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   -0.0187    2.1514    0.0123   30302.2767   1161.6288    1.1283  ⋯
           b   -0.0244    4.3161    0.0248   30208.2463   1208.5271    1.1281  ⋯
           c    0.0413    6.5381    0.0390   28410.2835   1151.4747    1.1324  ⋯
           d    0.0098    8.6366    0.0496   30302.0166   1199.0290    1.1334  ⋯
           e    0.1107   10.8906    0.0629   30114.2514   1245.8560    1.1303  ⋯
                                                                1 column omitted

Quantiles
  parameters       2.5%     25.0%     50.0%     75.0%     97.5%
      Symbol    Float64   Float64   Float64   Float64   Float64

           a    -4.6094   -1.1762   -0.0080    1.1483    4.4746
           b    -9.2585   -2.3415   -0.0303    2.3172    9.1260
           c   -13.9140   -3.4532    0.0078    3.5461   13.8935
           d   -18.1072   -4.6024   -0.0080    4.6961   18.3996
           e   -22.9666   -5.7514    0.1001    5.9582   23.1356

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    0.0459    5.0209    0.0508    9775.8402    9484.1439    1.0000 ⋯
           b   -0.0495    4.0080    0.0404    9831.4933    9129.9240    1.0000 ⋯
           d   -0.0231    2.0015    0.0203    9722.5839    9635.3466    1.0001 ⋯
           e   -0.0096    0.9985    0.0098   10272.4670   10005.3430    1.0002 ⋯
                                                                1 column omitted

Quantiles
  parameters      2.5%     25.0%     50.0%     75.0%     97.5%
      Symbol   Float64   Float64   Float64   Float64   Float64

           a   -9.6441   -3.3700    0.0169    3.4159    9.9293
           b   -7.8490   -2.7882   -0.0902    2.6991    7.7831
           d   -3.8987   -1.3695   -0.0466    1.3218    3.9356
           e   -1.9530   -0.6973   -0.0150    0.6775    1.9487

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.