Bayesian analysis is a powerful and flexible way of doing statistics, but it can be hard to explain to non-technical audiences. In this article, you will learn how to use simple examples, analogies, and visualizations to communicate the main ideas and benefits of Bayesian analysis, without getting lost in the math or jargon.
Bayesian analysis is a way of updating your beliefs about something based on new evidence. For example, suppose you want to know if a coin is fair or biased. You start with a prior belief, which is your initial guess based on some background information or intuition. Then you flip the coin a few times and observe the results. This is your data, which provides new evidence. Based on the data, you update your prior belief to get a posterior belief, which is your revised estimate of how likely the coin is fair or biased. This process of going from prior to posterior is called Bayesian inference.
Simple explanation of Bayesian : 1.Starting with a Guess: First, you start with an initial guess let's say you guess that there's a 50% chance of rain tomorrow. 2.Adding Clues and Data: Now, you gather more information. You look at things like weather forecasts, the season, and maybe even patterns you've noticed in the past. 3.Updating Your Guess: You take your initial guess and combine it with the clues you've collected. This helps you update your guess to make it more accurate. 4.Considering How Reliable the Clues Are: Some clues might be really strong and reliable, while others could be a bit uncertain. Bayesian analysis gives more weight to the reliable clues and less weight to the uncertain ones. 4.Repeating and Getting Better.
Imgineyou have a coin that you think might be biased. You flip the coin 10 times and get 7 heads. A Bayesian analyst would start with a prior belief about the probability that the coin is biased. This prior belief could be based on their knowledge of coins or their intuition. For example, they might believe that there is a 50% chance that the coin is biased. The Bayesian analyst would then update their prior belief based on the data they have collected. In this case, the data is the fact that they got 7 heads in 10 coin flips. The posterior belief is the Bayesian analyst's updated belief about the probability that the coin is biased. In this case, the posterior belief might be that there is a 70% chance that the coin is biased.
Bayesian analysis has several advantages over other methods of statistics. One is that it allows you to incorporate your prior knowledge and assumptions into your analysis, which can make it more realistic and informative. Another is that it gives you a measure of uncertainty and variability in your estimates, which can help you make better decisions and communicate your results more clearly. A third is that it can handle complex and nonlinear models that can capture the richness and diversity of real-world phenomena.
Bad example. It is not possible to bias a coin. A coin will always spin around its center of gravity. If you weight one side, you are just changing the center of gravity. It will still spend one half the time with each side up. If you flip it in the air and catch it, the probability of either side will always be 1/2 no matter how it is weighted.
This is incorrect. Nonlinear regression based on maximum likelihood estimation can provide the asymptotic standard error. The ASE may not be an uncertainty, but it would be incorrect to Bayesian analysis is necessary to provide uncertainty.
One way to explain Bayesian analysis to non-technical audiences is to use simple and familiar examples that illustrate the logic and intuition behind it. For example, you can use the coin flipping example to show how your prior and posterior beliefs change as you get more data. You can also use examples from everyday life, such as diagnosing a disease, predicting the weather, or rating a movie, to show how Bayesian analysis can help you deal with uncertainty and make informed choices.
How long to boil en egg. This easy example is also a reproducible experiment . 1. An egg must boil for at least X minutes to be hard boiled. 2. Buy some eggs of differing sizes and start boiling for the minimum time found a priori. 3. After you boil the eggs, some might not be hard boiled by the minimum time. This creates a size - time relation for the eggs, as well as makes statement one untrue. 4. We adjust the initial statement based on the results we have and repeat the proces until you find what you seek. Although we start from a statement that should be 100% true we can either find the true value for X, we may find a new limit Y for the boiling point or make a distribution of time depending on egg size.
Another way to explain Bayesian analysis to non-technical audiences is to use analogies that relate it to something they already understand or experience. For example, you can compare Bayesian inference to updating your GPS navigation based on new traffic information, or to revising your opinion of a person based on new interactions. You can also use analogies from sports, games, or art, such as betting on a horse race, playing poker, or painting a picture, to show how Bayesian analysis can help you balance your prior beliefs and new evidence.
An analogy to use is "Prediction of winner in a sports game" . It can be tracked with live betting. Calculating the possibility of one team winning is done using a priori predictions (bets before the match) and information from the game. For example football (also known as soccer to some). The odds are calculated based on offences, successful defence , outs, offsides, ball control etc. It is hard to properly categorise all events and how they affect a match, however the expected result is updated by real events, in real time and lead to an evolving point of view as to who is more dominant in the game , ergo more possible to win. One can easily see this happen in real time, if they watch a game and constantly check the live bet offers.
A third way to explain Bayesian analysis to non-technical audiences is to use visualizations that show the process and results of Bayesian inference in a graphical and interactive way. For example, you can use histograms, pie charts, or bar plots to show the distribution of your prior and posterior beliefs, and how they change with different data. You can also use graphs, maps, or images to show the relationship between your variables, and how they are affected by your model and assumptions. Visualizations can help you convey the uncertainty and variability in your estimates, and make your analysis more engaging and accessible.
A final way to explain Bayesian analysis to non-technical audiences is to use code that demonstrates how to implement and apply Bayesian inference in a practical and relevant way. For example, you can use a programming language like Python or R, and a library like PyMC3 or Stan, to create and fit a Bayesian model to your data, and to generate and analyze your posterior estimates. You can also use code to create and customize your own visualizations, and to perform various checks and diagnostics on your model and estimates. Code can help you show the steps and logic of Bayesian inference, and how it can be used to solve real-world problems.
Entropic Convex Duality in the Determination of Data-Constrained Kernel-Based Bayes-Jaynes Priors With +++ illustrations