Bayesian

Contributor

Arpita Kaushik,

Data Scientist

What is Bayesian Inference?

Bayesian inference is a way of updating our beliefs based on new data.

Instead of giving a yes-or-no answer, it tells you how likely something is, based on what you already know and what you just observed.

In experimentation, it helps you judge how confident you should be about your results as new data comes in.

It uses a mathematical rule called Bayes’ Theorem.

The formula is simple:

Posterior probability = (Likelihood × Prior probability) ÷ Evidence

Prior probability: What you believed before seeing the new data.
Likelihood: How consistent the new data is with different possible outcomes.
Evidence: The overall probability of the data across all possibilities.
Posterior probability: Your updated belief after considering the new data.

Instead of treating results as “statistically significant” or not (like Frequentist methods), Bayesian methods allow you to say things like, “Given the data, there’s a 95% chance that Variant B is better than Variant A.”

In Simpler Terms…

Imagine a doctor testing a patient for cancer.

They already know:

• Cancer is rare in the population (prior probability).
• The test is usually accurate but not perfect (sensitivity and false positive rate).

If the test is positive, the doctor doesn’t immediately conclude the patient has cancer. Instead, they apply Bayes’ Theorem to update the probability, using the test accuracy and background rates.

The updated probability helps the doctor decide whether to do more tests or start treatment.

Companies apply the same logic when analyzing experiments, marketing tests, or customer behavior patterns.

Why Bayesian Thinking Matters in Experimentation

You get continuous updates instead of fixed yes/no answers.
You can stop experiments once you’re confident enough, without risking invalid results due to peeking.
You can incorporate prior knowledge, like data from past tests, into new experiments.
You can easily express results in everyday language: “There’s an 85% chance this variant increases conversions by at least 5%.”

Bayesian vs. Frequentist Methods

Bayesian and Frequentist approaches are both powerful but think differently.

Frequentist: “How likely is it that we would see this data if there were no real effect?”
Bayesian: “Given what we know and what we observed, how likely is it that the effect is real?”

Bayesian analysis gives more intuitive answers but usually requires more computational resources.

Frequentist methods dominate traditional A/B testing tools, but many modern experimentation platforms now offer Bayesian options too.

Platforms like Convert Experiences provide both Frequentist and Bayesian methods for conducting A/B tests and surfacing actionable results.

Best Practices for Using Bayesian Methods

Choose informative priors when you have reliable historical data.
Use neutral or flat priors when you want your data to speak without bias.
Clearly communicate posterior probabilities to stakeholders in everyday language.
Understand the trade-offs: Bayesian methods are flexible but can be more complex to explain.
Be consistent — don’t switch between Bayesian and Frequentist mid-experiment without a good reason.

“Bayesian inference is a probabilistic method used to make more informed decisions. Let’s take an example to understand how companies use this method.

Use Case: A company wants to determine the likelihood that an individual has cancer. To calculate the probability that the person has cancer given a positive test, we need the following:

1. The general probability of a person having cancer based on population data (prior probability).

2. The sensitivity of the test (true positive rate).

3. The probability of a false positive (false positive rate).

By plugging these data points into Bayes’ Theorem, the doctor can calculate the probability that the person has cancer, given a positive test, and recommend the next steps in the diagnosis.”

Arpita Kaushik, Data Scientist