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

Uses a beta prior on the probability of success for a binomial distribution, determines a two-sided confidence interval from a beta posterior. A plotting function is also provided to show the probability regions defined by each confidence interval.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
binom.bayes(x, n,
conf.level = 0.95,
type = c("highest", "central"),
prior.shape1 = 0.5,
prior.shape2 = 0.5,
tol = .Machine$double.eps^0.5,
maxit = 1000, ...)
binom.bayes.densityplot(bayes,
npoints = 500,
fill.central = "lightgray",
fill.lower = "steelblue",
fill.upper = fill.lower,
alpha = 0.8, ...)
``` |

`x` |
Vector of number of successes in the binomial experiment. |

`n` |
Vector of number of independent trials in the binomial experiment. |

`conf.level` |
The level of confidence to be used in the confidence interval. |

`type` |
The type of confidence interval (see Details). |

`prior.shape1` |
The value of the first shape parameter to be used in the prior beta. |

`prior.shape2` |
The value of the second shape parameter to be used in the prior beta. |

`tol` |
A tolerance to be used in determining the highest probability density interval. |

`maxit` |
Maximum number of iterations to be used in determining the highest probability interval. |

`bayes` |
The output |

`npoints` |
The number of points to use to draw the density curves. Higher numbers give smoother densities. |

`fill.central` |
The color for the central density. |

`fill.lower,fill.upper` |
The color(s) for the upper and lower density. |

`alpha` |
The alpha value for controlling transparency. |

`...` |
Ignored. |

Using the conjugate beta prior on the distribution of p (the probability of success) in a binomial experiment, constructs a confidence interval from the beta posterior. From Bayes theorem the posterior distribution of p given the data x is:

`p|x ~ Beta(x + prior.shape1, n - x + prior.shape2)`

The default prior is Jeffrey's prior which is a Beta(0.5, 0.5)
distribution. Thus the posterior mean is `(x + 0.5)/(n + 1)`

.

The default type of interval constructed is "highest" which computes the highest probability density (hpd) interval which assures the shortest interval possible. The hpd intervals will achieve a probability that is within tol of the specified conf.level. Setting type to "central" constructs intervals that have equal tail probabilities.

If 0 or n successes are observed, a one-sided confidence interval is returned.

For `binom.bayes`

, a `data.frame`

containing the observed
proportions and the lower and upper bounds of the confidence interval.

For `binom.bayes.densityplot`

, a `ggplot`

object that can
printed to a graphics device, or have additional layers added.

Sundar Dorai-Raj ([email protected])

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1997)
*Bayesian Data Analysis*, London, U.K.: Chapman and Hall.

`binom.confint`

, `binom.cloglog`

,
`binom.logit`

, `binom.probit`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
# Example using highest probability density.
hpd <- binom.bayes(
x = 0:10, n = 10, type = "highest", conf.level = 0.8, tol = 1e-9)
print(hpd)
binom.bayes.densityplot(hpd)
# Remove the extremes from the plot since they make things hard
# to see.
binom.bayes.densityplot(hpd[hpd$x != 0 & hpd$x != 10, ])
# Example using central probability.
central <- binom.bayes(
x = 0:10, n = 10, type = "central", conf.level = 0.8, tol = 1e-9)
print(central)
binom.bayes.densityplot(central)
# Remove the extremes from the plot since they make things hard
# to see.
binom.bayes.densityplot(central[central$x != 0 & central$x != 10, ])
``` |

binom documentation built on May 29, 2017, 2:26 p.m.

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