We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statis- tical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathe- matical definition of randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the reg- ularities detected in binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are in- formative about the cognitive processes engaged by different formats.

This paper is a first step in modelling mathematical objects showing "subjective randomness", or what people believe to be random. Although there is no rigorous characterization of what subjective randomness might be, it has become clear through experimentation that is quite different from stochastic randomness. A classic example which illustrates this difference is the following: when asked which of the following sequences is most likely be to produced by flipping a fair coin 20 times, OOOOOOXXXXOOOXXOOOOO OOXOXOOXXOOXOXXXOOXO most people will answer "the second sequence" even though each sequence has been produced by a random generator.

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problemof model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definitionof randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the regularities detectedin binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are informative aboutthe cognitive processes engaged by different formats.

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definition of randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the regularities detected in binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are informative about the cognitive processes engaged by different formats.

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definition of randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the regularities detected in binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are informative about the cognitive processes engaged by different formats.