Bayesian Method: A more human-centered method

Replication crisis has been a serious issue in psychology, biology and medical research. Kruschke (2010) described that traditional statistics meet dilemma in (1) p-value, (2) point estimates, (3) power, (4) hardware limitation and (5)feeble foundation for empirical science. P-value which was maintained by traditional frequentist statistics seems not reliable and power were put forward as an alternative indicator. Power tells the extent of replication probability. However, it is hard to replicate an experiment. Researchers have to restore not only the procedure, variables and equipment, but environment as well. A complete replication can be also demanding and hard-working and under many situations chances for replication are limited, such as president voting, rocket emission. etc. Researchers begin to turn to another school of statistics, the Bayesian statistics.
Instead of looking for a “perfect model”, the method that Bayesian statistics introduced tend to give a “better explanation” based on current data. It focuses on prior distribution and posterior distribution. Probability in Bayesian statistics was interpreted as one form of expectation, which is, the “belief” or “confidence” that one thinks hypothesis become true, instead of frequency in frequentists. Probability can be fluctuating but frequency that frequentists proposed will show tendency toward to one direction or a certain number, being a rather objective number.
The idea of Bayesian method received support from politics predictions, informatics and machine learning. The reason that I argue it is a human-centered method comes from its introduction of prior and posterior probability. Let’s take an example of tossing coins, suppose that a coin that I tossed have 8 times up in the first row of 10 times (original experiment). As a participant, people might begin think about if there is something wrong with its density. Next 10-time row we will begin to test if our hypothesis is true and using outcome of next or more rows (replications) to support or correct our hypothesis, when this person has enough time and energy to do so. It works well for making predictions when cost and other conditions are limited. Machine learning requires some small data to train and generate for future predicting and correction, rather than a fixed value, so as to president voting and rocket emission.
Different start points do not means varied ends. Agreement can also be found in both schools. When the number of evidence N is infinite, Bayesian method tend to give a similar result to that of traditional statistics. Considered its advantages on (1)model flexibility and appropriateness, (2) rich informative inferences, (3)coherent power analysis and replication probability, (4)appropriateness of the prior distribution, Bayesian method is growing rapidly in today’s world.
Reference：
Kruschke, J. K. (2010). What to believe: Bayesian methods for data analysis. Trends in cognitive sciences, 14(7), 293–300.
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