Note- this work will form the core of our (Michael Goldstein and myself) contributed talk at the Valencia 7 meeting. The extended abstract may be downloaded (postscript or pdf).
Software testing has a fundamental role to play in the production of reliable systems. Exhaustive testing and remedying of all faults prior to release is rarely feasible. Test managers have to attempt to minimise the time and resources allocated to testing whilst ensuring that the subset of all possible test cases chosen maximises the confidence in the product of the supplier and consumer.
In a long-term collaboration between researchers at Durham and industrial partners has the seen the development of Bayesian methods to support testers working from a black-box testing perspective. The approach is based around the creation of a novel Bayesian graphical model for software testing. Details of the work may be found on our software testing homepage.
Although the Bayesian approach offers a powerful method
for combining expert judgements with experimental results, in large complex
problems we may be unable to specify carefully a meaningful full prior
distribution over all the variables, or if we can give such a full prior
specification the analysis may be too difficult to carry out. In particular,
there may be certain aspects of the structure for which we do not currently
make a full joint probabilistic specification for precisely these reasons.
A partial specification would allow us to have a richer
dependency structure in our model but equally
some parts of the model are intrinsically probabilistic;
test results are either successes or failures, for example. A need has
arisen to create graphical models which represent different levels of detail
in their prior specification and this is the area I am concerned with.
We have developed methods for Bayesian augmentation for
Bayes linear methods, introducing graphical models where beliefs relating
connected nodes are either fully specified or partially specified. We term
these Bayes linear/Bayes (BLB) models. In the software testing framework,
the models concerned have fully specified data inputs with only a Bayes
linear specification made over the parameters. Presently, we are writing
up the approach for publication. We exploit the conditional independence
structure of the model to perform updating locally. The propagation
of test results from a single data source is considered and revised expectations
and variances are obtained using a mixture of conditioning and Bayes linear
belief adjustment. Propagation of test results from multiple data sources
are then considered. In the BLB model defined, we have that the data
sources are separable given the parameters. Consequently the revision of
the parameters given the data sources is formed from a function of the
revision of the parameters by a single data source for each data source
observed. A local computation algorithm for the BLB model may be
obtained.The following technical report contains full details of the revision
and the local computation algorithm.
| Augmented Bayes linear/Bayes graphical models
Simon C Shaw, Michael Goldstein Department of Mathematical Sciences, University of Durham Status: technical report
|
Future developments in this field surround what we term conditional BLB models. In these models, we increase the specification over the parameter space by allowing some parameters to be fully specified. Conditional on these fully specified parameters, a partial specification is made for the remaining parameters. Given the fully specified parameters, the remaining model is a BLB model and we are interested in performing updating on the unconditional model. This involves merging the ideas about updating on BLB models with the ideas behind Bayes linear conditioning.
| Last revision:
26/03/02 |
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