Seminar Notice

                Statistical Laboratory
                 Iowa State University

DATE AND TIME:     Monday, September 8, 1997, 4:10 p.m.

PLACE:             319 Snedecor Hall

SPEAKER:           Sanjib Basu
                   Division of Statistics
                   Northern Illinois University

TITLE:             Estimation of Undetected Errors

                       ABSTRACT

    An unknown number, N, of errors/defects/faults exists in a software and
k reviewers with unknown competencies inspect in parallel to find these errors.
Given the list of errors detected by each inspector, the problem is to estimate
the number of undetected errors still remaining in the software.
    This is the well-known Binomial N estimation problem, but here we
have parallel informa-tion from k reviewers. Another similar problem arises in
capture-recapture sampling where we want to estimate the size of a closed
biological population based on multiple trappings.
    Our first approach to the undetected error problem will be through a
series of interesting but simple probability calculations. These calculations
establish that detection of errors is harder when the errors are uneven/non-
identical than when they are identical. However, it is better to have a few
good and a few bad reviewers (i.e., non-identical reviewers) rather than all
average reviewers. Also, after a while, increasing the number of reviewers
may not result in any detection.
    Our second approach will be more statistical in nature where we propose
Bayesian estimation methods for N. We address the following typical features
of software review in our estimation procedure: (i) Reviewers often differ in
their detection skills; (ii) Discussion among the reviewers often induces non-
independence; and (iii) Some errors are easier to detect, others are harder.
Several interesting phenomena happen. In the non-independent reviewer
model, we start with 2k many parameters but it turns out that it is enough to
specify prior distributions for only TWO of the 2k parameters. For the
heterogeneous errors case, we develop a flexible Bayesian model and
emonstrate how Gibbs sampling can be used to routinely calculate the Bayesian
estimator for N and other quantities of interest. We develop another Bayesian
model which can simultaneously incorporate heterogeneities of the errors and
the reviewers. These models are illustrated in simulated data and data from an
actual Bell Laboratories review of AT&T 5 ESS telephone switch.

COFFEE: 3:45 p.m., 104 Snedecor Hall