# Comparing samplers
In this tutorial, we are comparing two different sampling schemes on the
`mcycle` dataset with a Gaussian location-scale regression model and two
splines for the mean and the standard deviation. The `mcycle` dataset is
a “data frame giving a series of measurements of head acceleration in a
simulated motorcycle accident, used to test crash helmets” (from the
help page). It contains the following two variables:
- `times`: in milliseconds after impact
- `accel`: in g
We start off in R by loading the dataset and setting up the model with
the `rliesel::liesel()` function.
``` r
library(MASS)
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
data(mcycle)
with(mcycle, plot(times, accel))
```
``` r
model <- liesel(
response = mcycle$accel,
distribution = "Normal",
predictors = list(
loc = predictor(~ s(times)),
scale = predictor(~ s(times), inverse_link = "Exp")
),
data = mcycle
)
```
Installed Liesel version 0.2.4 is compatible.
## Metropolis-in-Gibbs
First, we try a Metropolis-in-Gibbs sampling scheme with IWLS kernels
for the regression coefficients ($\boldsymbol{\beta}$) and Gibbs kernels
for the smoothing parameters ($\tau^2$) of the splines.
``` python
import liesel.model as lsl
model = r.model
builder = lsl.dist_reg_mcmc(model, seed=42, num_chains=4)
builder.set_duration(warmup_duration=5000, 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_01: 0, 1, 1, 0 / 75 transitions
liesel.goose.engine - WARNING - Errors per chain for kernel_02: 1, 1, 1, 1 / 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_01: 1, 1, 0, 0 / 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_01: 0, 0, 1, 0 / 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_01: 0, 0, 0, 1 / 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_01: 0, 0, 0, 1 / 200 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 400 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_01: 0, 1, 1, 1 / 400 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 800 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_01: 1, 1, 1, 1 / 800 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 3300 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_01: 1, 0, 1, 0 / 3300 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_01: 0, 1, 0, 0 / 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 - INFO - Finished epoch
Clearly, the performance of the sampler could be better, especially for
the intercept of the mean. The corresponding chain exhibits a very
strong autocorrelation.
``` python
import liesel.goose as gs
results = engine.get_results()
gs.Summary(results)
```
Parameter summary:
|
|
|
kernel
|
mean
|
sd
|
q_0.05
|
q_0.5
|
q_0.95
|
sample_size
|
ess_bulk
|
ess_tail
|
rhat
|
|
parameter
|
index
|
|
|
|
|
|
|
|
|
|
|
|
loc_np0_beta
|
(0,)
|
kernel_04
|
-123.925
|
252.403
|
-529.979
|
-136.899
|
310.361
|
4000
|
32.770
|
283.680
|
1.093
|
|
(1,)
|
kernel_04
|
-1443.933
|
242.040
|
-1857.528
|
-1438.059
|
-1052.284
|
4000
|
154.026
|
326.176
|
1.025
|
|
(2,)
|
kernel_04
|
-713.112
|
170.964
|
-996.168
|
-709.703
|
-427.398
|
4000
|
157.377
|
733.196
|
1.027
|
|
(3,)
|
kernel_04
|
-566.761
|
106.593
|
-742.514
|
-566.403
|
-392.259
|
4000
|
345.613
|
699.904
|
1.021
|
|
(4,)
|
kernel_04
|
-1127.952
|
93.165
|
-1283.961
|
-1125.748
|
-978.007
|
4000
|
287.206
|
523.644
|
1.017
|
|
(5,)
|
kernel_04
|
-59.236
|
32.689
|
-112.265
|
-59.756
|
-5.968
|
4000
|
174.249
|
355.672
|
1.018
|
|
(6,)
|
kernel_04
|
-213.544
|
20.962
|
-246.796
|
-214.359
|
-179.102
|
4000
|
143.348
|
633.100
|
1.038
|
|
(7,)
|
kernel_04
|
115.530
|
71.315
