We present an agent-based stock market simulation in which traders utilise a hybrid mixture of common information criteria based inference procedures, including minimum message length (MML) inference. Traders in our model compete with each other using a range of different inference techniques to infer the parameters and appropriate order of simple autoregressive (AR) models of stock price evolution. We show that such traders are initially profitable while a significant population of random traders exist, and that MML inference traders outperform other inference traders in the presence of a noisy AR signal.