Bayes’ Way

The Bayesian method is named after Thomas Bayes, is a probability theory used in both statistics and mathematics. It describes the probability of an event which is based on prior knowledge of the conditions that may be related to the event. (Kruschke, 2010), Bayesian methods for data analysis has not attracted interest but has for cognitive scientists. Bayes’ rule is applying a mathematically correct formula. The traditional behavior of researchers has not followed the Bayesian model. Bayesian methods are accessible for researchers, however, traditional data analysis seems to be exactly that “traditional”. Traditional methods impose some constraints whereas the Bayesian method may make researchers think differently ad break out of the traditional methods.

The p-value in statistics, is the probability of obtaining the observed value. With null hypothesis testing (NHST) a researcher takes the data and determines if there is probability. With the p-value a set of data can have more than one value. In traditional data analysis, we can make corrections to the p-value by using a post-hoc analysis like the Tukey or Bonferroni test. With the Bayesian model, there is no need for a p-value.

Using a power analysis helps a researcher determine the amount of data or subjects needed for a study. Power increases with sample size. Computational constraints can occur for the researcher when the NHST leaves under estimates of power and replication probability (Kruschke, 2010). In the Bayesian model, prior distribution is used to consider uncertainty for parameter values. This will produce a subsequent distribution. The model is easily customizable to the research design.

The Bayesian model seems easy to use with no use of p-values, power analyses, ANOVA’s, homogeneity of variance, etc. There is no need for the NHST. Its methods are used for several other models like signal detection theory, categorization, and process dissociation. The Bayesian model can give distribution for the researcher that is meaningful.

The Bayesian model uses prior distribution of a model which takes uncertainty and shows credibility of parameter values when new data may be absent. It alters the credibility of the data. Prior distribution should be conventional to the audience (people reading or reviewing the data). In many treatments, prior distribution has little influence on posterior distributions. (Kruschke, 2010) Incorporating prior knowledge into Bayesian analysis is crucial. Bayesian model is a good method for cognitive scientists to use with empirical data instead of using traditional methods of data analysis.

References:

Bayesian Statistics in One Graph. www.slideshare.net

Kruschke, J (2010). What to believe: Bayesian methods for data analysis. Trends in Cognitive Sciences. Vol. 14 No7, 293–300.

Two Trends in Data Analysis. www.doingbayesiandataanalaysis.blogspot.com