We are constantly making decisions under uncertainty where information is limited and the outcome of the decision is not granted. You don’t know if

Ergodicity and Stationarity. Luck but Not for You

submited by

Style Pass

2024-09-29 14:00:06

We are constantly making decisions under uncertainty where information is limited and the outcome of the decision is not granted. You don’t know if your startup investment will go to zero. You don’t know if a given health treatment will save your life. You don’t know if you will win a hand in poker.

Luckily, statistics help us to manage uncertainty. Metrics such as mean, median, mode or percentiles give us information about the past. We can incorporate these metrics in our decision making process to trade-off the risk and reward.

The problem. Most people apply statistics wrongly in their decision making process. In this post we will explain the concepts of ergodicity and stationarity exemplified with three use cases:

All real-life use cases that can be modeled as stochastic processes are never ergodic nor stationary. Yet people keep applying statistics as if they were.

Ergodicity is a well-known concept in statistics. It’s a property of stochastic processes. If you observe a single system over a long period and give the same statistical properties as observing many systems at a single point in time, we say that it is ergodic.