It is quite clear to me that Bayesian method is good for scientific research and I hope myaffirmation on this argument can be clearly examined and understood by the so called antiBayesians (such as Gelman in 2008). Several successful attempts have been made to improve anddevelop the Bayesian method with the aid of the lessons learnt from challenges faced in solvingreal life situations (Uusitalo, 2007). In the article “Objections to Bayesian Statistics”, Gelman(2008) mentioned disadvantages of Bayesian methods; however, my perspective on this matter isin full support of the fact that the Bayesian method is a good approach in social science research.I am so optimistic that my points will be sufficient enough to convince the so called hypotheticalnon-Bayesian and make him understand that Bayesian inference has been proven right by ancientstatisticians to be sufficient, complete, unique, and in fact robust enough for scientific applications,and applications in other fields like engineering, philosophy, medicine, sport, and law.
The method of achieving Bayesian inference has been developed and these techniquesaddress issues by specifically sampling the posterior probability distribution (Uusitalo, 2007). Tomake the techniques more efficient enough, a Markov Chain Monte Carlo (MCMC) techniques isintroduce and then at the end of the series of operations, sample are distributed according to theposterior probability distribution solution and following order, inference are based (Berger, 1994). The purpose of Bayesian inference is to study how an ideal perfect reasoner would responseto certain pieces of information. When I choose a hypothesis space and a prior distribution, am notwriting my prior belief in my brain. I am writing down a hypothetical state of prior belief that mayor may not be a good approximation to what I think but whatever I use in a calculation is alwaysan idealization (Berger et. al., 1994).
Also, I would like to shed more light on what the anti-Bayesian thinks about the fact thatBayesian method now seem to be computed using Markov Chain Monte Carlo unlike the old dayswhen the Bayesian methods had at least the virtue of being mathematically clean (Gelman, 2008).Is he actually overlooking the fact that computer processors are becoming more efficient as wellas cheaper to produce. Accordingly, the availability of adequate hardware to run complex modelsis becoming less of causing delay, at least, in resource –rich countries (Uusitalo, 2007).
On the other hand, Bayesian analysis is able to handle highly complex models efficientlywhen frequentist approaches to estimation often fail. This especially the case for models withcategorical data or random effect where Bayes might even be faster than the default numericintegration procedures most often used (Uusitalo, 2007). I would like to support my points by saying: the Bayesian theorem provides a convenientsetting for a wide range of models, such as hierarchical models and missing data problems.Markov Chain Monte Carlo along with other numerical methods make computation tractable forvirtually all parameter models (Berger et. al, 1994).
Anybody can see that interpretation of results for the Bayesian theories is very different:for example, discussions made on confidence interval. We believe that Bayesian results are moreintuitive because the focus of Bayesian estimation is on predictive accuracy rather than “up ordown” significance testing. Also, the Bayesian frame work eliminates many of the contradictionsassociated with conventional hypothesis testing (as it was exemplified at Meeus et.
al., 2011). Begging your pardon, did you really mean Bayesian methods encourage undisciplinedmode of thinking (Gelman, 2008)? Well, that is really interesting but I don’t think it is really tothe point. Bayesian approach is based on subjective interpretation of probability should have beensaid instead and the important reason for using the Bayesian statistics is that it allows updatingknowledge instead of testing hypothesis and we believe this is what science is all about: updatingone’s knowledge (Berger et.
al. 1994). You cannot deny the fact that Bayesian frame work offers more direct expression ofuncertainty. The prior distribution to use is another discussion among Bayesian statisticians butthis case is settled because of many more distributions are available to use as an alternative to eachdistribution (Meeus et. al., 2011). The Bayesian method eliminates the worry about small samplesizes – Albeit, with possible sensitivity to priors (as it should be).
In general, I do not want to make the argument for using Bayesian statistics because of its’superiority’. That is, following De Finetti(1974a), we have to come to grips as to what probabilityis: long-run frequency of a particular result or uncertainty of our knowledge (as it is cited inBerger, 1994).