4.5 Sequential analysis: evolving with data

• We examined the increasing influence of the data and diminishing influence of the prior on the posterior as more and more data come in. Consider the nuances of this concept. The phrase “as more and more data come in” evokes the idea that data collection, and thus the evolution in our posterior understanding, happens incrementally.

Sequential Bayesian analysis (aka Bayesian learning)

In a sequential Bayesian analysis, a posterior model is updated incrementally as more data come in. With each new piece of data, the previous posterior model reflecting our understanding prior to observing this data becomes the new prior model.

• Data order invariant.

• The final posterior only depends upon the cumulative data.