Plot bivariate data with marginals using Graphics3D [duplicate]

I have some 2D data (a load of random walks) that I would like to show using a bivariate line plot with marginals attached (I would like the output to look similar to that in this question.)

The twist here, is that I need to plot the bivariate data above another plot, that happens to be 3D. To do this I am using Graphics3D to draw the data:

n = 50;
lRand = Table[RandomVariate[MultinormalDistribution[{0, 0}, {{1, 0}, {0, 1}}], {10}],
{i, 1, n, 1}];
lRW = Accumulate /@ lRand;
lRWAugmented = Table[{#[[1]], #[[2]], 0.1} & /@ lRW[[i]], {i, 1, n}];
Show[Plot3D[0.1, {x, -10, 10}, {y, -10, 10}, PlotStyle -> Opacity[0.2, Gray]],
Graphics3D[Line[lRWAugmented]]]


Which results in a plot like the one below:

Note I have omitted the plot below the top line graph, since it doesn't affect the answer to this question.

Does anyone know how I could add marginals to the top line plot? I don't really know where to begin to be honest!

• – Kuba
Apr 9 '16 at 7:50

Manipulate[Module[{x, y},

mysoln = Solve[{x, y}.Inverse[( {
{a[[1]] a[[1]],  ρ a[[1]] a[[2]]},
{ ρ a[[1]] a[[2]], a[[2]] a[[2]]}
} )].{x, y} == 1, x, Reals] // Quiet;

Show[{

ParametricPlot3D[{{x /. mysoln[[1]], y, -.2}, {x /. mysoln[[2]],
y, -.2}}, {y, -5, 5},
PlotRange -> {{-5, 5}, {-5, 5}, {-.2, .3}},
ImageSize -> 700,
PlotStyle -> {{Thick, Green}, {Thick, Green}},
Ticks -> {{{xx,
Text[Style[
"\!$$\*OverscriptBox[SubscriptBox[\(x$$, $$1$$], \
$$^$$]\)", 18, Italic, Red]]}}, None, None},
TicksStyle -> { Red, None, None},
BoxRatios -> {1, 1, 1},
AxesLabel -> {Text[
Style["\!$$\*SubscriptBox[\(x$$, $$1$$]\)", Italic, 14]],
Text[Style["\!$$\*SubscriptBox[\(x$$, $$2$$]\)", Italic, 14]],
Text[Style["p(x)", Italic, 16]]}],

Plot3D[PDF[MultinormalDistribution[{0, 0}, ( {
{a[[1]] a[[1]],  ρ a[[1]] a[[2]]},
{ ρ a[[1]] a[[2]], a[[2]] a[[2]]}
} )], {x, y}], {x, -5, 5}, {y, -5, 5},
PlotStyle -> Opacity[0.7],
PlotPoints -> 20,
PlotRange -> {{-5, 5}, {-5, 5}, {-.2, .3}}, Mesh -> {{0}},
MeshFunctions -> {#1 - xx &}, MeshStyle -> {Thick, Red},
ImageSize -> 700,
Ticks -> {{{xx,
Text[Style[
"\!$$\*OverscriptBox[SubscriptBox[\(x$$, $$1$$], \
$$^$$]\)", 18, Italic, Red]]}}, None, None},
TicksStyle -> { Red, None, None}, BoxRatios -> {1, 1, 1},
AxesLabel -> {Text[
Style["\!$$\*SubscriptBox[\(x$$, $$1$$]\)", Italic, 14]],
Text[Style["\!$$\*SubscriptBox[\(x$$, $$2$$]\)", Italic, 14]],
Text[Style["p(x)", Italic, 16]]}],

Graphics3D[{Opacity[0.5],
Polygon[{{xx, -5, 0}, {xx, -5, .3}, {xx, 5, .3}, {xx, 5,
0}, {xx, -5, 0}}]},
PlotRange -> {{-5, 5}, {-5, 5}, {-.2, .3}},
Ticks -> {{{xx,
Text[Style[
"\!$$\*OverscriptBox[SubscriptBox[\(x$$, $$1$$], \
$$^$$]\)", 18, Italic, Red]]}}, None, None},
TicksStyle -> { Red, None, None}, BoxRatios -> {1, 1, 1},
AxesLabel -> {Text[
Style["\!$$\*SubscriptBox[\(x$$, $$1$$]\)", Italic, 14]],
Text[Style["\!$$\*SubscriptBox[\(x$$, $$2$$]\)", Italic, 14]],
Text[Style["p(x)", Italic, 16]]}],

ParametricPlot3D[{-5, y,
PDF[NormalDistribution[ρ xx a[[2]]/a[[1]],
a[[2]] Sqrt[1 - ρ^2]], y]}, {y, -5, 5},
PlotRange -> {{-5, 5}, {-5, 5}, {-.2, .3}},
PlotStyle -> {Thick, Red},
Ticks -> {{{xx,
Text[Style[
"\!$$\*OverscriptBox[SubscriptBox[\(x$$, $$1$$], \
$$^$$]\)", 18, Italic, Red]]}}, None, None},
ImageSize -> 700, TicksStyle -> { Red, None, None},
BoxRatios -> {1, 1, 1},
AxesLabel -> {Text[
Style["\!$$\*SubscriptBox[\(x$$, $$1$$]\)", Italic, 14]],
Text[Style["\!$$\*SubscriptBox[\(x$$, $$2$$]\)", Italic, 14]],
Text[Style["p(x)", Italic, 16]]}]

}]],
{{a, {1, 1},
"\!$$\*SubscriptBox[\(σ$$, $$1$$]\) , \!$$\*SubscriptBox[\(\ σ$$, $$2$$]\)"}, {1, 1}, {2, 2}}, {{ρ,
0}, -.85, .85, .05}, {{xx, 0,
Text[Style[
"\!$$\*OverscriptBox[SubscriptBox[\(x$$, $$1$$], $$^$$]\)", 14,
Italic, Red]]}, -5, 5, .2},
AutoAction -> False]

• Thanks for your answer, although it is not quite what I was looking for (did you see the question that I linked to in my original question?) Sorry, it's my fault - I wasn't clear. I am looking to show both marginals in the same plane as the top line plot. The marginals should be reconstructed from the data, not from the PDF I used to make them - the above example is not exactly the same as my real question. Apologies for not being clear. Best, Ben Apr 9 '16 at 12:43