Plotting in HSSM¶

This tutorial demonstrates the plotting functionalities in HSSM.

While the ArviZ package provides many plotting utilities, HSSM aims complement the ArviZ package with additional types of plots specific for hierarchical sequential sampling models. In addition, HSSM also provides some plotting API directly from the HSSM model object with some additional tweaks for convenience.

Most of the plotting and summary functionalities can be found in hssm.plotting module, and additional convenience functions are exposed through the top-level HSSM model as well.

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# If running this on Colab, please uncomment the next line and
# !pip install hssm
# If running this on Colab, please uncomment the next line and
# !pip install hssm

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from pathlib import Path

import arviz as az
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

import hssm
import hssm.plotting

%matplotlib inline
%config InlineBackend.figure_format='retina'

import warnings

warnings.filterwarnings("ignore")
from pathlib import Path

import arviz as az
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

import hssm
import hssm.plotting

%matplotlib inline
%config InlineBackend.figure_format='retina'

import warnings

warnings.filterwarnings("ignore")

Model setup¶

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fixtures_dir = Path("../../tests/fixtures")
cav_data_test = pd.read_csv(fixtures_dir / "cavanagh_theta_test.csv")
cav_data_traces = az.from_netcdf(fixtures_dir / "cavanagh_idata.nc")
fixtures_dir = Path("../../tests/fixtures")
cav_data_test = pd.read_csv(fixtures_dir / "cavanagh_theta_test.csv")
cav_data_traces = az.from_netcdf(fixtures_dir / "cavanagh_idata.nc")

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# For demonstration purposes,
# `cav_data_test` is a subset of the `cavanagh_theta_nn` dataset
# with 5 subjects and 100 observation each

cav_data_test
# For demonstration purposes,
# `cav_data_test` is a subset of the `cavanagh_theta_nn` dataset
# with 5 subjects and 100 observation each

cav_data_test

Out[4]:

	participant_id	stim	rt	response	theta	dbs	conf
0	0	WL	0.928	-1.0	-0.521933	0	LC
1	0	WL	0.661	1.0	-0.219645	1	LC
2	0	WW	2.350	-1.0	-0.168728	1	HC
3	0	LL	1.250	-1.0	-0.104636	1	HC
4	0	LL	1.170	-1.0	1.122720	1	HC
...	...	...	...	...	...	...	...
495	4	WL	0.606	-1.0	-0.635942	0	LC
496	4	WL	0.745	-1.0	-0.166833	0	LC
497	4	WW	1.320	1.0	-0.283396	1	HC
498	4	LL	1.640	1.0	0.462584	1	HC
499	4	WL	0.822	1.0	-0.019645	0	LC

500 rows × 7 columns

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# Model parameter specification

cav_model = hssm.HSSM(
    model="ddm",
    data=cav_data_test,
    include=[
        {
            "name": "v",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
                "theta": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
            },
            "formula": "v ~  theta + (1|participant_id)",
            "link": "identity",
        },
    ],
)

# Perform sampling
# cav_model.sample()
# Model parameter specification

cav_model = hssm.HSSM(
    model="ddm",
    data=cav_data_test,
    include=[
        {
            "name": "v",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
                "theta": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
            },
            "formula": "v ~  theta + (1|participant_id)",
            "link": "identity",
        },
    ],
)

# Perform sampling
# cav_model.sample()

Model initialized successfully.

For demonstration purposes, we inject into the model an existing trace with posterior predictive sampling already performed. A posterior_predictive attribute is added to the traces object. A rt,response_mean variable is also added to the posterior attribute during predictive sampling.

Convenience functions from the top-level `hssm.HSSM` model object¶

The ArviZ package provides az.summary() and az.plot_trace_dist() functions that are very frequently used. HSSM previously provided model.summary() and model.plot_trace() convenience methods, but these have been removed in v0.4.0. Please use az.summary() and az.plot_trace_dist() directly.

1. Using `az.summary()`¶

Use az.summary() to get a summary of the posterior distribution. Note that when some parameters are the targets of regressions, ArviZ will also plot the computed values for each regressor on each observation, which is highly inefficient. You may need to filter out computed values manually.

