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I understand the strength of the Prior is set via parameter nu however, I can not find information what nu expresses in statistical terms, e.g. how strong would a prior that is similar to the number of variables x be in this example?

#Inverse Wishart (multivariate, variables=x)

    prior.miw<-list(R=list(V=diag(x), nu=x),G=list(G1=list(V=diag(x),
nu=x)))

I also saw a lot of examples for weak priors with nu=0.01, does it mean we have a 1/100 degree of believe in the prior compared to the posterior?

Tim M. Schendzielorz
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  • This is a statistical issue, you would be better off asking on the cross validated stack exchange – rg255 May 03 '20 at 12:06
  • Thanks for commenting, I also raised this question on Cross Validated. https://stats.stackexchange.com/questions/464461/for-prior-definition-in-bayesian-regression-with-r-package-mcmcglmm-how-to-conv . I still let it up here as ther question is specific for an R package. – Tim M. Schendzielorz May 04 '20 at 14:41
  • Ok, although it's in relation to a package it's really a stats question. This is my rough and basic explanation from my experience. Bayes theorem says that we can work out the probability of a distribution given the data, P(theta|data), as (P(data|theta) × P(theta)) / P(data), where P(theta) is the prior distribution. For a gaussian distribution, that prior has two properties - mu (the mean, or central tendency) and sigma (standard deviation, or spread). For a gaussian prior then, the certainty we place on the mean of the prior, or belief, is determined by sigma. – rg255 May 06 '20 at 09:08
  • @rg255 thanks for your comment. How does the sd sigma relate then to the parameter nu? It expresses somehow the strength of your prior in MCMCglmm, but opposite to sigma, the bigger nu, the stronger the belief. – Tim M. Schendzielorz May 07 '20 at 11:31

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