Example data sets and results for BARS:

Below are two examples which illustrate the use of the BARS procedure. The first example is one in which we expect to detect a signal, while the second example does not contain a signal.

Example 1:

First read in the data set (example1.txt). The first column in this data set is x, and the second is y.

      barsdata = read.table("example1.txt", header=F)
      x = barsdata[,1]
      y = barsdata[,2]

Run BARS (default value for alpha is 0.05)

      out = barsN.fun(x,y)

Plot the original data with the BARS fit overlayed:

      plot(x, y, xlab="", ylab="")
      lines(x, out$postmodes)

Click here to see the resultant plot.

To find the location of the maximum height of the BARS curve:


To find the confidence (credible) interval for the peak location


The BARS test is significant if the above credible interval is a proper subset of the data range. To determine the data range, issue the commands


For this example, the data range is (1770, 92705), while the credible interval is (15957.63, 30849.87), a proper subset of the data range. Therefore, we conclude that the test is significant and that a signal exists.

Example 2:

Click here for the data set, and here for the resultant plot (here we use the same R commands as in the previous example). For this second example in which we do not expect to detect a signal, we find that the data range is (3, 90263), while the credible interval is (23692.26, 90263.00). The credible interval is not s proper subset of the data range, so we fail to reject the null hypothesis that no signal exists.