mcmc04

Main MCMC Page	mcmc04 Dataset

Additional Information

Dataset
Name:

mcmc04

Procedure:

Markov Chain Monte Carlo
Certification Method & Definitions

Data:

11 Observations
12 Constant Leading Digits
Average Level of Difficulty
Generated Data

Model:

2 Parameters ( $\mu$ , $\sigma^2$ )
$y_i = \mu + \varepsilon_i, \ \ \varepsilon_i \sim N(0,\sigma^2)$

Prior:

Joint prior density for $\mu$ and $\sigma$ is
proportional to $\frac{1}{\sigma}d\mu d\sigma$

This dataset was generated to assess computational inaccuracy of MCMC software. The generated data is based on work published by Stephen Simon and James Lesage. They identified two types of error that can particularly affect ANOVA computations, cancellation error and accumulation error. These same types of errors can also affect MCMC computations. Software that is not written to control these errors can produce inaccurate output which can sometimes be serious enough to change the qualitative conclusions of the data analysis.

Even though the primary focus of these datasets is identification of problems caused by cancellation or accumulation error, these datasets may also identify errors in other aspects of MCMC software.

The formula used to generate this data is:

$y_{i}=10^{11}+\phi(i),\ \ \ i=1,\ldots,11,$ where
$\phi (k) = \left\{ \begin{array}{ll} 0.2&\mbox{if }k=1\\ 0.1&\mbox{if }k=2,4,6,8,10\\ 0.3&\mbox{if }k=3,5,7,9,11. \end{array} \right.$