Exchangeability and Dependence Mixtures

Exchangeability captures the idea that the future is statistically identical to the past, irrespective of the order of observations. De Finetti's Theorem states that any infinitely exchangeable sequence of random variables is a mixture of independent and identically distributed (IID) sequences. This module explores both infinite mixtures and the boundary case of finite exchangeability.

Experiment

In this Interactive Module, you can select different latent laws and observe how the sequence and count probabilities change.

To see how these concepts behave in practice, try the following steps:

1. Select the "Mild" latent law and observe the IID comparison values.
2. Select the "Finite one success" latent law to observe a distribution that is finite exchangeable over length 3, and note the negative covariance.