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set(list(cav_model.traces.posterior.data_vars.keys()))
set(list(cav_model.traces.posterior.data_vars.keys()))

Out[7]:

{'a',
 't',
 'v',
 'v_1|participant_id',
 'v_1|participant_id_sigma',
 'v_Intercept',
 'v_theta',
 'z'}

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az.summary(cav_data_traces)
az.summary(cav_data_traces)

Out[8]:

	mean	sd	eti89_lb	eti89_ub	ess_bulk	ess_tail	r_hat	mcse_mean	mcse_sd
v_Intercept	0.42	0.27	-0.015	0.83	261	235	1.00	0.017	0.013
v_theta	0.062	0.048	-0.014	0.14	619	593	1.01	0.002	0.0014
a	1.044	0.024	1	1.1	831	696	1.00	0.00084	0.00063
z	0.504	0.0195	0.47	0.53	766	511	1.00	0.0007	0.00047
t	0.337	0.0134	0.31	0.36	645	411	1.01	0.00054	0.00038
...	...	...	...	...	...	...	...	...	...
v[495]	1.05	0.172	0.78	1.3	746	776	1.00	0.0063	0.0041
v[496]	1.08	0.169	0.82	1.4	790	688	1.00	0.006	0.004
v[497]	1.08	0.17	0.81	1.3	780	646	1.00	0.0061	0.004
v[498]	1.12	0.17	0.85	1.4	860	699	1.00	0.0058	0.004
v[499]	1.09	0.169	0.82	1.4	805	684	1.00	0.0059	0.004

511 rows × 9 columns

Compare this with the output of ArviZ az.summary():

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# Because of posterior predictive sampling, an `rt,response_mean` field was added to
# the traces object by default. ArviZ include these values by default.

# This is equivalent to calling
# cav_model.summary(include_computed_values=True)

az.summary(cav_model.traces)
# Because of posterior predictive sampling, an `rt,response_mean` field was added to
# the traces object by default. ArviZ include these values by default.

# This is equivalent to calling
# cav_model.summary(include_computed_values=True)

az.summary(cav_model.traces)

Out[9]:

	mean	sd	eti89_lb	eti89_ub	ess_bulk	ess_tail	r_hat	mcse_mean	mcse_sd
v_Intercept	0.42	0.27	-0.015	0.83	261	235	1.00	0.017	0.013
v_theta	0.062	0.048	-0.014	0.14	619	593	1.01	0.002	0.0014
a	1.044	0.024	1	1.1	831	696	1.00	0.00084	0.00063
z	0.504	0.0195	0.47	0.53	766	511	1.00	0.0007	0.00047
t	0.337	0.0134	0.31	0.36	645	411	1.01	0.00054	0.00038
...	...	...	...	...	...	...	...	...	...
v[495]	1.05	0.172	0.78	1.3	746	776	1.00	0.0063	0.0041
v[496]	1.08	0.169	0.82	1.4	790	688	1.00	0.006	0.004
v[497]	1.08	0.17	0.81	1.3	780	646	1.00	0.0061	0.004
v[498]	1.12	0.17	0.85	1.4	860	699	1.00	0.0058	0.004
v[499]	1.09	0.169	0.82	1.4	805	684	1.00	0.0059	0.004

511 rows × 9 columns

2. Using `az.plot_trace_dist()`¶

Use az.plot_trace_dist() to plot trace distributions. Note that you may need to call plt.tight_layout() afterwards for better layout:

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az.plot_trace_dist(cav_data_traces)
az.plot_trace_dist(cav_data_traces)

Out[10]:

<arviz_plots.plot_collection.PlotCollection at 0x12c0d27b0>

No description has been provided for this image

HSSM-specific plots¶

HSSM also offers various types of plots specific to hierarchical sequential sampling models.

1. Posterior predictive plots¶

Posterior predictive plots hssm.plot_predictive() plots the distribution of posterior predictive samples against the observed data.

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hssm.plotting.plot_predictive(cav_model, predictive_group="posterior_predictive");
hssm.plotting.plot_predictive(cav_model, predictive_group="posterior_predictive");

The predictive_group argument lets you choose between the posterior_predictive and the prior_predictive groups.

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hssm.plotting.plot_predictive(
    cav_model, predictive_group="prior_predictive", x_range=(-10, 10)
);
hssm.plotting.plot_predictive(
    cav_model, predictive_group="prior_predictive", x_range=(-10, 10)
);

No prior_predictive samples found. Generating prior_predictive samples using the provided DataTree object and the original data. This will modify the provided DataTree object, or if not provided, the traces object stored inside the model.

