Advantages of Bayesian statistics

Bayesian methods are increasingly popular due to the advantages they offer over frequents statistical methods:

•  A Bayesian analysis provides direct statements about the quantities of interest, providing more intuitive results and feeding naturally into a decision making process.

• Bayesian statistics allows us to obtain some useful information even from a single piece of evidence, whereas many more samples would be required for a frequents statistical result.

• The Bayesian approach allows all evidence to be taken into account in an explicit way.

Different forms of evidence can be combined in the overall probability model or included via the prior belief. Analyzing the data using different priors allows the data to be interpreted from different points of view, such as regulatory or business.

• The Bayesian framework more naturally allows for the modeling of biases or Systematic error and for modeling any hierarchical structure in the data or in the problem. For instance in a clinical trial with 200 subjects at 5 different hospitals, we can model not just the overall effect of the treatment studied, but also variations in outcome between different hospitals.

• Bayesian statistics provides greater flexibility. It offers a natural way to adapt an experiment in progress in the light of results collected so far, or to halt the experiment early if the result is clearer than expected and no more data is needed to achieve the desired degree of certainty.