 1000, 1000, 1000 / 1000 transitions
    liesel.goose.engine - WARNING - Errors per chain for kernel_04: 1000, 1000, 1000, 1000 / 1000 transitions
    liesel.goose.engine - INFO - Finished epoch

Some tabular summary statistics of the posterior samples:

``` python
import liesel.goose as gs

results = engine.get_results()
gs.Summary(results)
```

<p>
<strong>Parameter summary:</strong>
</p>
<table border="0" class="dataframe">
<thead>
<tr style="text-align: right;">
<th>
</th>
<th>
</th>
<th>
kernel
</th>
<th>
mean
</th>
<th>
sd
</th>
<th>
q_0.05
</th>
<th>
q_0.5
</th>
<th>
q_0.95
</th>
<th>
sample_size
</th>
<th>
ess_bulk
</th>
<th>
ess_tail
</th>
<th>
rhat
</th>
</tr>
<tr>
<th>
parameter
</th>
<th>
index
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
</tr>
</thead>
<tbody>
<tr>
<th rowspan="2" valign="top">
concentration_p0_beta
</th>
<th>
(0,)
</th>
<td>
kernel_00
</td>
<td>
-0.181
</td>
<td>
1.327
</td>
<td>
-1.305
</td>
<td>
-0.743
</td>
<td>
2.069
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(1,)
</th>
<td>
kernel_00
</td>
<td>
-0.254
</td>
<td>
1.126
</td>
<td>
-1.868
</td>
<td>
-0.197
</td>
<td>
1.246
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th rowspan="9" valign="top">
loc_np0_beta
</th>
<th>
(0,)
</th>
<td>
kernel_03
</td>
<td>
0.242
</td>
<td>
1.007
</td>
<td>
-1.481
</td>
<td>
0.715
</td>
<td>
1.019
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(1,)
</th>
<td>
kernel_03
</td>
<td>
-0.057
</td>
<td>
1.423
</td>
<td>
-1.486
</td>
<td>
-0.109
</td>
<td>
1.475
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(2,)
</th>
<td>
kernel_03
</td>
<td>
-0.107
</td>
<td>
0.608
</td>
<td>
-1.094
</td>
<td>
0.066
</td>
<td>
0.537
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(3,)
</th>
<td>
kernel_03
</td>
<td>
0.588
</td>
<td>
0.783
</td>
<td>
-0.668
</td>
<td>
0.766
</td>
<td>
1.488
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(4,)
</th>
<td>
kernel_03
</td>
<td>
-0.550
</td>
<td>
1.340
</td>
<td>
-1.466
</td>
<td>
-1.248
</td>
<td>
1.762
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(5,)
</th>
<td>
kernel_03
</td>
<td>
1.342
</td>
<td>
0.435
</td>
<td>
0.778
</td>
<td>
1.381
</td>
<td>
1.830
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(6,)
</th>
<td>
kernel_03
</td>
<td>
-0.468
</td>
<td>
0.603
</td>
<td>
-1.227
</td>
<td>
-0.423
</td>
<td>
0.201
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(7,)
</th>
<td>
kernel_03
</td>
<td>
0.322
</td>
<td>
0.885
</td>
<td>
-0.499
</td>
<td>
0.005
</td>
<td>
1.777
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(8,)
</th>
<td>
kernel_03
</td>
<td>
0.064
</td>
<td>
1.296
</td>
<td>
-1.605
</td>
<td>
-0.043
</td>
<td>
1.946
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
loc_np0_tau2
</th>
<th>
()
</th>
<td>
kernel_02
</td>
<td>
1.682
</td>
<td>
1.263
</td>
<td>
0.623
</td>
<td>
1.366
</td>
<td>
3.730
</td>
<td>
4000
</td>
<td>
69.478
</td>
<td>
649.803
</td>
<td>
1.045
</td>
</tr>
<tr>
<th>
loc_p0_beta
</th>
<th>
(0,)
</th>
<td>
kernel_04
</td>
<td>
-0.250
</td>
<td>
1.297
</td>
<td>
-1.715
</td>
<td>
-0.266
</td>
<td>
1.248
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th rowspan="2" valign="top">
scale_p0_beta
</th>
<th>
(0,)
</th>
<td>
kernel_01
</td>
<td>
0.182
</td>
<td>
1.311
</td>
<td>
-1.729
</td>
<td>
0.362
</td>
<td>
1.732
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
<tr>
<th>
(1,)
</th>
<td>
kernel_01
</td>
<td>
0.314
</td>
<td>
1.146
</td>
<td>
-1.338
</td>
<td>
0.358
</td>
<td>
1.878
</td>
<td>
4000
</td>
<td>
4.032
</td>
<td>
4.032
</td>
<td>
inf
</td>
</tr>
</tbody>
</table>
<p>
<strong>Error summary:</strong>
</p>
<table border="0" class="dataframe">
<thead>
<tr style="text-align: right;">
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
count
</th>
<th>
relative
</th>
</tr>
<tr>
<th>
kernel
</th>
<th>
error_code
</th>
<th>
error_msg
</th>
<th>
phase
</th>
<th>
</th>
<th>
</th>
</tr>
</thead>
<tbody>
<tr>
<th rowspan="2" valign="top">
kernel_00
</th>
<th rowspan="2" valign="top">
90
</th>
<th rowspan="2" valign="top">
nan acceptance prob
</th>
<th>
warmup
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th>
posterior
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th rowspan="2" valign="top">
kernel_01
</th>
<th rowspan="2" valign="top">
90
</th>
<th rowspan="2" valign="top">
nan acceptance prob
</th>
<th>
warmup
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th>
posterior
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th rowspan="2" valign="top">
kernel_03
</th>
<th rowspan="2" valign="top">
90
</th>
<th rowspan="2" valign="top">
nan acceptance prob
</th>
<th>
warmup
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th>
posterior
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th rowspan="2" valign="top">
kernel_04
</th>
<th rowspan="2" valign="top">
90
</th>
<th rowspan="2" valign="top">
nan acceptance prob
</th>
<th>
warmup
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
<tr>
<th>
posterior
</th>
<td>
4000
</td>
<td>
1.000
</td>
</tr>
</tbody>
</table>

