Pólya’s urns and Laplace’s rule of succession
Abstract
Abstract This chapter introduces the classic Pólya’s urn scheme as a foundational model for interdependent events. It begins with the two-colour model, emphasising its connection to Bayesian inference through Laplace’s rule of succession, and establishes the important property of exchangeability via the de Finetti representation theorem. The discussion then extends to the multi-colour case, which serves as a basic model for innovation, representing the discovery of pre-existing types. However, it is demonstrated that this scheme, with its fixed set of possibilities, fails to reproduce the characteristic power laws observed in real innovation processes.
Fields of Study & Subjects
Probability and Statistical Research
Bayesian Methods and Mixture Models
Innovation Diffusion and Forecasting
Publication details
- Journal / source
- Oxford University Press eBooks
- Pages
- 127–145
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Book chapter