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:

      out$peaklocationmode


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

      out$peaklocationquantile


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

      min(x)
      max(x)



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.