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5 Concrete Benefits of Bayesian Statistics

Understand the benefits before diving into the math

Many of us (myself included) have felt discouraged from using Bayesian statistics for analysis. Supposedly, Bayesian statistics has a bad reputation: it is difficult and heavily dependent on math. Also, because of its relevance to many fields, Data Science included, writers and professionals, want to get a head start by publishing articles on how the formula works.

I believe data professionals, academics, existing books, and online courses are responsible for creating the negative stereotype of Bayes’ hard work. We can all agree that not everyone is attracted to mathematical formulas. Also, Bayesian statistics does depend on the logic of probability, so it appears mathematically complex. Hence, the lack of enthusiasm.

Let me help you break free from any fright when you see Bayes’ Theorem. Here are five tangible benefits of Bayesian Statistics. By the end of this article, you will feel encouraged to tackle any formula others through at you.

1- Intuitive and solid model testing and comparison

It provides a natural way of combining old information with new data, within a solid theoretical framework. You can incorporate past information about a variable and form a prior distribution for future analysis. When new observations become available, your previous prediction can be used as old information.

These predictive distributions allow for in-depth testing of any particular aspect of a model. You can compare data simulated from these distributions with the real data. Bayesian hypothesis testing enables us to quantify evidence and track its progression as new data come in. This is important because there is no need to know the intention with which the data were collected.

2- Straightforward interpretation of results

The confidence interval (CI) is often portrayed as a simple measure of uncertainty [1]. Well, this is not the case, and interpretation of this concept is not straightforward.

I have seen data professionals concluding that the percentage of consumers who bought product X, had a 95% confidence interval of 1% ≤ consumers ≤ 5%. This is often incorrectly interpreted as having an implicit meaning: ‘There is a 95% probability that the true percentage of consumers who bought product X lies in the range of 1% to 5%.’ So, what CI captures is uncertainty about the interval we have calculated, rather than the real percentage of consumers who bought product X. A 95% confidence interval means that across the infinity of intervals that we calculate, the true value of the parameter will lie in this range 95% of the time.

So, what CI captures is uncertainty about the interval we have calculated, rather than the real percentage of consumers who bought product X. We have to imagine taking repeated samples from a particular population and for each set of fictitious samples, we estimate a confidence interval. A 95% confidence interval means that across the infinity of intervals that we calculate, the true value will lie in the range (1%-5% in the example above) 95% of the time. So, it is easy to get distracted and misinterpret the results. Therefore, you could provide the wrong recommendation.

By contrast, in Bayesian statistics, credible intervals have a more common-sense interpretation. It aligns much better with the view that they quantify the uncertainty estimated. For example, suppose a test shows that the distribution of potential consumers who bought product X. If the result lies between 25 and 55 is 0.95, then 25 ≤ result ≤ 45 is a 95% credible interval. No hassle.

3- Model flexibility

Recent Bayesian models rely heavily on computational simulation to carry out analyses. This might seem excessive compared with the other type of statistics, namely Frequentist statistics [1]. However, Bayesian models can easily be extended to include data-generating processes of any complexity. This is not the case for Frequentist approaches, where the difficulty of analysis usually increases depending on the complexity of the model you have chosen.

4- Less important to remember mathematical formulas less opportunity for misuse of tests.

There are considerable entry barriers for those attempting to learn Frequentist inference. Some examples include a range of mathematical and statistical results (with complicated names) that are necessary to know to do inference. The assumptions behind each of these results are not always clear, particularly when using statistical software for inference. This is a problem because there is a high chance of misusing the software.

By contrast, in Bayesian inference you typically build models from the ground up, starting with the assumptions about a process. While this might seem a bit repetitive, it means that you do not need a working knowledge of every different statistical test. Also, there are fewer opportunities to misuse Bayesian models because it is necessary to explicitly state the assumptions as part of the model building process.

5- The best predictions

Leading researchers, both in business and academia, use Bayesian statistics for prediction. An example is Nate Silver’s correct prediction of the 2008 US presidential election results. Nate has managed to predict every state correctly [2]. Despite when most media sources were saying that the race was tied.

Where to go from here?

Now that you have five concrete benefits of Bayesian Statistics, I hope you feel encouraged to tackle Bayes’ Theorem. As promised, I did not present you with any formula or complex graph. I believe that understanding the why before taking any action should be the norm. Otherwise, some tasks appear meaningless and often challenging to execute. Now, I suggest further reading, of course, so here is my recommendation:

If you don’t have the necessary background, you can get started with statistics and probability with this course I have put together:

Enjoy!

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References:

[1] Confidence Interval — https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/introduction-confidence-intervals/v/confidence-intervals-and-margin-of-error

[2] Frequentist Inference — https://www.sciencedirect.com/topics/mathematics/frequentist

[3] Silver, N. (2012). The signal and the noise: The art and science of prediction. New York: Penguin.