MCMCglmm multivariate with multiple residuals

I am trying to extend a univariate model to a multivariate one within MCMCglmm. Multiple (some correlated) traits were assessed for a number of individuals whose mothers are known (i.e. we know half sib families). There is replication of the families (not the individuals), however due to processing constraints, some replicates everything was taken, and … Read more

In Metropolis Algorithm, if draws $\theta^{t-1}$ and $\theta^t$ have the same marginals, why is the target is the same as the stationary distribution?

In the Metropolis algorithm, suppose I start my algorithm at time $t-1$ with a draw $\theta^{t-1}$ from my target distribution $p(\theta|y)$. It can be shown that $\theta^t$ and $\theta^{t-1}$ are symmetric in that $$P(\theta^t = \theta_a, \theta^{t-1} = \theta_b) = P(\theta^{t-1} = \theta_a, \theta^{t} = \theta_b)$$ Based on this, it is written in … Read more

comparing multivariate posteriors

Do there exist standard methods for summarizing high-dimensional multivariate posteriors, in particular to determine how much overlap exists between two separately estimated posteriors? The R package ‘ks’ provides functionality for kernel smooths in up to 6 dimensions. In a different context (designed for summarizing multivariate niche space in ecology), the R package ‘hypervolume’ has some … Read more

Metropolis Hastings: What motivates the use of Metropolis-Hastings?

I am confused with metropolis hastings. This is a simple question. In the metropolis hastings, it is assumed that we know the un-normalised posterior, π(x). We can obtain the density by normalising π(x). No doubt, if you have a closed-form expression of π(x), this can be difficult because you still evaluate the integral ∫π(x). If … Read more

Numerical methods for one-dimensional Bayesian inference

I am doing inference using a Bayesian model that has only one variable, which boils down to computing a (one-dimensional) cumulative distribution and a quantile function given the log of a probability density function. This is much simpler than the usual multivariate setting, so I would like to have a very fast (order of milliseconds) … Read more

Proposal distribution on a pair of ordered continous parameters

I’d like to sample a pair of continuous parameters which has the constraint that one has to be smaller than the other one. I understand one approach is by rejection sampling by rejecting the samples that are violating this constraint. Another way would be propose a pair of parameters using a 2D Gaussian distribution that … Read more

Designing better Metropolis-Hastings proposal distributions (for correlated parameters)

Question: Is there a rule of thumb for setting a non-diagonal covariance matrix for your Metropolis-Hastings proposal distribution? References are appreciated. Background: Say I have some posterior distribution I am interested in obtaining samples from p(θ|y). I choose an initial proposal distribution for a Metropolis-Hastings algorithm. It is q(θ∗|θ)=N(θ∗;θ,diag[σ21,…,σ2p]). Notice that the covariance matrix is … Read more

Effective Sample Size for posterior inference from MCMC sampling

When obtaining MCMC samples to make inference on a particular parameter, what are good guides for the minimum number of effective samples that one should aim for? And, does this advice change as the model becomes more or less complex? Answer The question you are asking is different from “convergence diagnostics”. Lets say you have … Read more

Parameters’ value for weakly informative normal inverse wishart prior

What should one take as parameters for a normal inverse Wishart prior to be weakly informative? Is there a standard? Thank you Answer AttributionSource : Link , Question Author : Lisoo , Answer Author : Community

Bimodal posterior distribution

Do you know in which situations is it possible to have a bimodal posterior distribution for some parameters? I couldn’t find any information on the web. Thanks for your help. Answer AttributionSource : Link , Question Author : Prunus avium , Answer Author : Community