I have yet to see any convincing criticism of Bayesian reasoning when performed using priors derived from the Principle of Maximum Entropy [0]. By incorporating all information available and nothing more, such a prior neither makes unwarranted assumptions nor throws away information (as is very commonly done with other methods). In principle the process of generating such a prior demands absolutely no subjectivity, rather it it the result of a logical deduction from all information available. In practice some information may be difficult to specify or incorporate, however this is automatically accounted for by the Principle of Maximum Entropy as it guarantees that nothing is assumed that is unspecified and being unable to incorporate some information will merely result in all possibilities being considered without bias. In the very worst case when you have no relevant information which can be incorporated this regresses to an uninformative prior (such as the uniform distribution) which are easily and rigourously handled by this principle even in far more complex cases where other approaches fail entirely. Furthermore, given a different prior this process can tell you exactly what additional (unwarranted) assumptions are made.<p>Once the priors are specified, the actual process of Bayesian Reasoning is formal logical reasoning generalised to the case when you possess incomplete information. It tells you exactly the degree of belief you can assign to a proposition given some information; and given this information assigning either less or more belief than the precise amount this deductive process tells you are equally grave mistakes.<p>For further information on the Principle of Maximum Entropy I recommend reading Prior Probabilities (1968) [1] and chapters 11 and 12 of Probability Theory: The Logic of Science [2]. If you are unconvinced of the theoretical validity or universality of Bayesian reasoning I heartily recommend reading chapters 1 and 2 of Probability Theory: The Logic of Science [2].<p>[0]: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Principle_of_maximum_entropy" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Principle_of_maximum_entropy</a>
[1]: <a href="http:&#x2F;&#x2F;bayes.wustl.edu&#x2F;etj&#x2F;articles&#x2F;prior.pdf" rel="nofollow">http:&#x2F;&#x2F;bayes.wustl.edu&#x2F;etj&#x2F;articles&#x2F;prior.pdf</a>
[2]: <a href="http:&#x2F;&#x2F;bayes.wustl.edu&#x2F;etj&#x2F;prob&#x2F;book.pdf" rel="nofollow">http:&#x2F;&#x2F;bayes.wustl.edu&#x2F;etj&#x2F;prob&#x2F;book.pdf</a>