Plot Bivariate Data with Marginals

Question

I would like to plot bivariate data along with the marginal distributions. I've arranged the plots in a GraphicsGrid as below but the marginals are centered away from the bivariate plot and I wonder if there isn't a better way.

There are several related questions but none that I can find that quite work for what I'd like to do. For example, Visualization of Bivariate Distributions and Align plots with a shift.

Here is the GraphicsGrid version using PDF plots, (I'll have Histograms and a Listplot in the actual version.)

Module[{jointPDF, marg1PDF, marg2PDF, mu1, mu2, s1, s2, rho, size,
        jointPlot, marg1Plot, marg2Plot, x1, x2},

  mu1 = mu2 = 0;
  s1 = s2 = 1;
  rho = 0.4;
  jointPDF = PDF[MultinormalDistribution[{mu1,mu2}, {{s1, rho}, {rho, s2}}],{x1, x2}];
  marg1PDF = PDF[NormalDistribution[mu1, s1], x1];
  marg2PDF = PDF[NormalDistribution[mu2, s2], x2];
  size = 300;

  jointPlot = ContourPlot[jointPDF, {x1, -4, 4}, {x2, -4, 4}, AspectRatio -> 1, ImageSize -> size, Contours -> 15, ContourShading -> None];
  marg1Plot = Rotate[Plot[marg1PDF, {x1, -4, 4}, Axes -> False, ImageSize -> size, AspectRatio -> 1/3], -Pi/2];
  marg2Plot = Rotate[Plot[marg2PDF, {x2, -4, 4}, Axes -> False, ImageSize -> size, AspectRatio -> 1/3], Pi];

  GraphicsGrid[{
     {jointPlot, marg1Plot},
     {marg2Plot,}
   }]
]

Which produces this output:

I'd like the marginals to sit more tightly on the joint distribution's plot axes but can't figure out how.

Thanks.

Answer 1

Epilog may be useful to you:

Module[{jointPDF, marg1PDF, marg2PDF, mu1, mu2, s1, s2, rho, size, 
  jointPlot, marg1Plot, marg2Plot, x1, x2}, mu1 = mu2 = 0;
 s1 = s2 = 1;
 rho = 0.4;
 jointPDF = 
  PDF[MultinormalDistribution[{mu1, 
     mu2}, {{s1, rho}, {rho, s2}}], {x1, x2}];
 marg1PDF = PDF[NormalDistribution[mu1, s1], x1];
 marg2PDF = PDF[NormalDistribution[mu2, s2], x2];
 size = 300;
 jointPlot = 
  ContourPlot[jointPDF, {x1, -4, 4}, {x2, -4, 4}, 
       AspectRatio -> 1, 
       ImageSize -> size, Contours -> 15, ContourShading -> None,
       Epilog -> {
         Line[Table[{x1, 4.1 + 4 marg1PDF}, {x1, -4, 4, .1}]],
         Line[Table[{4.1 + 4 marg2PDF, x2}, {x2, -4, 4, .1}]]
       },
       PlotRangePadding -> 0, 
       PlotRangeClipping -> False, 
       ImagePadding -> {{10, 55}, {20, 55}}
   ]
 ]

Answer 2

There was also a very complete answer to my question given in a near duplicate as pointed out by Lou in the comment above, see: How can I make an X-Y scatter plot with histograms next to the X-Y axes?.

In my example, a simple change from GraphicsGrid to Grid fixed the issue with the marginal plots standing off so far.

Module[
 {jointPDF, marg1PDF, marg2PDF, mu1, mu2, s1, s2, rho, size, jointPlot, marg1Plot, marg2Plot, x1, x2},

  mu1 = mu2 = 0;
  s1 = s2 = 1;
  rho = 0.4;
  jointPDF = PDF[MultinormalDistribution[{mu1,mu2}, {{s1, rho}, {rho, s2}}],{x1, x2}];
  marg1PDF = PDF[NormalDistribution[mu1, s1], x1];
  marg2PDF = PDF[NormalDistribution[mu2, s2], x2];
  size = 300;

  jointPlot = ContourPlot[jointPDF, {x1, -4, 4}, {x2, -4, 4}, AspectRatio -> 1, ImageSize -> size, Contours -> 15, ContourShading -> None];
  marg1Plot = Rotate[Plot[marg1PDF, {x1, -4, 4}, Axes -> False, ImageSize -> size, AspectRatio -> 1/3], -Pi/2];
  marg2Plot = Rotate[Plot[marg2PDF, {x2, -4, 4}, Axes -> False, ImageSize -> size, AspectRatio -> 1/3], Pi];

  Grid[{
     {jointPlot, marg1Plot},
     {marg2Plot,},
     Spacings -> {0.75, 0}
   }]
]

The Spacings-> {0.75,0} deals with the additional space of axes labels in the y direction.

The amended code produces this:

Many thanks to Lou and Sjoerd for their help.