Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. Introduction to Bayes' rule[edit] A geometric visualisation of Bayes' theorem. Main article: Bayes' rule Formal[edit] where denotes a conditional probability; more specifically, it means given. stands for any hypothesis whose probability may be affected by data (called evidence below). Note that, for different values of , only the factors and affect the value of . Note that Bayes' rule can also be written as follows: where the factor represents the impact of on the probability of . . . .

Elementary Concepts in Statistics In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis. The selected topics illustrate the basic assumptions of most statistical methods and/or have been demonstrated in research to be necessary components of our general understanding of the "quantitative nature" of reality (Nisbett, et al., 1987). We will focus mostly on the functional aspects of the concepts discussed and the presentation will be very short. Further information on each of the concepts can be found in statistical textbooks. Recommended introductory textbooks are: Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of elementary theory and assumptions of statistics, see the classic books by Hays (1988), and Kendall and Stuart (1979). What are Variables? Variables are things that we measure, control, or manipulate in research. Correlational vs. Dependent vs.

Statistics How To The R Project for Statistical Computing