LN_MeanReg {BayesLN} | R Documentation |

## Bayesian Estimate of the conditional Log-normal Mean

### Description

This function produces a bayesian estimate of the conditional log-normal mean assuming a GIG prior for the variance and an improper prior for the regression coefficients of the linear regression in the log scale.

### Usage

```
LN_MeanReg(
y,
X,
Xtilde,
method = "weak_inf",
y_transf = TRUE,
h = NULL,
CI = TRUE,
alpha_CI = 0.05,
type_CI = "two-sided",
nrep = 1e+05
)
```

### Arguments

`y` |
Vector of observations of the response variable. |

`X` |
Design matrix. |

`Xtilde` |
Matrix of covariate patterns for which an estimate is required. |

`method` |
String that indicates the prior setting to adopt. Choosing |

`y_transf` |
Logical. If |

`h` |
Leverage. With the default option |

`CI` |
Logical. With the default choice |

`alpha_CI` |
Level of alpha that determines the credibility (1- |

`type_CI` |
String that indicates the type of interval to compute: |

`nrep` |
Number of simulations. |

### Details

In this function the same procedure as LN_Mean is implemented allowing for the inclusion of covariates.
Bayesian point and interval estimates for the response variabile in the original scale are provided considering the model:
`log(y_i)=X\beta`

.

### Value

The function returns a list including the prior and posterior parameters, the point estimate of the log-normal mean conditioned with respect to the covariate
points included in `Xtilde`

. It consists of the mean of the posterior
distribution for the functional `\exp\{\tilde{x}_i^T\beta+\sigma^2/2\}`

and the posterior variance.

### Source

Fabrizi, E., & Trivisano, C. *Bayesian Conditional Mean Estimation in Log-Normal Linear Regression Models with Finite
Quadratic Expected Loss.* Scandinavian Journal of Statistics, 43(4), 1064-1077. (2016).

### Examples

```
library(BayesLN)
data("fatigue")
# Design matrices
Xtot <- cbind(1, log(fatigue$stress), log(fatigue$stress)^2)
X <- Xtot[-c(1,13,22),]
y <- fatigue$cycle[-c(1,13,22)]
Xtilde <- Xtot[c(1,13,22),]
#Estimation
LN_MeanReg(y = y,
X = X, Xtilde = Xtilde,
method = "weak_inf", y_transf = FALSE)
```

*BayesLN*version 0.2.10 Index]