Bayesian Evaluation of Informative Hypotheses by Herbert Hoijtink, Irene Klugkist, Paul Boelen

By Herbert Hoijtink, Irene Klugkist, Paul Boelen

This e-book presents the philosophical, statistical and mental starting place for the evaluate of expert hypotheses.

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In the Gibbs sampler, parameters are sampled iteratively and in a fixed (s) sequence. Let s = 1, . . , S denote the iteration number and {µ(s) , σ 2 } the parameter values sampled in the sth iteration. 12), the Gibbs sampler consists of four steps: 1. Specify initial values for the model parameters, {µ(0) , σ 2 (s) 2. For j = 1, . . , J, sample µj from (s) (s) (s−1) (s−1) p(µj |µ1 , . . , µj−1 , µj+1 , . . , µJ 2 (s) 2 , σ2 (s−1) (0) }. , y, D). (s) 3. Sample σ from p(σ |µ , y, D). 4. Repeat steps 2 and 3 until S draws have been obtained for all model parameters.

We have seen that the prior distribution used in the Bayesian analysis can affect the resulting estimates and this is usually the case if the prior specified is informative. The resulting estimate for µ under the third prior was clearly different from the estimate based on the first or second prior (the latter two being uninformative). 1)? Or should we trust our prior knowledge, which may be the result of many research years in the field and several previous observed samples with a mean around 6?

21) with i = 1, . . , 94 respondents and εi ∼ N (0, σ 2 ). , the True amnesiacs). Furthermore, it is expected that Controls score higher than each of these three groups. This leads to the following inequality constrained hypothesis: µcon > µamn > {µpat , µsim }. In this and the next section it is shown how parameter estimates are obtained by a sample from the posterior conditional on the constraints – that is, after including the inequality constraints as prior knowledge. nl/ms/informativehypotheses for software for the estimation of inequality constrained analysis of variance models.

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