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.
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 likey 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 0.0043 2.1531 0.0125 29550.7875 1208.2502 1.1322 ⋯
b -0.0101 4.2826 0.0249 29586.1705 1286.6040 1.1226 ⋯
c 0.0295 6.4946 0.0385 28454.8904 1233.1812 1.1280 ⋯
d 0.0804 8.5783 0.0494 30242.1330 1221.9348 1.1255 ⋯
e -0.0268 10.7756 0.0625 29744.9271 1301.6755 1.1239 ⋯
1 column omitted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
a -4.5481 -1.1607 0.0074 1.1660 4.5881
b -9.0943 -2.3255 -0.0114 2.3283 9.0090
c -13.6051 -3.5136 0.0160 3.4791 13.9290
d -18.1835 -4.5789 0.0602 4.6961 18.2168
e -23.0803 -5.8993 -0.0269 5.8061 22.7915
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 0.0349 4.9962 0.0503 9855.1061 10004.1962 1.0000 ⋯
b 0.0918 4.0185 0.0407 9712.4930 9464.4058 0.9999 ⋯
d -0.0086 2.0229 0.0200 10248.0100 9590.9378 1.0001 ⋯
e 0.0005 1.0036 0.0103 9561.1911 9717.5356 1.0000 ⋯
1 column omitted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
a -9.7727 -3.3430 0.1216 3.3540 10.0076
b -7.7217 -2.6732 0.1085 2.9130 7.9032
d -3.9749 -1.3598 0.0006 1.3415 3.9466
e -1.9746 -0.6730 0.0079 0.6892 1.9618
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.