By Gudmund R. Iversen
Empirical researchers, for whom Iversen's quantity presents an advent, have normally lacked a grounding within the method of Bayesian inference. consequently, purposes are few. After outlining the restrictions of classical statistical inference, the writer proceeds via an easy instance to give an explanation for Bayes' theorem and the way it will possibly conquer those barriers. usual Bayesian functions are proven, including the strengths and weaknesses of the Bayesian method. This monograph hence serves as a spouse quantity for Henkel's assessments of value (QASS vol 4).
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Additional info for Bayesian statistical inference
One way to deal with a continuous variable is to find the mathematical function for the curve in Figure 1. The actual mathematical function contains the same information as the curve itself, and the function can be used in the continuous version of Bayes' theorem. Mathematicians have equations for a large variety of curves, and for the analysis of a population proportion it turns out that it is particularly convenient to look at functions that are polynomials in p. Here are some examples of such polynomials: None of these will give the curve in Figure 1 when they are plotted.
10. A property of the beta distribution is that the mean and variance can be found directly from a and b. From this follows that a and b can be found from the mean and variance. Let the mean of p be denoted µ and the standard deviation be denoted s. When the distribution of p is the beta distribution with parameters a and b, we have the following relationships between the mean and variance and the two constants a and b, Solving for a and b gives us a and b as the following functions of the mean and the variance, If we know the mean and variance, these two expressions can be used to find a and b.
There are two major ways we can find our particular beta prior distribution; that is, to find the two constants a and b that determine the distribution. The first way is simply by trial and error, preferably using a computer, plotting beta distributions for various values of a and b and simply picking the one that most closely represents our prior knowledge. Figure 1 shows the curve for the beta distribution with a = 6 and b = 14. The curves for nearby values of a and b would not be very different, and there could well be other curves that represent our limited knowledge equally well.
Bayesian statistical inference by Gudmund R. Iversen