Analysis of runif data

1. Proportion of age peaks selected in the results

This graph shows the proportion of the number of prefered inverted ages as a function of the distance between the 2 true ages on which the synthetic data was conditioned. Where the separation is small - the inversion struggles to distinguish between the 2 components and a large number of single ages are prefered. As the gap widens - the algorithm performs better at resolving the difference.

Figure 1: This graph shows the proportion of results that prefer one age (black), 2 ages (red) and 3 ages(green) as we increase the true age of the second component age from 2 to 9Myr. The age of the first component is at 1Myr and the mixing proportion is 50:50.

2. Analysis of the results for A1=1 Ma A2=3Ma

Notice that Figure 1 shows that when the second age is at 3Mry, we observed favoured solutions with both 1 and 2 age components. This section compares the properties and covariances of these results.

The plot below summaries the results of this analysis and highlights the major challenges binomfit has in correctly infering these models.

• The code prefers the single age model ~90% of the time
• The best that the single age model can do is to return some average of the 2 ages which is why the single age model is rounghly normally distributed about 2Ma
• The true ages do not lie within 2se of the favoured age. This is not surprising as the se is a measure of uncertainty on the mean rather than a measure of spread in the data
• When 2 ages are prefered, the ages are biased away from the true ages (compare the means - blue dashed lines with the true ages as black lines)
• The inverted ages are not normally distributed
• Several very old ages are infered as the first age approaches the mean of the 2 true ages; presumably to account for outliers
• The infered proportions deviate strongly from 50% - which was how the age model was conditioned

# Multiple plot function ggplot objects can be passed in ..., or to plotlist
# (as a list of ggplot objects) - cols: Number of columns in layout -
# layout: A matrix specifying the layout. If present, 'cols' is ignored.  If
# the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE), then
# plot 1 will go in the upper left, 2 will go in the upper right, and 3 will
# go all the way across the bottom.
multiplot <- function(..., plotlist = NULL, file, cols = 1, layout = NULL) {
    require(grid)

    # Make a list from the ... arguments and plotlist
    plots <- c(list(...), plotlist)

    numPlots = length(plots)

    # If layout is NULL, then use 'cols' to determine layout
    if (is.null(layout)) {
        # Make the panel ncol: Number of columns of plots nrow: Number of rows
        # needed, calculated from # of cols
        layout <- matrix(seq(1, cols * ceiling(numPlots/cols)), ncol = cols, 
            nrow = ceiling(numPlots/cols))
    }

    if (numPlots == 1) {
        print(plots[[1]])

    } else {
        # Set up the page
        grid.newpage()
        pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))

        # Make each plot, in the correct location
        for (i in 1:numPlots) {
            # Get the i,j matrix positions of the regions that contain this subplot
            matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))

            print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row, layout.pos.col = matchidx$col))
        }
    }
}

3. Analysis of the results for A1=1 Ma A2=7Ma

Notice that Figure 1 shows that when the second age is at 7Mry, we only observed favoured solutions with 2 age components. This section compares the properties and covariances of these results.

In this case the inverted ages are well resolved. This is reflected in:

• Each peaks has ~50% population which is how we specified the age model
• Both of the true ages lie robustly within 2sd of the model ages
• The model ages vary over a small range
• The model ages are roughly normally distributed about the mean
• The mean of all the inverted ages (red lines in Fig3c) is equal to the true peak ages (green dashed lines in Fig3c)

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