Integration with MCMCChains.jl
MCMC packages like Turing often produce results in the form of an MCMCChains.Chain. There is special support in PairPlots.jl for plotting these chains.
Note
The integration between PairPlots and MCMCChains only works on Julia 1.9 and above. On previous versions, you can work around this by running pairplot(DataFrame(chn))
.
Plotting chains
For this example, we'll use the following code to generate a Chain
. In a real code, you would likely receive a chain as a result of sampling from a model.
chn1 = Chains(randn(10000, 5, 3) .* [1 2 3 4 5] .* [1;;;2;;;3], [:a, :b, :c, :d, :e])
Chains MCMC chain (10000×5×3 Array{Float64, 3}):
Iterations = 1:1:10000
Number of chains = 3
Samples per chain = 10000
parameters = a, b, c, d, e
Summary Statistics
parameters mean std mcse ess_bulk ess_tail rhat ⋯
Symbol Float64 Float64 Float64 Float64 Float64 Float64 ⋯
a 0.0087 2.1719 0.0128 29078.8818 1272.2126 1.1254 ⋯
b 0.0194 4.3197 0.0257 28958.9071 1186.2168 1.1268 ⋯
c -0.0505 6.4955 0.0392 27476.6687 1233.0089 1.1248 ⋯
d -0.0670 8.5873 0.0497 29778.4916 1214.1447 1.1270 ⋯
e 0.0089 10.8199 0.0620 30341.2674 1158.7179 1.1306 ⋯
1 column omitted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
a -4.5579 -1.1667 0.0055 1.1716 4.6097
b -9.0888 -2.3089 0.0133 2.3259 9.0911
c -13.8758 -3.5349 -0.0036 3.4746 13.5973
d -18.4743 -4.6921 0.0040 4.5636 18.0720
e -22.7805 -5.8415 0.0308 5.8826 22.7212
You can plot the results from all chains in the Chains object:
using CairoMakie, PairPlots
pairplot(chn1)
The labels are taken from the column names of the chains. You can modify them by passing in a dictionary mapping column names to strings, LaTeX strings, or Makie rich text objects.
Plotting individual chains separately
If you have multiple parallel chains and want to plot them in different colors, you can pass each one to pairplot
:
pairplot(chn1[:,:,1], chn1[:,:,2], chn1[:,:,3])
You can title the series indepdendently as well:
c1 = Makie.wong_colors(0.5)[1]
c2 = Makie.wong_colors(0.5)[2]
c3 = Makie.wong_colors(0.5)[3]
pairplot(
PairPlots.Series(chn1[:,:,1], label="chain 1", color=c1, strokecolor=c1),
PairPlots.Series(chn1[:,:,2], label="chain 2", color=c2, strokecolor=c2),
PairPlots.Series(chn1[:,:,3], label="chain 3", color=c3, strokecolor=c3),
)
If your chains are well converged, then the different series should look the same.
Comparing the results of two simulations
You may want to compare the results of two simulations. Consider the following chains:
chn2 = Chains(randn(10000, 5, 1) .* [1 2 3 4 5], [:a, :b, :c, :d, :e])
chn3 = Chains(randn(10000, 4, 1) .* [5 4 2 1], [:a, :b, :d, :e]);
Chains MCMC chain (10000×4×1 Array{Float64, 3}):
Iterations = 1:1:10000
Number of chains = 1
Samples per chain = 10000
parameters = a, b, d, e
Summary Statistics
parameters mean std mcse ess_bulk ess_tail rhat ⋯
Symbol Float64 Float64 Float64 Float64 Float64 Float64 ⋯
a 0.0729 5.0101 0.0509 9686.7627 9473.6454 0.9999 ⋯
b 0.0117 3.9851 0.0396 10114.8015 9902.1024 1.0003 ⋯
d -0.0504 1.9901 0.0202 9717.6067 10009.0295 1.0000 ⋯
e 0.0071 1.0006 0.0101 9730.3603 9795.9200 1.0003 ⋯
1 column omitted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
a -9.6929 -3.3055 0.0661 3.4106 9.9951
b -7.6775 -2.6939 0.0380 2.7174 7.8472
d -3.8895 -1.3944 -0.0667 1.2783 3.9334
e -1.9285 -0.6637 0.0087 0.6682 1.9847
Just pass them all to pairplot
:
pairplot(chn2, chn3)
Note how the parameters of the chains do not have to match exactly. Here, chn2
has an additional variable not present in chn3
.