Figure 3
From: Error statistics of hidden Markov model and hidden Boltzmann model results
False positive rate and true positive rate plotted against score threshold. This figure is demonstrative of the ease by which error statistics estimates can be had and demonstrates low-score-linear and high-score-concave regions. The bottom panel depicts an enlargement of the upper left corner of the top panel. In both panels, from top to bottom the curves are (1) forward score true positive rate, (2) maximum score true positive rate, (3) forward score false positive rate, and (4) maximum score false positive rate. For example, for a score threshold of 100, the maximum score false positive rate is 10-55 and the forward score false positive rate is 10-51; for this threshold, the maximum score true positive rate is 10-5.2 and the forward score true positive rate is 10-4.8. The low-score-linear and high-score-concave regions of the false positive rate curves are qualitatively as expected, based upon the Gumbel distribution approximation and its break down, respectively. For the true positive rate curves, the demonstration of low-score linearity and the bend/phase transition near the score of 125 may be novel. Despite the extreme statistics, the values for these plots are easily computed; we employed N = 1000 importance samples for each of 1000 maximum score thresholds and each of 1000 forward score thresholds.