HalfT {demest} | R Documentation

## Specify a half-t distribution.

### Description

If `x` has a t distribution, then `abs(x)` has a half-t distribution, also known as a folder t distribution. In package demest, most standard deviation or scale parameters have half-t priors.

### Usage

    HalfT(df = 7, scale = NULL, max = NULL, mult = 1)

### Arguments

`df` | Degrees of freedom of the half-t distribution. A positive number, defaulting to 7
`scale` | Scale parameter for the half-t distribution. A positive number.
`max` | A positive number. If finite, the half-t distribution is truncated at this point.
`mult` | Multiplier applied to `scale` if `scale` is generated automatically. Defaults to 1.

### Details

A half-t distribution with degrees of freedom n and scale A has density

p(y) \propto ((y^2)/n + A^2)^(-(n+1)/2).

Setting a maximum value that the standard deviation or scale parameter can take (and so specifying a truncated half-t distribution) can reduce numerical problems, and dramatically improve convergence. By default, the maximum value is set to the 0.999 quantile.Users can specify alternative values, including infinity.

`HalfT` is typically used to specify the prior for a main effect or interaction. In this case, if a value for `scale` is not specified, a default value is determined when function `estimateModel`, `estimateCounts`, or `estimateAccount` is called. Let s be the standard deviation of data y, or of `log(y)` in the case of a Poisson model without exposure. Let d be the degree of an interaction: for instance, an interaction between age and sex has degree 2, and an interaction between age, sex, and region has degree 3. Let m be the `mult` argument. The default value for `scale` is then

Model | Term | Default
Poisson with exposure | Main effect | m
Poisson with exposure | Interaction of degree d | m 0.5^{d-1}
Poisson without exposure | Main effect \ ms
Poisson without exposure | Interaction of degree d | ms 0.5^{d-1}
binomial | Main effect | m
binomial | Interaction of degree d | m 0.5^{d-1}
normal | Main effect | ms
normal | Interaction of degree d | ms 0.5^{d-1}.

### Value

Object of class `HalfT`.

### References

Brazauskas, V., and Kleefeld, A. (2011) Folded and log-folded-t distributions as models for insurance loss data. Scandinavian Actuarial Journal 59-74.

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis 1, 515-534.

Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B., 2014. Bayesian Ddata Analysis. Third Edition. Boca Raton, FL, USA: Chapman & Hall/CRC. Section 16.3.

### See Also

`Error`, `Exch`, `Exch`

### Examples

    HalfT()
    HalfT(scale = 0.5)
    HalfT(df = 1, scale = 10)
    HalfT(scale = 0.5, max = 4)
    HalfT(mult = 0.5)
    HalfT(mult = 2)

[Package demest version 0.0.0.3.1 Index]