Sampling: [a, rt,response, t, v_1|participant_id_offset, v_1|participant_id_sigma, v_Intercept, v_theta, z]

This API is designed to be a light wrapper around Seaborn's sns.histplot() API. It accepts most arguments that sns.histplot() accepts. It also returns an ax object in matplotlib, so you can manipulate it further.

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ax = hssm.plotting.plot_predictive(cav_model)
sns.despine()
ax.set_ylabel("")
plt.title("Posterior Predictive Plot")
ax = hssm.plotting.plot_predictive(cav_model)
sns.despine()
ax.set_ylabel("")
plt.title("Posterior Predictive Plot")

Out[13]:

Text(0.5, 1.0, 'Posterior Predictive Plot')

You can also plot subsets of data in subplots:

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hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    col_wrap=3,  # limits to 3 columns per row
)
hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    col_wrap=3,  # limits to 3 columns per row
)

Out[14]:

<seaborn.axisgrid.FacetGrid at 0x130179e80>

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hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    col_wrap=3,  # limits to 3 columns per row
    predictive_group="prior_predictive",
)
hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    col_wrap=3,  # limits to 3 columns per row
    predictive_group="prior_predictive",
)

Out[15]:

<seaborn.axisgrid.FacetGrid at 0x130e3e350>

2-dimensional grids are also possible:

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hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    row="conf",
)
hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    row="conf",
)

Out[16]:

<seaborn.axisgrid.FacetGrid at 0x1311ba990>

When grids are used, this function returns a sns.FacetGrid object. You can also further customize your plot with this object as well. For example, you can set the titles each individual subplot according to a template or save the figure to disk (g.savefig()).

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g = hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    row="conf",
)

g.set_titles(template="{row_name} | Participant {col_name}")
g = hssm.plotting.plot_predictive(
    cav_model,
    col="participant_id",
    row="conf",
)

g.set_titles(template="{row_name} | Participant {col_name}")

Out[17]:

<seaborn.axisgrid.FacetGrid at 0x1301c5a90>

2. Quantile probability plots¶

Quantile probability plots [hssm.plot_quantile_probability()][hssm.plotting.plot_quantile_probability] are a type of plots useful for SSMs. For more information on quantile probability plots, please see here.

hssm.plotting.plot_quantile_probability() works similarly to hssm.plotting.plot_predictive() in that when only producing one plot (no grid), it returns an axis object, and when it returns multiple plots, it produces a FacetGrid object

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# Single plot, returns an axis object, which can be worked on further

ax = hssm.plotting.plot_quantile_probability(
    cav_model, cond="stim", predictive_style="points"
)
ax.set_ylim(0, 3);
# Single plot, returns an axis object, which can be worked on further

ax = hssm.plotting.plot_quantile_probability(
    cav_model, cond="stim", predictive_style="points"
)
ax.set_ylim(0, 3);

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ax = hssm.plotting.plot_quantile_probability(
    cav_model, cond="stim", predictive_style="ellipse", ellipse_confidence=0.95
)
ax.set_ylim(0, 3);
ax = hssm.plotting.plot_quantile_probability(
    cav_model, cond="stim", predictive_style="ellipse", ellipse_confidence=0.95
)
ax.set_ylim(0, 3);

The `quantile_by` argument¶

An important aspect of the underlying computations in the plot_quantile_probability() function is given by the quantile_by argument. This argument specifies an extra level of disaggregation in the quantile_probability() computations. E.g. if you pass participant_id, quantiles will first be computed at the participant level (on top of the levels you specify via grouping of the plot into subplots) and then aggregated.

The default is None so if you call this plot without specifying quantile_by, quantiles are computed at the basic subplot level.

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ax = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    predictive_style="ellipse",
    quantile_by=["participant_id"],
    ellipse_confidence=0.95,
)
ax.set_ylim(0, 4)
ax.set_xlim(0.15, 0.85);
ax = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    predictive_style="ellipse",
    quantile_by=["participant_id"],
    ellipse_confidence=0.95,
)
ax.set_ylim(0, 4)
ax.set_xlim(0.15, 0.85);

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# Multiple plots, returns a FacetGrid

g = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    col="participant_id",
    col_wrap=3,
    grid_kwargs=dict(
        ylim=(0, 3)
    ),  # additional kwargs to the grid can be passed through `grid_kwargs`
)
# Multiple plots, returns a FacetGrid

g = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    col="participant_id",
    col_wrap=3,
    grid_kwargs=dict(
        ylim=(0, 3)
    ),  # additional kwargs to the grid can be passed through `grid_kwargs`
)

