Abstract: Mainly because of their nice mathematical properties, Gaussian Kalman filter models have been widely used, especially for forecasting. However, in many situations Gaussian models may not do well, and as an alternative, non-Gaussian models may be more appropriate. Unlike Gaussian models, non-Gaussian models are hard to construct. In 1965, Bather developed some methods for constructing ``invariant conditional distributions'', which can be considered as special forms of non-Gaussian Kalman filter models. In this paper, we propose a non-Gaussian Kalman filter model, based on the family of invariant conditional distributions. This model is suitable for tracking reliability growth, and is applied to a well known set of data on software failures. Implementing the model requires numerical techniques for which the Gibbs Sampling algorithm is used.
Key words and phrases: Software reliability, reliability growth, forecasting, Gibbs sampling, Kalman filtering, non-Gaussian filtering, invariant conditional distributions.