View source: R/SpecPrior-generators.R
HalfT | R Documentation |
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.
HalfT(df = 7, scale = NULL, max = NULL, mult = 1)
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 |
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} .
|
Object of class HalfT
.
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.
Error
, Exch
, Exch
HalfT()
HalfT(scale = 0.5)
HalfT(df = 1, scale = 10)
HalfT(scale = 0.5, max = 4)
HalfT(mult = 0.5)
HalfT(mult = 2)
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