The predictive_group argument works here too:

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# Multiple plots, returns a FacetGrid

g = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    col="participant_id",
    predictive_group="prior_predictive",
    col_wrap=3,
    grid_kwargs=dict(
        ylim=(0, 3)
    ),  # additional kwargs to the grid can be passed through `grid_kwargs`
)
# Multiple plots, returns a FacetGrid

g = hssm.plotting.plot_quantile_probability(
    cav_model,
    cond="stim",
    col="participant_id",
    predictive_group="prior_predictive",
    col_wrap=3,
    grid_kwargs=dict(
        ylim=(0, 3)
    ),  # additional kwargs to the grid can be passed through `grid_kwargs`
)

Model Cartoon Plots¶

This part showcases the plot_model_cartoon() function, which is part of the HSSM plotting submodule. The idea with these plots is to provide a pictorial representation of the underlying process that we recover with our model fits. You can explore various options to include posterior uncertainty graphically in these plots.

2 choices¶

Fully decomposed¶

Posterior Predictive¶

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ax_1 = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);
ax_1 = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);

No posterior_predictive samples found. Generating posterior_predictive samples using the provided DataTree object and the original data. This will modify the provided DataTree object, or if not provided, the traces object stored inside the model.

Prior Predictive¶

Note, the model cartoon plots look particularly unwieldy when using the prior predictive. If you want, take a look at the prior specifications and you can reason why and how it translates into such an unruly plot.

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ax_2 = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    predictive_group="prior_predictive",
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);
ax_2 = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    predictive_group="prior_predictive",
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);

No split by group | Inclue posterior uncertainty¶

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ax = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=100,
    bins=10,
    col="stim",
    row="participant_id",
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    alpha_mean=1.0,
    alpha_predictive=0.01,
    alpha_trajectories=0.5,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);
ax = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=100,
    bins=10,
    col="stim",
    row="participant_id",
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    alpha_mean=1.0,
    alpha_predictive=0.01,
    alpha_trajectories=0.5,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);

No posterior_predictive samples found. Generating posterior_predictive samples using the provided DataTree object and the original data. This will modify the provided DataTree object, or if not provided, the traces object stored inside the model.

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ax = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    predictive_group="prior_predictive",
    alpha_mean=1.0,
    alpha_predictive=0.01,
    alpha_trajectories=0.5,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);
ax = hssm.plotting.plot_model_cartoon(
    cav_model,
    n_samples=10,
    bins=20,
    col="stim",
    row="participant_id",
    groups=["dbs"],
    plot_predictive_mean=True,
    plot_predictive_samples=True,
    predictive_group="prior_predictive",
    alpha_mean=1.0,
    alpha_predictive=0.01,
    alpha_trajectories=0.5,
    # extra arguments for the underlying plot_model_cartoon() function
    n_trajectories=2,
);

N Choices¶

Data simulation¶

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stim_v = [0.0, 0.75, 1.0]
stim_names = ["low", "medium", "high"]
datasets = []

a_vec = np.random.normal(loc=1.25, scale=0.3, size=5)

for v_tmp in stim_v:
    for participant_id in range(5):
        a_tmp = a_vec[participant_id]
        data_tmp = hssm.simulate_data(
            model="race_no_bias_angle_4",
            theta=dict(
                a=a_tmp,
                v0=v_tmp,
                v1=v_tmp + 0.25,
                v2=v_tmp + 0.5,
                v3=v_tmp + 0.75,
                z=0.5,
                t=0.2,
                theta=0.1,
            ),
            size=200,
        )
        data_tmp["stim"] = stim_names[stim_v.index(v_tmp)]
        data_tmp["participant_id"] = str(participant_id)
        datasets.append(data_tmp)

dataset = pd.concat(datasets).reset_index(drop=True)
param_dict = {
    "v": {
        "low": np.repeat(stim_v[0], 5),
        "medium": np.repeat(stim_v[1], 5),
        "high": np.repeat(stim_v[2], 5),
    },
    "a": {"participant_id"},
}
stim_v = [0.0, 0.75, 1.0]
stim_names = ["low", "medium", "high"]
datasets = []

a_vec = np.random.normal(loc=1.25, scale=0.3, size=5)

