Given that you have a lot of points, a contourf
sounds more adapted ?
Assuming you have p(x,t)
for each x
and t
create a matrix out of it and give x
and t
for horizontal and vertical axis.
Something like
using Distributions, Plots
x = range(-5, 5, length = 100);
s = range(0.01, 3.0, length = 100);
Z = reduce(hcat, [pdf(Normal(0, exp(sig)), x) for sig in s])
contourf(x, s, Z', xlabel = "x", ylabel = "sig")
Note that you can still replace contourf
by heatmap
to get more or less the same result