Bayesian Approaches in People Analytics
Why they are better than classical approaches
Ask any statistician if they are a Frequentist or a Bayesian and you might get an eyeroll or evasive answer. If they are a passionate Bayesian statistician you might be in for a long lecture about the merits of a Bayesian approach. There is plenty of debate among statisticians about which is better but more recently, the Bayesian approach is becoming more commonly used. If you have no idea what the difference is, that is simply because the vast majority of introductory statistics classes sweep that issue under the rug and teach you the frequentist (aka classical) approach. If you’ve ever used a p-value or hypothesis tests, you are using frequentist methods.
In my last post, I analyzed some regression data in both ways. The first used the classical approach you most likely learned in your introductory statistics class and the second used a more modern Bayesian approach.
For many simple problems (such as the simple linear regression I shared previously), the 2 approaches will lead to the same conclusions. However, there are some important distinctions that I’ll get to in a minute. So one could argue, if the two methods give you the same answer, does it matter which you use?
If you had asked me the question 10 years ago, I would have answered that it didn’t matter. Nowadays with additional experience, I believe the difference matters and that a Bayesian approach is the way to go. It might be a while before it trickles down to introductory statistics classes but I can’t wait for that to happen.
Why does it matter?
1 - The interpretation is simpler and more intuitive in the Bayesian approach
Do you struggle with the concept of a p-value? Do you find yourself wanting to say something like “There is a 3% chance that the null hypothesis is true?” You can’t say that in the frequentist approach. And you are not alone in getting the interpretation wrong.
I’ve taught hundreds of people in statistical methods (both in academia and industry) and so many get the frequentist interpretation wrong.
Would a Bayesian approach help? It is a more intuitive way to describe the output of an analysis. Of course, no analysis approach will solve the problem of bad data or doing the wrong analysis.
I would love to retire p-values with their singular focus on a single value answer and statistical significance as the dominant analysis approaches. I prefer approaches that de-emphasize cut-and-dry decisions based on statistical significance. A Bayesian approach is superior because of its primary emphasis on intervals rather than p-values.
Yes, you can do confidence intervals in a classical approach. However, despite what many people think, confidence is not the same as probability. And most of the time when people say “confidence” in the context of confidence intervals, they really are thinking in terms of probabilities. This confusion is what trips up many people with the frequentist analysis approach.
2 - Previous obstacles and objections to a Bayesian approach are no longer relevant
In the past, frequentist statisticians would raise objections to a Bayesian approach, such as the difficulty in doing the analysis and the subjectivity of the analysis.
Let’s address those two concerns. First, Bayesian approaches were indeed harder to do before with some specialized coding skills. Believe me, I remember wrangling with WinBUGS (the latest Bayesian software at the time) back in grad school and finding it a lot harder to use and work with than other statistical software packages. Those days are in the past. In the example I shared last week the code is essentially the same between the two approaches. It is so much easier to implement Bayesian approaches than it used to be (besides packages in R and Python) there are even easier-to-use tools like JASP which is a free download that will show you side-by-side comparisons of frequentist and Bayesian methods for many common statistical methods.
Second, the argument was that Bayesian approaches were subjective because you could arbitrarily specify a prior distribution. Essentially you could set initial values representing your beliefs about the analysis results. This was viewed as too subjective because it is possible to set the prior distribution to manipulate the result to get what you wanted. In my regression example, you may have noticed that I said nothing about a prior distribution. That is because there are many defaults that can remove some of that subjectivity. A common default is “weakly informative priors” which are less subjective and let the data drive more of the analysis result, rather than making too strong of assumptions. It is hard to criticize using a weakly informative prior which is more objective than an arbitrary prior. These priors are often set as defaults which makes it even easier to use Bayesian approaches than in the past, where you had to be more explicit about the priors you were using in the analysis.
So if you have a method that is just as easy to use, gives similar answers to the prevailing standard, and is easier to use, then why not use it? So go Bayesian and you may find yourself being the trendsetter.
I recognize that I’m simplifying this discussion to make this accessible to non-statisticians. There’s a lot of additional detail I’ve glossed over and more reasons to consider a Bayesian approach but that additional detail doesn’t change the conclusion I’ve presented. Here’s one example if you really want to dig into the weeds of this.
If you want a great resource to learn more about a Bayesian approach with an applied, practical approach look no further than Regression and Other Stories by Andrew Gelman, Jennifer Hill, and Aki Vehtari. They even provide an online version you can access for free. They go into a lot of additional reasons for a Bayesian approach (particularly chapter 4 of this book).