for v_tmp in stim_v:
    for participant_id in range(5):
        a_tmp = a_vec[participant_id]
        data_tmp = hssm.simulate_data(
            model="race_no_bias_angle_4",
            theta=dict(
                a=a_tmp,
                v0=v_tmp,
                v1=v_tmp + 0.25,
                v2=v_tmp + 0.5,
                v3=v_tmp + 0.75,
                z=0.5,
                t=0.2,
                theta=0.1,
            ),
            size=200,
        )
        data_tmp["stim"] = stim_names[stim_v.index(v_tmp)]
        data_tmp["participant_id"] = str(participant_id)
        datasets.append(data_tmp)

dataset = pd.concat(datasets).reset_index(drop=True)
param_dict = {
    "v": {
        "low": np.repeat(stim_v[0], 5),
        "medium": np.repeat(stim_v[1], 5),
        "high": np.repeat(stim_v[2], 5),
    },
    "a": {"participant_id"},
}

HSSM Model¶

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race_model = hssm.HSSM(
    model="race_no_bias_angle_4",
    data=dataset,
    include=[
        {
            "name": "v0",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 0.0, "sigma": 1.5},
            },
            "formula": "v0 ~ 1 + stim",
            "link": "identity",
        },
        {
            "name": "a",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 1.5, "sigma": 0.5},
            },
            "formula": "a ~ 1 + (1|participant_id)",
            "link": "identity",
        },
    ],
    p_outlier=0.00,
)
race_model = hssm.HSSM(
    model="race_no_bias_angle_4",
    data=dataset,
    include=[
        {
            "name": "v0",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 0.0, "sigma": 1.5},
            },
            "formula": "v0 ~ 1 + stim",
            "link": "identity",
        },
        {
            "name": "a",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 1.5, "sigma": 0.5},
            },
            "formula": "a ~ 1 + (1|participant_id)",
            "link": "identity",
        },
    ],
    p_outlier=0.00,
)

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Model initialized successfully.

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idata_race = race_model.sample(
    sampler="numpyro",
    chains=2,
    cores=2,
    chain_method="vectorized",
    draws=500,
    tune=500,
    idata_kwargs=dict(log_likelihood=False),  # no need to return likelihoods here
)
idata_race = race_model.sample(
    sampler="numpyro",
    chains=2,
    cores=2,
    chain_method="vectorized",
    draws=500,
    tune=500,
    idata_kwargs=dict(log_likelihood=False),  # no need to return likelihoods here
)

Using default initvals.

NUTS[numpyro]: [v3, theta, t, z, v2, v1, v0_Intercept, v0_stim, a_Intercept, a_1|participant_id_sigma, a_1|participant_id_offset]

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warmup:  10%|█         | 100/1000 [00:07<01:01, 14.69it/s, 10 steps of size 5.27e-03. acc. prob=0.76]

warmup:  15%|█▌        | 150/1000 [00:09<00:47, 17.93it/s, 12 steps of size 1.61e-01. acc. prob=0.78]

warmup:  20%|██        | 200/1000 [00:10<00:36, 22.14it/s, 6 steps of size 8.55e-02. acc. prob=0.78]

warmup:  25%|██▌       | 250/1000 [00:12<00:31, 24.04it/s, 3 steps of size 3.20e-02. acc. prob=0.78]

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warmup:  45%|████▌     | 450/1000 [00:23<00:32, 17.11it/s, 9 steps of size 1.18e-01. acc. prob=0.79]

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sample:  55%|█████▌    | 550/1000 [00:28<00:24, 18.49it/s, 11 steps of size 5.52e-02. acc. prob=0.90]

sample:  60%|██████    | 600/1000 [00:31<00:21, 18.70it/s, 1 steps of size 5.52e-02. acc. prob=0.87]

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sample:  70%|███████   | 700/1000 [00:41<00:23, 12.70it/s, 4 steps of size 5.52e-02. acc. prob=0.89]

sample:  75%|███████▌  | 750/1000 [00:46<00:22, 11.25it/s, 58 steps of size 5.52e-02. acc. prob=0.90]

sample:  80%|████████  | 800/1000 [00:49<00:15, 13.01it/s, 4 steps of size 5.52e-02. acc. prob=0.88]

sample:  85%|████████▌ | 850/1000 [00:51<00:10, 14.28it/s, 16 steps of size 5.52e-02. acc. prob=0.88]

sample:  90%|█████████ | 900/1000 [00:53<00:05, 16.78it/s, 61 steps of size 5.52e-02. acc. prob=0.85]

sample:  95%|█████████▌| 950/1000 [00:57<00:03, 14.92it/s, 42 steps of size 5.52e-02. acc. prob=0.86]

sample: 100%|██████████| 1000/1000 [01:02<00:00, 13.88it/s, 33 steps of size 5.52e-02. acc. prob=0.87]

sample: 100%|██████████| 1000/1000 [01:02<00:00, 16.12it/s, 33 steps of size 5.52e-02. acc. prob=0.87]