|
12.799
|
108.984
|
239.090
|
4000
|
154.495
|
199.531
|
1.024
|
|
(8,)
|
kernel_04
|
30.199
|
18.463
|
3.722
|
28.654
|
61.787
|
4000
|
143.278
|
197.396
|
1.036
|
|
loc_np0_tau2
|
()
|
kernel_03
|
735262.000
|
559525.062
|
253877.688
|
592855.656
|
1666969.462
|
4000
|
1352.310
|
2737.206
|
1.003
|
|
loc_p0_beta
|
(0,)
|
kernel_05
|
-23.949
|
1.557
|
-26.545
|
-23.892
|
-21.367
|
4000
|
13.121
|
20.016
|
1.246
|
|
scale_np0_beta
|
(0,)
|
kernel_01
|
8.056
|
10.744
|
-6.509
|
5.540
|
27.736
|
4000
|
37.591
|
150.933
|
1.103
|
|
(1,)
|
kernel_01
|
-1.407
|
5.931
|
-11.598
|
-1.060
|
8.103
|
4000
|
210.887
|
401.406
|
1.014
|
|
(2,)
|
kernel_01
|
-17.430
|
9.659
|
-33.542
|
-17.559
|
-2.789
|
4000
|
28.120
|
129.904
|
1.123
|
|
(3,)
|
kernel_01
|
10.911
|
5.240
|
2.846
|
10.915
|
19.429
|
4000
|
39.408
|
147.850
|
1.088
|
|
(4,)
|
kernel_01
|
2.692
|
4.240
|
-4.188
|
2.627
|
9.817
|
4000
|
56.953
|
294.239
|
1.073
|
|
(5,)
|
kernel_01
|
4.076
|
1.937
|
1.095
|
3.922
|
7.346
|
4000
|
24.444
|
117.743
|
1.118
|
|
(6,)
|
kernel_01
|
-0.588
|
3.199
|
-6.105
|
-0.386
|
4.074
|
4000
|
21.601
|
122.160
|
1.138
|
|
(7,)
|
kernel_01
|
-0.311
|
3.659
|
-5.933
|
-0.648
|
6.267
|
4000
|
92.055
|
165.632
|
1.033
|
|
(8,)
|
kernel_01
|
-1.197
|
1.925
|
-4.500
|
-1.071
|
1.700
|
4000
|
26.872
|
131.637
|
1.122
|
|
scale_np0_tau2
|
()
|
kernel_00
|
137.908
|
162.827
|
10.762
|
85.152
|
428.775
|
4000
|
27.860
|
179.005
|
1.113
|
|
scale_p0_beta
|
(0,)
|
kernel_02
|
2.763
|
0.070
|
2.653
|
2.762
|
2.879
|
4000
|
163.264
|
926.926
|
1.024
|
Error summary:
|
|
|
|
|
count
|
relative
|
|
kernel
|
error_code
|
error_msg
|
phase
|
|
|
|
kernel_01
|
90
|
nan acceptance prob
|
warmup
|
17
|
0.001
|
|
posterior
|
0
|
0.000
|
|
kernel_02
|
90
|
nan acceptance prob
|
warmup
|
4
|
0.000
|
|
posterior
|
0
|
0.000
|
``` python
fig = gs.plot_trace(results, "loc_p0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "loc_np0_tau2")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "loc_np0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_p0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_np0_tau2")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_np0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
To confirm that the chains have converged to reasonable values, here is
a plot of the estimated mean function:
``` python
summary = gs.Summary(results).to_dataframe().reset_index()
```
``` r
library(dplyr)
```
Attaching package: 'dplyr'
The following object is masked from 'package:MASS':
select
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"]$value)
f <- X %*% beta
beta0 <- summary %>%
filter(variable == "loc_p0_beta") %>%
group_by(var_index) %>%
summarize(mean = mean(mean)) %>%
ungroup()
beta0 <- beta0$mean
ggplot(data.frame(times = mcycle$times, mean = beta0 + f)) +
geom_line(aes(times, mean), color = palette()[2], size = 1) +
geom_point(aes(times, accel), data = mcycle) +
ggtitle("Estimated mean function") +
theme_minimal()
```
## NUTS sampler
As an alternative, we try a NUTS kernel which samples all model
parameters (regression coefficients and smoothing parameters) in one
block. To do so, we first need to log-transform the smoothing
parameters. This is the model graph before the transformation:
``` python
lsl.plot_vars(model)
```
Before transforming the smoothing parameters with the
`lsl.transform_parameter()` function, we first need to copy all model
nodes. Once this is done, we need to update the output nodes of the
smoothing parameters and rebuild the model. There are two additional
nodes in the new model graph.
