Inference by Conversion

We are discussing a modeling technique based on the idea to generate data sequences with a number of suggested models. These sequences are transformed, or converted, into an observed data sequence by a suitable function, or a program. The motivation for doing so is in cases where the likelihood of observed data is hard to compute, which is circumvented with an indirect approximation by trying to replicate the data. It is shown that this approach produces desirable metrics on the models of interest and a consistent method for model selection, at least in some cases. Keywords— Kolmogorov complexity, algorithmic information theory, data compression, randomness, randomized algorithms, statistical inference, model selection, minimum description length, Bayesian data analysis, prediction.