Author: Gustavo A. Ballen and Sandra Reinales
Date: 2025-08-19

# Prior-Posterior comparisons

#### Gustavo A. Ballen and Sandra Reinales

#### 2025-08-19

After carrying out a divergence time analysis with `Beast2`, for example, we might be interested in comparing the prior and the posterior of node ages. We can use the function `crossplot` to generate a plot where the x-axis represents one analysis and the y-axis another, for instance, prior versus posterior:

    # load the package
    library(tbea)

    # crossplot operates over files or dataframes. Let's create
    # two dataframes to exemplified the desirable structure of input data

    log1 <- data.frame(sample=seq(from=1, to=10000, by = 100),
                       node1=rnorm(n =100, mean=41, sd=0.5),
                       node2=rnorm(n =100, mean=50, sd=1),
                       node3=rnorm(n =100, mean=25, sd=1))

    log2 <- data.frame(sample=seq(from=1, to=10000, by = 100),
                       node1=rnorm(n =100, mean=41, sd=0.2),
                       node2=rnorm(n =100, mean=50, sd=0.8),
                       node3=rnorm(n =100, mean=25, sd=0.5))

    head(log1)

    ##   sample    node1    node2    node3
    ## 1      1 41.31601 51.74525 23.02448
    ## 2    101 40.66821 50.77049 23.20232
    ## 3    201 40.46920 48.64849 23.19390
    ## 4    301 41.16130 47.93125 23.11945
    ## 5    401 41.05605 50.77709 25.37174
    ## 6    501 41.20240 50.11384 25.17615

    # run crossplot over nodes 1 and 2 using 'idx.cols' instead of 'pattern', and
    # plot the mean instead of the median.
    crossplot(log1, log2,
              idx.cols=c(2,3),
              stat="mean",
              bar.lty=1,
              bar.lwd=1,
              identity.lty=2,
              identity.lwd=1,
              extra.space=0.5,
              main="My first crossplot",
              xlab="log 1",
              ylab="log 2",
              pch=19)

    # now, load empirical data
    data(cynodontidae.prior)
    data(cynodontidae.posterior)

    # as crossplot operates also over files, let's create temporal
    # files for illustration
    write.table(cynodontidae.prior, "prior.tsv",
                row.names=FALSE, col.names=TRUE, sep="\t")

    write.table(cynodontidae.posterior, "posterior.tsv",
                row.names=FALSE, col.names=TRUE, sep="\t")

    # crossplot
    crossplot(log1="prior.tsv",
              log2="posterior.tsv",
              stat="median",
              skip.char="#",
              pattern="mrca.date",
              bar.lty=1,
              bar.lwd=2,
              identity.lty=2,
              identity.lwd=2,
              main="Prior-posterior comparison\nCynodontidae",
              xlab="Prior node age (Ma)",
              ylab="Posterior node age (Ma)",
              pch=20, cex=2, col="blue2")

This kind of plot has been used in the literature when comparing prior and posterior MCMC samples, as well as when comparing the same kind of estimates coming from different independent runs or types of analysis. The function `measureSimil` integrates the area under the curve defined as the intersection between both distributions. It is a descriptive measure of how similar two distributions are. The function can both plot the resulting distributions and their intersection, as well as print out its value, or skip the plot and just return the value:

    # integrate the area under the curve
    measureSimil(d1=cynodontidae.prior$mrca.date.backward.Hydrolycus.,
                 d2=cynodontidae.posterior$mrca.date.backward.Hydrolycus.,
                 ylim=c(0, 5),
                 xlab="Age (Ma)",
                 ylab="Density",
                 main="Similarity between prior and posterior\nof the node Hydrolycus")

    ## [1] 0.8078552

    # file cleanup
    file.remove("prior.tsv")

    ## [1] TRUE

    file.remove("posterior.tsv")

    ## [1] TRUE