``` python
import tensorflow_probability.substrates.jax.bijectors as tfb
nodes, _vars = model.pop_nodes_and_vars()
gb = lsl.GraphBuilder()
gb.add(_vars["response"])
```
GraphBuilder(0 nodes, 1 vars)
``` python
_ = gb.transform(_vars["loc_np0_tau2"], tfb.Exp)
_ = gb.transform(_vars["scale_np0_tau2"], tfb.Exp)
model = gb.build_model()
lsl.plot_vars(model)
```
Now we can set up the NUTS sampler, which is straightforward because we
are using only one kernel.
``` python
parameters = [name for name, var in model.vars.items() if var.parameter]
builder = gs.EngineBuilder(seed=42, num_chains=4)
builder.set_model(lsl.GooseModel(model))
builder.add_kernel(gs.NUTSKernel(parameters))
builder.set_initial_values(model.state)
builder.set_duration(warmup_duration=5000, 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: 45, 31, 51, 61 / 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: 9, 21, 13, 8 / 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: 40, 50, 49, 46 / 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: 93, 93, 97, 91 / 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: 196, 196, 192, 191 / 200 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 400 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 388, 371, 382, 381 / 400 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 800 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 789, 760, 772, 768 / 800 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 3300 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 3138, 3198, 3213, 3213 / 3300 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: 46, 47, 48, 49 / 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: 999, 999, 998, 998 / 1000 transitions
liesel.goose.engine - INFO - Finished epoch
The results are mixed. On the one hand, the NUTS sampler performs much
better on the intercepts (for both the mean and the standard deviation),
but on the other hand, the Metropolis-in-Gibbs sampler with the IWLS
kernels seems to work better for the spline coefficients.
``` python
results = engine.get_results()
gs.Summary(results)
```
Parameter summary:
|
|
|
kernel
|
mean
|
sd
|
q_0.05
|
q_0.5
|
q_0.95
|
sample_size
|
ess_bulk
|
ess_tail
|
rhat
|
|
parameter
|
index
|
|
|
|
|
|
|
|
|
|
|
|
loc_np0_beta
|
(0,)
|
kernel_00
|
69.469
|
94.074
|
-19.308
|
24.245
|
235.016
|
4000
|
4.338
|
11.485
|
3.937
|
|
(1,)
|
kernel_00
|
-34.872
|
29.647
|
-79.634
|
-31.955
|
12.604
|
4000
|
4.462
|
10.910
|
3.398
|
|
(2,)
|
kernel_00
|
-225.643
|
173.152
|
-489.674
|
-190.451
|
-2.248
|
4000
|
4.560
|
12.395
|
3.057
|
|
(3,)
|
kernel_00
|
-29.091
|
129.928
|
-242.193
|
-10.036
|
216.950
|
4000
|
4.723
|
11.857
|
2.639
|
|
(4,)
|
kernel_00
|
-712.810
|
135.987
|
-969.966
|
-716.210
|
-480.268
|
4000
|
4.894
|
11.407
|
2.437
|
|
(5,)
|
kernel_00
|
-82.669
|
42.168
|
-153.224
|
-73.919
|
-23.744
|
4000
|
5.571
|
12.573
|
1.928
|
|
(6,)
|
kernel_00
|
-130.846
|
30.345
|
-176.981
|
-132.647
|
-81.529
|
4000
|
5.781
|
18.869
|
1.858
|
|
(7,)
|
kernel_00
|
29.494
|
41.749
|
-25.851
|
29.180
|
105.536
|
4000
|
4.729
|
11.952
|
2.677
|
|
(8,)
