# What is an exchangeability martingale?

Exchangeability martingales can be used to find strange or odd data points.

The mechanics of exchangeability martingales is still a bit of a mystery to me.

However, posted below are the basic components and how each step gets us to the desired result of an exchangeability martingale.

### What are exchangeability martingales?

Exchangeability martingales are a function of the p-values generated from a set of data.

### What is a p-value?

P-values are probability values. They indicate the probability that the data point occurred by chance. Small p-values indicate something unlikely occurred. P-values are generated from your data points using conformal predictors, and are basically an estimate of the strangeness of the data.

### What are conformal predictors?

Conformal predictors test how well a new data point fits to previously observed data.

### How do you create the exchangeability martingale value?

Using a sequence of the p-values, generate an exchangeability martingale.

### What does an exchangeability martingale value mean?

They track deviation from the exchangeability assumption. When the exchangeability martingale gets too high, the exchangeability assumption is considered violated. Therefore, a sequence of small p-values equates to a large martingale value.

### What is the exchangeability assumption?

The exchangeability assumption assumes that sampling a set of data consistently produces subsets of data that are exchangeable. This is "equivalent to assuming that the examples are generated from the same probability distribution independently."

### References

Plug-in martingales for testing exchangeability on-line