🔹 24. Common Mistakes
❌ Mistake 1: Thinking the prior is always subjective - A prior can come from historical data, previous studies, domain knowledge.
❌ Mistake 2: Confusing likelihood with posterior - Likelihood = P(Data | Parameter), Posterior = P(Parameter | Data). They are not the same.
❌ Mistake 3: Ignoring the base rate - The prior probability can have a major impact, especially when an event is rare.
❌ Mistake 4: Confusing confidence intervals with credible intervals - They have different statistical interpretations.
❌ Mistake 5: Thinking Bayesian methods ignore data - They don't. Bayesian inference combines prior information with observed evidence.
🔹 25. Interview Perspective
💡 What is Bayesian Statistics?
Bayesian Statistics is an approach to statistical inference that combines prior information with observed data to produce a posterior distribution representing updated beliefs about unknown parameters.
💡 What are Prior, Likelihood and Posterior?
Prior represents information before observing the new data, likelihood describes how compatible the observed data is with different parameter values, and posterior represents the updated distribution after combining the prior and likelihood.
💡 MLE vs MAP?
MLE estimates parameters using only the likelihood, while MAP combines the likelihood with a prior distribution.
🎯 Practice Questions
Q1. What are the three main components of Bayesian inference?
Q2. What is the difference between prior and posterior probability?
Q3. What is the difference between MLE and MAP?
Q4. Why is the base rate important in Bayesian reasoning?
Q5. What is the main difference between a confidence interval and a credible interval?
🎯 Key Takeaways
✅ Bayesian Statistics = Prior + Data → Posterior
✅ Prior = Belief/information before observing new data.
✅ Likelihood = How compatible the observed data is with different parameter values.
✅ Posterior = Updated belief after considering the data.
✅ Posterior ∝ Prior × Likelihood
✅ MLE uses likelihood.
✅ MAP uses prior + likelihood.
✅ Bayesian methods naturally represent uncertainty using probability distributions.
✅ Naive Bayes is a major Machine Learning algorithm based on Bayes' theorem.
✅ Bayesian inference is especially useful when information arrives sequentially and beliefs need to be updated.
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