Overlapping Histogram Count

(Code provided at the bottom)

Consider the results of two experiments

Trial A	Trial B
0.397371	-0.600645
-0.110611	-1.075366
0.518151	-1.940370
1.218424	-2.646937
-0.187323	-1.301777

After tidying up the data I create a plot of overlapping histograms.

Under the plot of the overlapping histograms I would like to include a bar representing the amount of overlap. I would also like the graphic to include an interval selection linking the two.

I am unsure how to do this.

Thanks for any advice.

-Eitan

import pandas as pd
import altair as alt
import numpy as np
np.random.seed(42)

# Generating Data
source = pd.DataFrame({'Trial A': np.random.normal(0, 0.8, 1000),
                   'Trial B': np.random.normal(-2, 1, 1000)})

interval = alt.selection_interval(encodings=['x'])

# Tidying Data
source = pd.melt(
    source,
    id_vars=source.index.name,
    value_vars=source.columns,
    var_name='Experiment',
    value_name='Measurement'
)

# Overlapping Histograms 
hist = alt.Chart(source).mark_area(
    opacity=0.3,
    interpolate='step'
).encode(
    alt.X('Measurement', bin=alt.Bin(maxbins=100)),
    alt.Y('count()', stack=None),
    alt.Color('Experiment')
).add_selection(interval)

# Amount of overlap (???)
bar = alt.Chart(source).mark_bar().encode(
    x = alt.X('count()', scale=alt.Scale(domain=(0, 2100)))
).transform_filter(interval)

hist & bar

[jakevdp]

Yeah, TBH I probably couldn’t have answered this when you first asked it, but creating the http://github.com/altair-viz/altair-transform package has given me more practice with thinking in terms of Vega-Lite transforms…

[jakevdp]

Here’s the same with an interval selection to choose which points to include:

import pandas as pd
import altair as alt
import numpy as np
np.random.seed(42)

# Generating Data
source = pd.DataFrame({'Trial A': np.random.normal(0, 0.8, 1000),
                   'Trial B': np.random.normal(-2, 1, 1000)})

interval = alt.selection_interval()

scatter = alt.Chart(source).mark_point().encode(
    x='Trial A',
    y='Trial B',
    color=alt.condition(interval, alt.value('steelblue'), alt.value('lightgray'))
).add_selection(
    interval
)

base = alt.Chart(source).transform_fold(
    ['Trial A', 'Trial B'],
    ['Experiment', 'Measurement']
).transform_filter(
    interval
).transform_bin(
    field='Measurement',
    bin=alt.Bin(maxbins=50),
    as_=['Measurement_min', 'Measurement_max']
).transform_aggregate(
    count='count()',
    groupby=['Measurement_min', 'Measurement_max', 'Experiment']
)

hist = base.mark_area(
    opacity=0.3,
    interpolate='step'
).encode(
    x=alt.X('Measurement_min:Q', bin='binned'),
    x2='Measurement_max:Q',
    y=alt.Y('count:Q', stack=None),
    color='Experiment:N'
)

overlap = base.transform_impute(
    impute='count',
    key='Measurement_min',
    value=0,
    groupby=['Experiment']
).transform_aggregate(
    overlap='min(count)',
    groupby=['Measurement_min']
).mark_bar().encode(
    x='sum(overlap):Q'
)

scatter | (hist & overlap)