Make `util.plot_gp_dist` transparency-proof

Description of your problem

The plot_gp_dist function handles fill_alpha in a weird way (at least to me):

    for i, p in enumerate(percs[::-1]):
        upper = np.percentile(samples, p, axis=1)
        lower = np.percentile(samples, 100 - p, axis=1)
        color_val = colors[i]
        ax.fill_between(x, upper, lower, color=cmap(color_val), alpha=fill_alpha, **fill_kwargs)

Because the region between 1% and 99% and the region between 2% and 98% overlap, the fill_alpha parameter might not have the intended effect. The stacking of multiple transparent regions will result in the center percentiles not having transparency at all? There are 40 semi-transparent rectangles stacked in the center. The stacking of colors and color mixing might also distort the colormap towards the center.

Test-Graphs using rtcovidlive/rtlive-global with dataset from here, but heavily cropped.

What it looks like now (fill_alpha=0.6):

When setting fill_alpha=0.6, fill_kwargs={"edgecolor":"none"} the hard lines disappear or get softer. Still not 60% transparent:

What i expected (modified code with fill_alpha=0.6, fill_kwargs={"edgecolor":"none"}):

Code replacing these lines:

    cmap = plt.get_cmap(palette)
    N = 81
    percs = np.linspace(1, 99, N)
    colors = 1 - np.abs(percs - 50) / (np.max(percs) - 50)
    samples = samples.T
    x = x.flatten()
    percs_bounds = np.percentile(samples, percs, axis=1)
    for i, p in enumerate(percs[:(N-1)//2]):
        color_val = colors[i]
        ax.fill_between(x, percs_bounds[i], percs_bounds[i + 1], facecolor=cmap(color_val), alpha=fill_alpha, edgecolor="none", **fill_kwargs)
        ax.fill_between(x, percs_bounds[-i-1], percs_bounds[-i-2], facecolor=cmap(color_val), alpha=fill_alpha, edgecolor="none", **fill_kwargs)
    if N % 2 == 0:
        ax.fill_between(x, percs_bounds[N//2 - 1], percs_bounds[N//2], facecolor=cmap(1.0), alpha=fill_alpha, edgecolor="none", **fill_kwargs)

Fixing or changing this behavior has to be considered a BC-break, I guess. But maybe I'm also missing something and this style of "progressive transparency" was intended?

Versions and main components

• PyMC3 Version: 3.11.2
• Aesara Version: ?
• Python Version: 3.8.8
• Operating system: Windows 10
• How did you install PyMC3: conda env create -f environment.yml

Start in pymc3/gp/util.py at plot_gp_dist, especially the fill_alpha handling around lines 152-161. Reproduce the overlapping percentile regions with fill_alpha=0.6 and the reported edgecolor setting, then compare the result with the expected graph in the issue. Done means the transparency and color behavior is resolved or explicitly defined, with the backward-compatibility impact addressed.