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Bayesian versus frequentist (non-bayesian / classical) statistics

Concepts

1. Bayes’ theorem: describes probability of an event, based on prior knowledge of conditions that might be related to the event.

   • Bayes’ formula: *P(A

     B)* = *P(B

     A)P(A)* / P(B)

2. Characteristics of bayesian method:
   • The use of random variable / unknown quantities to model all sources of uncertainty in statistical models including uncertainty resulting from lack of information
   • The need to determine the prior probability distribution taking into account the available (prior) information
   • The sequential use of Bayes’ formula
   • While for frequentist, a hypothesis is a proposition (True/ False), in Bayesian statistics the probability that can be assigned to a hypothesis can also be in a range from 0 to 1 if the truth value is uncertain
3. Frequentist inference: draws conclusions from sample data by emphasizing the frequency or proportion of the data. Used for statistical hypoehtsis testing and confidence intervals, etc..

References:

1. Wikipedia: Bayes theorem
2. Wikipedia: Bayesian probability
3. Wikipedia: Bayesian statistics
4. Probabilisticworld: Frequentist and Bayesian approaches in statistics
5. Egerton consulting: A comparison of classical and bayesian statistics
6. Sciencedirect topic: Classical Statistic
7. Sciencedirect topic: Bayesian statistic
8. C. Sims: Bayesian and classical inference
9. PlanSpace: What’s the diffference between Bayesian and non-Bayesian statistics
10. Zrnold Zellner: Bayesian and non-Bayesian approaches to statistical inference and decision-making