"What is Bayesian Analysis?"

Contributed by: Kate Cowles, Rob Kass, & Tony O'Hagan

This article is a brief overview of the history of Bayesian Analysis and a basic breakdown of the mathematics behind the method. The article says Bayes has been around since the late 1700s, however it's popularity and practicality of practice were severely strained. Modern Bayesian analysis as we know today was developed in the second half of the 20th century by Jimmy Savage and Dennis Lindley. Still, fully developing the method was difficult until the breakthrough of the computer age in the 1980s and 1990s. Finally, statisticians had the computational ability to handle the mass data and complex equations needed to do Bayesian analysis.

The breakdown of Bayesian Analysis is at a basic level is an estimator that estimates the probability of a hypothesis coming true as evidence is gathered. The method starts out by using the "prior distribution". As more data becomes available, also known as the "y", it contains the parameters and it is expressed in a "likelihood" which is set in proportion to the observed data. This new data is combined with the prior equation to formulate a "posterior distribution". Long story short, this is a method of probability theory, and the evidence and corresponding likelihood is all calculated. The authors argue the major benefit of Bayes Analysis is the analysis itself is very objective and can be applied to a wide variety of scenarios. The weakness the authors point out is that Bayes is still built on a prior distribution, which can be very subjective.

My major issue with the article is that it does not do a good job of demonstrating how Bayes is used in practicality. At a basic level I can see that it is used to predict outcomes and the probability of a hypothesis coming true, however a real-life example or even a logical but fictional scenario would be very helpful in showing the public how Bayes works.

Source:

https://bayesian.org/Bayes-Explained

p(θ)

Contributed by: Kate Cowles, Rob Kass, & Tony O'Hagan

*International Society for Bayesian Analysis***Summary:**This article is a brief overview of the history of Bayesian Analysis and a basic breakdown of the mathematics behind the method. The article says Bayes has been around since the late 1700s, however it's popularity and practicality of practice were severely strained. Modern Bayesian analysis as we know today was developed in the second half of the 20th century by Jimmy Savage and Dennis Lindley. Still, fully developing the method was difficult until the breakthrough of the computer age in the 1980s and 1990s. Finally, statisticians had the computational ability to handle the mass data and complex equations needed to do Bayesian analysis.

The breakdown of Bayesian Analysis is at a basic level is an estimator that estimates the probability of a hypothesis coming true as evidence is gathered. The method starts out by using the "prior distribution". As more data becomes available, also known as the "y", it contains the parameters and it is expressed in a "likelihood" which is set in proportion to the observed data. This new data is combined with the prior equation to formulate a "posterior distribution". Long story short, this is a method of probability theory, and the evidence and corresponding likelihood is all calculated. The authors argue the major benefit of Bayes Analysis is the analysis itself is very objective and can be applied to a wide variety of scenarios. The weakness the authors point out is that Bayes is still built on a prior distribution, which can be very subjective.

**Critique:**My major issue with the article is that it does not do a good job of demonstrating how Bayes is used in practicality. At a basic level I can see that it is used to predict outcomes and the probability of a hypothesis coming true, however a real-life example or even a logical but fictional scenario would be very helpful in showing the public how Bayes works.

**I would also say that Bayes if possible should have the mathematics broken down in a simpler level so the general public could maybe learn the basics and then possibly be encouraged to delve deeper. The overall complexity of the method can scare even people with some statistical background in my opinion. I enjoy the idea of using math to form an estimate, but the practicality of actually executing the method is difficult in my opinion.**Source:

https://bayesian.org/Bayes-Explained

p(θ)

Dillon, overall I agree with your critique that Bayesian could 'scare some people away' due to its statistical nature, but I disagree in terms of why that scares people away. I think the mathematical formula in and of itself is not difficult, particularly with the computer-powered calculators we have access to. I think the bigger issue is the concept of applying the formula to, what is frequently, a convoluted word problem. In this regards, repeated examples definitely help explain the theory and can help the analysts gain a better understanding of how to complete the mental aspect of this technique.

ReplyDeleteI agree, you worded it better. With today's computers the math should not be a big deal.

DeleteI would say the only caveat is that this would assume you have access to such computational programs. Other methods are arguably more easily implemented in my opinion. If you can use Bayes though it certainly is a worthwhile endeavor.

I am personally not a fan of numbers or math, but I am not opposed to using this method if the computer could calculate it for me. I think something that could scare people who are not comfortable with numbers is assigning percentages or probabilities to complex problems to start the Bayes process. Also the Bayes theorem might be objective, but it relies on the information the analyst includes which like all methods depends on the source reliability.

DeleteI agree with both of you. Utilizing Bayesian analysis for complex word problems can be challenging. If applied properly and analyst are provided with most likely outcomes, isn't the data still skewed because the predictions are based off of previous events? What are your thoughts on this?

ReplyDeleteI guess I would say is it would matter what the specific problem is. I would say there are some issues where past behavior is a good starting point and other issues where it would be skewed and problematic. I guess that is up to the analyst, at the end of the day any method has some bias and isn't perfect.

DeleteGood point. Also-I think it is safe to say that due to some of the complexities of Bayes Analysis, it could be hard to sell to a DM without a hard science background or understanding of the method. I bring this up because of my experience in a Brigade Combat Team. What I am trying to say is that Bayesian analysis would more likely be used in strategic intelligence. Thoughts on this?

ReplyDeleteAgreed. At a tactical level I question the practicality, and you're right Bayes would be hard to explain quickly such as in a tactical scenario. Bayes also is best when a lot of evidence is gathered over time, something that can really only be done at the strategic level.

DeleteDillon I agree with your assessment in the critique, it is an article that helps you understand what Bayes is in broad strokes, but fails to give any type of practical knowledge of how the technique is really being utilized. I feel like this is an article more designed to give you a conversational rather practical knowledge of Bayes. By that I mean if someone at work or on a team mentions it the underlying principles would be familiar to you, but deeper digging, not to mention practice, would be necessary before it could be put into practice.

ReplyDelete