Darwinian Model Building

We present a way to generate heuristic mathematical models based on the Darwinian principles of variation and selection in a pool of individuals over many generations. Each individual has a genotype (the hereditary properties) and a phenotype (the expression of these properties in the environment). Variation is achieved by cross-over and mutation operations on the genotype which consists in the present case of a single chromosome. The genotypes 'live' in the environment of the data. Nested Sampling is used to optimize the free parameters of the models given the data, thus giving rise to the phenotypes. Selection is based on the phenotypes.The evidences which naturally follow from the Nested Sampling Algorithm are used in a second level of Nested Sampling to find increasingly better models.The data in this paper originate from the Leiden Cytology and Pathology Laboratory (LCPL), which screens pap smears for cervical cancer. We have data for 1750 women who on average underwent 5 tests each. The data on individual women are treated as a small time series. We will try to estimate the next value of the prime cancer indicator from previous tests of the same woman.