LN_Mean {BayesLN} R Documentation

## Bayesian Estimate of the Log-normal Mean

### Description

This function produces a Bayesian estimate of the log-normal mean, assuming a GIG prior for the variance and an improper flat prior for the mean in the log scale.

### Usage

```LN_Mean(
x,
method = "weak_inf",
x_transf = TRUE,
CI = TRUE,
alpha_CI = 0.05,
type_CI = "two-sided",
nrep = 1e+05
)
```

### Arguments

 `x` Vector containing the sample. `method` String that indicates the prior setting to adopt. Choosing `"weak_inf"` a weakly informative prior setting is adopted, whereas selecting `"optimal"` the hyperparameters are aimed at minimizing the frequentist MSE. `x_transf` Logical. If `TRUE`, the `x` vector is assumed already log-transformed. `CI` Logical. With the default choice `TRUE`, the posterior credibility interval is computed. `alpha_CI` Level of alpha that determines the credibility (1-`alpha_CI`) of the posterior interval. `type_CI` String that indicates the type of interval to compute: `"two-sided"` (default), `"UCL"` (i.e. Upper Credible Limit) for upper one-sided intervals or `"LCL"` (i.e. Lower Credible Limit) for lower one-sided intervals. `nrep` Number of simulations for the computation of the credible intervals.

### Details

Summarizing the posterior mean of the log-normal expectation might be delicate since several common priors used for the variance do not produces posteriors with finite moments. The proposal by Fabrizi and Trivisano (2012) of adopting a generalized inverse Gaussian (GIG) prior for the variance in the log scale σ^2 has been implemented. Moreover, they discussed how to specify the hyperparameters according to two different aims.

Firstly, a weakly informative prior allowed to produce posterior credible intervals with good frequentist properties, whereas a prior aimed at minimizing the point estimator MSE was proposed too. The choice between the two priors can be made through the argument `method`.

The point estimates are exact values, whereas the credible intervals are provided through simulations from the posterior distribution.

### Value

The function returns a list which includes the prior and posterior parameters, the point estimate of the log-normal mean that consists in the mean of the posterior distribution of the functional \exp\{μ+σ^2/2\} and the posterior variance.

### Source

Fabrizi, E., & Trivisano, C. Bayesian estimation of log-normal means with finite quadratic expected loss. Bayesian Analysis, 7(4), 975-996. (2012).

### Examples

```# Load data
data("NCBC")
# Optimal point estimator
LN_Mean(x = NCBC\$al, x_transf = FALSE, method = "optimal", CI = FALSE)
# Weakly informative prior and interval estimation
LN_Mean(x = NCBC\$al, x_transf = FALSE, type_CI = "UCL")

```

[Package BayesLN version 0.2.2 Index]