|
kernel_00
|
20.231
|
9.427
|
5.199
|
20.017
|
38.063
|
4000
|
5.258
|
13.983
|
2.151
|
|
loc_np0_tau2_transformed
|
()
|
kernel_00
|
11.376
|
0.689
|
10.245
|
11.377
|
12.506
|
4000
|
10.741
|
23.437
|
1.277
|
|
loc_p0_beta
|
(0,)
|
kernel_00
|
-17.948
|
3.408
|
-23.355
|
-18.022
|
-12.076
|
4000
|
9.897
|
53.404
|
1.330
|
|
scale_np0_beta
|
(0,)
|
kernel_00
|
-8.401
|
4.703
|
-16.181
|
-7.819
|
-2.281
|
4000
|
4.401
|
11.172
|
3.516
|
|
(1,)
|
kernel_00
|
4.151
|
6.940
|
-6.551
|
3.753
|
16.141
|
4000
|
25.731
|
81.149
|
1.100
|
|
(2,)
|
kernel_00
|
-14.150
|
8.351
|
-28.065
|
-13.854
|
-1.076
|
4000
|
9.980
|
64.035
|
1.310
|
|
(3,)
|
kernel_00
|
14.462
|
6.344
|
3.769
|
14.785
|
24.659
|
4000
|
10.223
|
34.126
|
1.301
|
|
(4,)
|
kernel_00
|
6.075
|
4.746
|
-1.435
|
6.085
|
13.940
|
4000
|
12.279
|
81.324
|
1.236
|
|
(5,)
|
kernel_00
|
5.980
|
2.517
|
1.815
|
6.063
|
9.952
|
4000
|
9.152
|
41.744
|
1.355
|
|
(6,)
|
kernel_00
|
1.213
|
2.341
|
-2.705
|
1.275
|
4.874
|
4000
|
13.211
|
102.812
|
1.209
|
|
(7,)
|
kernel_00
|
1.880
|
4.552
|
-4.995
|
1.612
|
9.654
|
4000
|
16.937
|
399.531
|
1.159
|
|
(8,)
|
kernel_00
|
-0.124
|
1.276
|
-2.398
|
-0.052
|
1.820
|
4000
|
26.935
|
1328.627
|
1.095
|
|
scale_np0_tau2_transformed
|
()
|
kernel_00
|
4.447
|
1.022
|
2.551
|
4.586
|
5.955
|
4000
|
9.088
|
29.637
|
1.357
|
|
scale_p0_beta
|
(0,)
|
kernel_00
|
3.004
|
0.076
|
2.878
|
3.005
|
3.127
|
4000
|
15.581
|
183.202
|
1.177
|
Error summary:
|
|
|
|
|
count
|
relative
|
|
kernel
|
error_code
|
error_msg
|
phase
|
|
|
|
kernel_00
|
1
|
divergent transition
|
warmup
|
2586
|
0.129
|
|
posterior
|
0
|
0.000
|
|
2
|
maximum tree depth
|
warmup
|
15753
|
0.788
|
|
posterior
|
3994
|
0.998
|
|
3
|
divergent transition + maximum tree depth
|
warmup
|
797
|
0.040
|
|
posterior
|
0
|
0.000
|
``` python
fig = gs.plot_trace(results, "loc_p0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "loc_np0_tau2_transformed")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "loc_np0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_p0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_np0_tau2_transformed")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
``` python
fig = gs.plot_trace(results, "scale_np0_beta")
```
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
Again, here is a plot of the estimated mean function:
``` python
summary = gs.Summary(results).to_dataframe().reset_index()
```
``` r
library(dplyr)
library(ggplot2)
library(reticulate)
summary <- py$summary
model <- py$model
beta <- summary %>%
filter(variable == "loc_np0_beta") %>%
group_by(var_index) %>%
summarize(mean = mean(mean)) %>%
ungroup()
beta <- beta$mean
X <- model$vars["loc_np0_X"]$value
f <- X %*% beta
beta0 <- summary %>%
filter(variable == "loc_p0_beta") %>%
group_by(var_index) %>%
summarize(mean = mean(mean)) %>%
ungroup()
beta0 <- beta0$mean
ggplot(data.frame(times = mcycle$times, mean = beta0 + f)) +
geom_line(aes(times, mean), color = palette()[2], size = 1) +
geom_point(aes(times, accel), data = mcycle) +
ggtitle("Estimated mean function") +
theme_minimal()
```
