"""
Second-level fMRI model: true positive proportion in clusters
=============================================================

This script showcases
the so-called "All resolution inference" procedure
(:footcite:t:`Rosenblatt2018`),
in which the proportion of true discoveries in arbitrary clusters is estimated.
The clusters can be defined from the input image, i.e. in a circular way, as
the error control accounts for arbitrary cluster selection.
"""

# %%
# Fetch dataset
# --------------
# We download a list of left vs right button press contrasts from a
# localizer dataset. Note that we fetch individual t-maps that represent the
# :term:`BOLD` activity estimate divided
# by the uncertainty about this estimate.
from nilearn.datasets import fetch_localizer_contrasts

n_subjects = 16
data = fetch_localizer_contrasts(
    ["left vs right button press"],
    n_subjects,
)
# %%
# Estimate second level model
# ---------------------------
# We define the input maps and the design matrix for the second level model
# and fit it.
import pandas as pd

second_level_input = data["cmaps"]
design_matrix = pd.DataFrame(
    [1] * len(second_level_input), columns=["intercept"]
)

# %%
# Model specification and fit
from nilearn.glm.second_level import SecondLevelModel

second_level_model = SecondLevelModel(smoothing_fwhm=8.0, n_jobs=2)
second_level_model = second_level_model.fit(
    second_level_input, design_matrix=design_matrix
)

# %%
# To estimate the :term:`contrast` is very simple.
# We can just provide the column name of the design matrix.
z_map = second_level_model.compute_contrast(output_type="z_score")

# %%
# We threshold the second level :term:`contrast`
# at uncorrected p < 0.001 and plot
from scipy.stats import norm

p_val = 0.001
p001_uncorrected = norm.isf(p_val)

from nilearn.glm import cluster_level_inference

proportion_true_discoveries_img = cluster_level_inference(
    z_map, threshold=[3, 4, 5], alpha=0.05
)

from nilearn import plotting

plotting.plot_stat_map(
    proportion_true_discoveries_img,
    threshold=0.0,
    display_mode="z",
    vmax=1,
    cmap="inferno",
    title="group left-right button press, proportion true positives",
)

plotting.plot_stat_map(
    z_map,
    threshold=p001_uncorrected,
    display_mode="z",
    title="group left-right button press (uncorrected p < 0.001)",
)

plotting.show()

# %%
# References
# ----------
#
# .. footbibliography::