And the corresponding trace plots:

``` python
fig = gs.plot_trace(results, "loc_p0_beta")
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](03-gev_files/figure-commonmark/traces-1.png)

``` python
fig = gs.plot_trace(results, "loc_np0_tau2")
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](03-gev_files/figure-commonmark/traces-2.png)

``` python
fig = gs.plot_trace(results, "loc_np0_beta")
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](03-gev_files/figure-commonmark/traces-3.png)

``` python
fig = gs.plot_trace(results, "scale_p0_beta")
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](03-gev_files/figure-commonmark/traces-4.png)

``` python
fig = gs.plot_trace(results, "concentration_p0_beta")
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](03-gev_files/figure-commonmark/traces-5.png)

We need to reset the index of the summary data frame before we can
transfer it to R.

``` python
summary = gs.Summary(results).to_dataframe().reset_index()
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/arviz/stats/diagnostics.py:592: RuntimeWarning: divide by zero encountered in scalar divide
      (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)

After transferring the summary data frame to R, we can process it with
packages like dplyr and ggplot2. Here is a visualization of the
estimated spline vs. the true function:

``` r
library(dplyr)
```


    Attaching package: 'dplyr'

    The following objects are masked from 'package:stats':

        filter, lag

    The following objects are masked from 'package:base':

        intersect, setdiff, setequal, union

``` r
library(ggplot2)
library(reticulate)

summary <- py$summary

beta <- summary %>%
  filter(variable == "loc_np0_beta") %>%
  group_by(var_index) %>%
  summarize(mean = mean(mean)) %>%
  ungroup()

beta <- beta$mean
X <- py_to_r(model$vars["loc_np0_X"]$value)
estimate <- X %*% beta

true <- sin(2 * pi * x0)

ggplot(data.frame(x0 = x0, estimate = estimate, true = true)) +
  geom_line(aes(x0, estimate), color = palette()[2]) +
  geom_line(aes(x0, true), color = palette()[4]) +
  ggtitle("Estimated spline (red) vs. true function (blue)") +
  ylab("f") +
  theme_minimal()
```

![](03-gev_files/figure-commonmark/spline-11.png)