normmixp {Bolstad} | R Documentation |

## Bayesian inference on a normal mean with a mixture of normal priors

### Description

Evaluates and plots the posterior density for `\mu`

, the mean of a
normal distribution, with a mixture of normal priors on `\mu`

### Usage

```
normmixp(
x,
sigma.x,
prior0,
prior1,
p = 0.5,
mu = NULL,
n.mu = max(100, length(mu)),
...
)
```

### Arguments

`x` |
a vector of observations from a normal distribution with unknown mean and known std. deviation. |

`sigma.x` |
the population std. deviation of the observations. |

`prior0` |
the vector of length 2 which contains the means and standard deviation of your precise prior. |

`prior1` |
the vector of length 2 which contains the means and standard deviation of your vague prior. |

`p` |
the mixing proportion for the two component normal priors. |

`mu` |
a vector of prior possibilities for the mean. If it is |

`n.mu` |
the number of possible |

`...` |
additional arguments that are passed to |

### Value

A list will be returned with the following components:

`mu` |
the
vector of possible |

`prior` |
the
associated probability mass for the values in |

`likelihood` |
the scaled likelihood function for |

`posterior` |
the posterior
probability of |

### See Also

### Examples

```
## generate a sample of 20 observations from a N(-0.5, 1) population
x = rnorm(20, -0.5, 1)
## find the posterior density with a N(0, 1) prior on mu - a 50:50 mix of
## two N(0, 1) densities
normmixp(x, 1, c(0, 1), c(0, 1))
## find the posterior density with 50:50 mix of a N(0.5, 3) prior and a
## N(0, 1) prior on mu
normmixp(x, 1, c(0.5, 3), c(0, 1))
## Find the posterior density for mu, given a random sample of 4
## observations from N(mu, 1), y = [2.99, 5.56, 2.83, 3.47],
## and a 80:20 mix of a N(3, 2) prior and a N(0, 100) prior for mu
x = c(2.99, 5.56, 2.83, 3.47)
normmixp(x, 1, c(3, 2), c(0, 100), 0.8)
```

*Bolstad*version 0.2-41 Index]