Description Usage Arguments Details Value Note Author(s) References See Also Examples

The function `mu.mblmodwoc`

uses a mixed Bayesian/likelihood approach to
determine conservative sample sizes, in the sense that the desired posterior credible interval coverage and length for a normal mean are guaranteed
over a given proportion of data sets that can arise according to the prior information.

1 | ```
mu.mblmodwoc(len, alpha, beta, level = 0.95, worst.level = 0.95, m = 50000, mcs = 3)
``` |

`len` |
The desired total length of the posterior credible interval for the mean |

`alpha` |
First prior parameter of the Gamma density for the precision (reciprocal of the variance) |

`beta` |
Second prior parameter of the Gamma density for the precision (reciprocal of the variance) |

`level` |
The desired fixed coverage probability of the posterior credible interval (e.g., 0.95) |

`worst.level` |
The probability that the length of the posterior credible interval of fixed coverage probability |

`m` |
The number of points simulated from the preposterior distribution of the data. For each point, the length of the highest posterior density interval of fixed coverage probability |

`mcs` |
The Maximum number of Consecutive Steps allowed in the same direction in the march towards the optimal sample size, before the result for the next upper/lower bound is cross-checked. In our experience, mcs = 3 is a good choice. |

Assume that a sample will be collected in order to estimate
the mean of a normally distributed random variable. Assume that the precision (reciprocal of the variance) of
this random variable is unknown, but has prior information in the form of a
Gamma(*alpha*, *beta*) density.
The function `mu.mblmodwoc`

returns the required sample size to attain the desired length *len*
for the posterior credible interval of fixed coverage probability *level* for the unknown mean.
The Modified Worst Outcome Criterion used is conservative, in the sense that the posterior credible interval
length *len* is guaranteed over the *worst.level* proportion of all
possible data sets that can arise according to the prior information, for a fixed coverage probability *level*.

This function uses a Mixed Bayesian/Likelihood (MBL) approach.
MBL approaches use the prior information to derive the predictive distribution
of the data, but uses only the likelihood function for final inferences.
This approach is intended to satisfy investigators who recognize that prior
information is important for planning purposes but prefer to base final
inferences only on the data.

The required sample size given the inputs to the function.

The sample size is calculated via Monte Carlo simulations, and therefore may vary from one call to the next.

It is also correct to state that the coverage probability of the posterior credible interval of fixed length *len* will be at least *level* with probability *worst.level* with the sample size returned.

Lawrence Joseph lawrence.joseph@mcgill.ca and Patrick Belisle

Joseph L, Belisle P.

Bayesian sample size determination for Normal means and differences between Normal means

The Statistician 1997;46(2):209-226.

`mu.mblacc`

, `mu.mblalc`

, `mu.mbl.varknown`

, `mu.acc`

, `mu.alc`

, `mu.modwoc`

, `mu.varknown`

, `mu.freq`

, `mudiff.mblacc`

, `mudiff.mblalc`

, `mudiff.mblmodwoc`

, `mudiff.mblacc.equalvar`

, `mudiff.mblalc.equalvar`

, `mudiff.mblmodwoc.equalvar`

, `mudiff.mbl.varknown`

, `mudiff.acc`

, `mudiff.alc`

, `mudiff.modwoc`

, `mudiff.acc.equalvar`

, `mudiff.alc.equalvar`

, `mudiff.modwoc.equalvar`

, `mudiff.varknown`

, `mudiff.freq`

1 | ```
mu.mblmodwoc(len=0.2, alpha=2, beta=2)
``` |

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