Filling Styles using a single Plot in Mathematica - wolfram-mathematica

Question

Could I specify different filling colors for within a single plot like the bellow or would I need to "Show" several Plots ? Let`s say I would like the filling style to be the same as the PlotStyle.
priorMean = 50;
priorVar = 100;
llhMean = 30;
llhVar = 40;
postMean=35.71;
postVar=28.57;
Plot[
Evaluate#MapThread[
Function[{\[Mu], \[Sigma]},
PDF[NormalDistribution[\[Mu], Sqrt[\[Sigma]]], x]],
{{priorMean, llhMean, postMean}, {priorVar, llhVar, postVar}}],
{x, 0, 100}, Filling -> Axis, PlotStyle -> {Red, Green, Blue}]

Answer 1

You'll need to use FillingStyle to fill in. I think you got stuck in the syntax for FillingStyle, which is not the same as that for PlotStyle, although you'd expect it to be. You'll have to assign a color for each curve as FillingStyle -> {1 -> color1, 2 -> color2}, etc. Here's an example:
colors = {Red, Green, Blue};
Plot[Evaluate#
MapThread[
Function[{\[Mu], \[Sigma]},
PDF[NormalDistribution[\[Mu], Sqrt[\[Sigma]]], x]], {{priorMean,
llhMean, postMean}, {priorVar, llhVar, postVar}}], {x, 0, 100},
Filling -> Axis, PlotStyle -> colors,
FillingStyle ->
MapIndexed[#2 -> Directive[Opacity[0.3], #] &, colors]]

Answer 2

I propose making an extension to the definition of Plot. I have done this before.
toDirective[{ps__} | ps__] := Flatten[Directive ## Flatten[{#}]] & /# {ps}
makefills = MapIndexed[#2 -> Join ## toDirective#{Opacity[0.3], #} &, #] &;
Unprotect[Plot];
Plot[a__, b : OptionsPattern[]] :=
Block[{$FSmatch = True},
With[{fills = makefills#OptionValue[PlotStyle]},
Plot[a, FillingStyle -> fills, b]
]] /; ! TrueQ[$FSmatch] /; OptionValue[FillingStyle] === "Match"
With this in place, you can use FillingStyle -> "Match" to auto-style the fills to match the main styles.
Plot[{Sin[x], Cos[x], Log[x]}, {x, 0, 2 Pi},
PlotRange -> {-2, 2},
PlotStyle -> {{Blue, Dashing[{0.04, 0.01}]},
{Thick, Dashed, Orange},
{Darker#Green, Thick}},
Filling -> Axis,
FillingStyle -> "Match"
]

Answer 3

You could do something like
With[{colours = {Red, Green, Blue}},
Plot[Evaluate#
MapThread[
Function[{\[Mu], \[Sigma]},
PDF[NormalDistribution[\[Mu], Sqrt[\[Sigma]]], x]],
{{priorMean, llhMean, postMean}, {priorVar, llhVar, postVar}}],
{x, 0, 100},
Filling ->
MapIndexed[#2[[1]] -> {Axis, Directive[Opacity[.3, #1]]} &, colours],
PlotStyle -> colours]]

Answer 4

This gets a result:
Plot[Evaluate#
MapThread[
Function[{\[Mu], \[Sigma]},
PDF[NormalDistribution[\[Mu], Sqrt[\[Sigma]]], x]], {{priorMean,
llhMean, postMean}, {priorVar, llhVar, postVar}}], {x, 0, 100},
Filling -> {1 -> {Axis, Red}, 2 -> {Axis, Green}, 3 -> {Axis, Blue}},
PlotStyle -> {Red, Green, Blue}]
Found in the help under FillingStyle, Scope, Filling Style.
And alternatively:
f = MapThread[
Function[{\[Mu], \[Sigma]},
PDF[NormalDistribution[\[Mu], Sqrt[\[Sigma]]], x]],
{{priorMean, llhMean, postMean}, {priorVar, llhVar, postVar}}];
c = {Red, Green, Blue};
Show[Array[
Plot[f[[#]], {x, 0, 100}, Filling -> {1 -> {Axis, c[[#]]}},
PlotRange -> {Automatic, 0.08}, PlotStyle -> c[[#]]] &, 3]]