plot() recipe returns unexpected prediction intervals

[azev77]

# Load dataset.
using HTTP, CSV, DataFrames, Dates
link = "https://bit.ly/3vtTaW5";
r = HTTP.get(link);
df = CSV.read(r.body, DataFrame; missingstring="NA");

using AbstractGPs, Plots
X = 0:1.0:(length(df.date)-1) 
Y = df.value;
XH = 0:1.0:(length(df.date)-1 +5) 

f = GP(Matern32Kernel()) # Define GP prior w Matern32 kernel
fx = f(X, 0.001)         # Finite projection at the inputs `X` 
logpdf(fx, Y)            # -512 # Data's log-likelihood w.r.t prior GP `f`. 
p_fx = posterior(fx, Y)  # Exact posterior given `Y`.
logpdf(p_fx(X), Y)       # 184 # Data's LL w.r.t prior posterior GP `p_fx`.

px = XH[end-4:end]
pm = mean.(marginals(p_fx(XH))[end-4:end])
ps = std.(marginals(p_fx(XH))[end-4:end])

# Plot posterior.
scatter(X, Y; label="Data")
plot!(XH, f(XH, 0.001); label="Prior")
plot!(p_fx(XH), label="Posterior" )
scatter!(px, pm, lab = "oos prediction μ")
scatter!(px, pm - 1.0*ps, lab="oos prediction μ - σ") 
scatter!(px, pm + 1.0*ps, lab="oos prediction μ + σ") 

It looks like the plot() recipe returns μ ± 1.0σ instead of (what I'd expect) μ ± 1.96σ.
Is this intended? Can this be customized?

[azev77]

Looks like it might be set to 1.0 here:

AbstractGPs.jl/src/util/plotting.jl

Line 6 in 0e223c8

scale::Float64 = pop!(plotattributes, :ribbon_scale, 1.0)

Not sure & idk how to modify it...

[theogf]

The 1.96sigma corresponds to the 95%quantile but there is no particular reason to prefer it to just 1sigma or 2 sigma.
What would you expect 1.96 in particular?

[azev77]

What would you expect 1.96 in particular?

Not sure what you mean.

How can I make plot(p_fx(XH) ) return a plot with μ ± 1.96σ?

[theogf]

If I am not mistaking you can pass the kwarg scale=1.96

[theogf]

No sorry it should be ribbon_scale=1.96

[azev77]

It works now:

    plot(p_fx(XH), lab="oos prediction μ - σ")
    plot!(p_fx(XH),ribbon_scale=1.96, lab="oos prediction μ - 1.96σ")

It would be great to make this clearer in the docs

[azev77]

While we're here. I asked the following question in other repos:
A recent paper makes 1 year ahead predictions for the distribution of GDP growth, with current GDP growth & NFCI as conditioning variables. Their data & Matlab code is here.
Target variable y_{t+1} = GDP_Growth_{t+1}
predictors X_t =(y_t, NFCI_t) = (GDP_Growth_{t}, NFCI_t)
Goal: predict the conditional distribution P(y_{t+1} | y_{t}, NFCI_t )

The authors use quantile regression.
Is it possible to produce this kind of figure w/ AbstractGPs?
Are GPs good at this type of thing rel to NGBoost.py?