# Plot Bivariate Data with Marginals

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.

• – user9660 Mar 23 '15 at 16:43
• Lou, no I had not. That question is exactly on point. Many thanks, Peter. – pjc42 Mar 23 '15 at 18:39
• Lou, mathematica.stackexchange.com/questions/2984/… is really my question and is well answered there. Thank you for pointing me to this. The trick is to use Grid[] rather than GraphicsGrid[] to combine the plots – pjc42 Mar 23 '15 at 23:45

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}]]
},
PlotRangeClipping -> False,
ImagePadding -> {{10, 55}, {20, 55}}
]
]


• Sjoerd, brilliant, thank you. I had not thought of using Epilog because I was focused on using Histogram for the marginals and spent a lot of time trying to get Rotate and Translate to work. However, I think I can make your answer work on the Histograms by using an Interpolation on BinList and then using this interpolation function as the margPDF's in your answer. I think this will do. Many thanks. – pjc42 Mar 23 '15 at 18:32

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.

• If you look closely at the alignment of the marginal distributions in this answer, the peaks do not align with the means (peaks are not at zero). This is caused by the different padding/spacing of the plots. The use of Epilog in @Sjoerd's answer avoids this issue by using the same frame of reference. – Bob Hanlon Mar 24 '15 at 2:42
• You're right, good point. Thanks. – pjc42 Mar 24 '15 at 18:13