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warmup:  10%|█         | 100/1000 [00:04<00:40, 22.32it/s, 12 steps of size 3.18e-03. acc. prob=0.76]

warmup:  15%|█▌        | 150/1000 [00:07<00:44, 19.06it/s, 12 steps of size 1.57e-01. acc. prob=0.77]

warmup:  20%|██        | 200/1000 [00:10<00:41, 19.20it/s, 12 steps of size 2.69e-01. acc. prob=0.78]

warmup:  25%|██▌       | 250/1000 [00:11<00:34, 21.95it/s, 5 steps of size 1.67e-01. acc. prob=0.78]

warmup:  30%|███       | 300/1000 [00:14<00:31, 22.45it/s, 9 steps of size 6.15e-02. acc. prob=0.78]

warmup:  35%|███▌      | 350/1000 [00:16<00:28, 22.92it/s, 24 steps of size 1.47e-01. acc. prob=0.78]

warmup:  40%|████      | 400/1000 [00:18<00:25, 23.97it/s, 2 steps of size 1.20e-01. acc. prob=0.78]

warmup:  45%|████▌     | 450/1000 [00:24<00:37, 14.50it/s, 23 steps of size 2.45e-01. acc. prob=0.79]

warmup:  50%|█████     | 500/1000 [00:26<00:28, 17.26it/s, 3 steps of size 8.67e-02. acc. prob=0.78]

sample:  55%|█████▌    | 550/1000 [00:28<00:23, 19.38it/s, 12 steps of size 8.67e-02. acc. prob=0.83]

sample:  60%|██████    | 600/1000 [00:29<00:18, 22.17it/s, 2 steps of size 8.67e-02. acc. prob=0.78]

sample:  65%|██████▌   | 650/1000 [00:30<00:12, 27.65it/s, 13 steps of size 8.67e-02. acc. prob=0.71]

sample:  70%|███████   | 700/1000 [00:31<00:09, 31.03it/s, 15 steps of size 8.67e-02. acc. prob=0.70]

sample:  75%|███████▌  | 750/1000 [00:32<00:06, 36.52it/s, 4 steps of size 8.67e-02. acc. prob=0.69]

sample:  80%|████████  | 800/1000 [00:33<00:05, 35.93it/s, 19 steps of size 8.67e-02. acc. prob=0.70]

sample:  85%|████████▌ | 850/1000 [00:35<00:04, 36.80it/s, 4 steps of size 8.67e-02. acc. prob=0.70]

sample:  90%|█████████ | 900/1000 [00:36<00:02, 39.57it/s, 12 steps of size 8.67e-02. acc. prob=0.69]

sample:  95%|█████████▌| 950/1000 [00:37<00:01, 39.74it/s, 3 steps of size 8.67e-02. acc. prob=0.69]

sample: 100%|██████████| 1000/1000 [00:38<00:00, 36.02it/s, 16 steps of size 8.67e-02. acc. prob=0.70]

sample: 100%|██████████| 1000/1000 [00:38<00:00, 25.65it/s, 16 steps of size 8.67e-02. acc. prob=0.70]

There were 996 divergences after tuning. Increase `target_accept` or reparameterize.

We recommend running at least 4 chains for robust computation of convergence diagnostics

The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details

The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details

Plot¶

In [30]:

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ax = hssm.plotting.plot_model_cartoon(
    race_model,
    n_samples=10,
    col="stim",
    row="participant_id",
    plot_pp_mean=True,
    plot_pp_samples=False,
    n_trajectories=1,
    ylims=(0, 5),
    alpha_pp=0.2,
    xlims=(0.0, 2),
);
ax = hssm.plotting.plot_model_cartoon(
    race_model,
    n_samples=10,
    col="stim",
    row="participant_id",
    plot_pp_mean=True,
    plot_pp_samples=False,
    n_trajectories=1,
    ylims=(0, 5),
    alpha_pp=0.2,
    xlims=(0.0, 2),
);

No posterior_predictive samples found. Generating posterior_predictive samples using the provided DataTree object and the original data. This will modify the provided DataTree object, or if not provided, the traces object stored inside the model.