Add a non-informative component to a mixture prior.
1 2 3 4 5 6 7 8 9 10
orior (mixture of conjugate distributions).
weight given to the non-informative component (0 <
mean of the non-informative component. It is recommended to set this parameter explicitly.
number of observations the non-informative prior corresponds to, defaults to 1.
optional arguments are ignored.
Sampling standard deviation for the case of Normal mixtures.
It is recommended to robustify informative priors derived
gMAP using unit-information priors . This
protects against prior-data conflict, see for example
Schmidli et al., 2015.
The procedure can be used with beta, gamma and normal mixture
priors. A unit-information prior (see Kass and Wasserman,
1995) corresponds to a prior which represents the observation of
n=1 at the null hypothesis. As the null is problem dependent we
strongly recommend to make use of the
accordingly. See below for the definition of the default mean.
The weights of the mixture priors are rescaled to
while the non-informative prior is assigned the
New mixture with an extra non-informative component named
betaMix: The default
mean is set to 1/2 which
represents no difference between the occurrence rates for one of the
two outcomes. As the uniform
Beta(1,1) is more appropriate in
n+1 as the sample
size such that the default robust prior is the uniform instead of
Beta(1/2,1/2) which strictly defined would be the unit
information prior in this case.
gammaMix: The default
mean is set to the mean of the
prior mixture. It is strongly recommended to explicitly set the
mean to the location of the null hypothesis.
normMix: The default
mean is set to the mean
of the prior mixture. It is strongly recommended to explicitly set
the mean to the location of the null hypothesis, which is very
often equal to 0. It is also recommended to explicitly set the
sampling standard deviation using the
Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics 2014;70(4):1023-1032.
Kass RE, Wasserman L A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion J Amer Statist Assoc 1995; 90(431):928-934.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
bmix <- mixbeta(inf1=c(0.2, 8, 3), inf2=c(0.8, 10, 2)) plot(bmix) rbmix <- robustify(bmix, weight=0.1, mean=0.5) rbmix plot(rbmix) gmnMix <- mixgamma(inf1=c(0.2, 2, 3), inf2=c(0.8, 2, 5), param="mn") plot(gmnMix) rgmnMix <- robustify(gmnMix, weight=0.1, mean=2) rgmnMix plot(rgmnMix) nm <- mixnorm(inf1=c(0.2, 0.5, 0.7), inf2=c(0.8, 2, 1), sigma=2) plot(nm) rnMix <- robustify(nm, weight=0.1, mean=0, sigma=2) rnMix plot(rnMix)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.