By Marc Kery and Michael Schaub (Auth.)
Bayesian facts has exploded into biology and its sub-disciplines, reminiscent of ecology, over the last decade. The loose software WinBUGS, and its open-source sister OpenBugs, is at present the single versatile and general-purpose software on hand with which the typical ecologist can behavior normal and non-standard Bayesian statistics.
- Comprehensive and richly commented examples illustrate a variety of types which are such a lot correct to the learn of a latest inhabitants ecologist
- All WinBUGS/OpenBUGS analyses are thoroughly built-in in software program R
- Includes whole documentation of all R and WinBUGS code required to behavior analyses and indicates all the required steps from having the knowledge in a textual content dossier out of Excel to reading and processing the output from WinBUGS in R
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Extra resources for Bayesian Population Analysis using Win: BUGS. A hierarchical perspective
5 Histogram of body length of 10 asp vipers (a) and histogram of 1 million sample means of the body length of 10 asp vipers (b). Red line: population mean, blue line: mean of sample (means). 5a shows one data set; do not forget that yours will be different. , the value of the parameter that we want to estimate when calculating the sample mean), and the blue line is the mean for our particular sample of 10 snakes. We see that here the sample mean is too small relative to the population mean. To see whether the difference between the blue line and the red line is simply sampling variation, we can repeatedly draw such samples and plot the means.
Although the two prior distributions are both vague on their scales, the posterior distributions will not be exactly the same. In spite of all this, it must be said that it is easy to exaggerate priorrelated difficulties with the Bayesian approach. For once, and perhaps to console some doubters, typically parameter estimates from the Bayesian analysis of a model with vague priors numerically match pretty closely the MLEs from a frequentist analysis of the model. Second, with reasonable sample sizes, the data overwhelm the prior in their influence on the posterior distribution because the effect of the prior diminishes as sample size increases.
66. This example illustrates how the information about our postwork activity (D in Lindley’s recipe) influences our knowledge about the weather on a given night. In other words, it shows how our prior knowledge about the weather, p(θ), was updated by the observed data D to become p(θ|D). This example deals with observable events of a binary nature and nicely illustrates the use of conditional probability for learning from data, which is the basis for using Bayes rule for statistical inference about unknown quantities.
Bayesian Population Analysis using Win: BUGS. A hierarchical perspective by Marc Kery and Michael Schaub (Auth.)