what is the reason to draw the scatterplot matrix for the mcmc sample? - bayesian

I found some bayesian paper try to draw the scatter plot matrix for the parameters.
I just wondering what is the goal to draw this scatter plot matrix?
what is the meaning if I see some linear or nonlinear relationships between samples.
Thanks

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how to find the equation of 3d surface by using its coordinates?

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See the following image for what I am trying to do:
I couldn't figure out how to do it with meshgrid since I don't have any data for the inside of the cube just the surfaces. To make a contour plot for one of the surfaces I use two axes to make the meshgrid and then calculate the z data but that is just one face. So I have to do that process individually for each face.
I thought I could manually add patches and rotate them to position colored with their value but that didn't seem like the best way. I was wondering if I was missing something easier.

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Is it possible to do the same thing in Matplotlib? Alternatively, is it possible to map the colourmap by the function that one intends to plot on the surface?
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Basically, each section is made up of three plots. One scatter plot, and two histograms that show the density of points in each region, one for each axis.
Any help would be great. Thanks.