# msjd: Mean Squared Jump Distance of a Markov Chain In dirmcmc: Directional Metropolis Hastings Algorithm

## Description

We calculate mean square euclidean jumping distance. The target covariance is unknown and the assumption of elliptical contour might not hold here, hence, we dont implement the variance scaled version. And this version is computationally faster as well.

## Usage

 `1` ```msjd(X) ```

## Arguments

 `X` chain (Matrix) (in d dim)

## Details

Mean squared jump distance of a markov chain is a measure used to diagnose the mixing of the chain. It is calculated as the mean of the squared eucledean distance between every point and its previous point. Usually, this quantity indicates if the chain is moving enough or getting stuck at some region.

## Value

Mean squared jump distance of the chain.

## Author(s)

Abhirup Mallik, malli066@umn.edu

`iact` for integrated auto correlation times, `mcmcdiag` for summary of diagnostic measures of a chain, `multiESS` for Multivariate effective sample size.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## Not run: ## Banana Target lupost.banana <- function(x,B){ -x[1]^2/200 - 1/2*(x[2]+B*x[1]^2-100*B)^2 } Banana Gradient gr.banana <- function(x,B){ g1 <- -x[1]/100 - 2*B*(x[2]+B*x[1]^2-100*B) g2 <- -(x[2]+B*x[1]^2-100*B) g <- c(g1,g2) return(g) } out.metdir.banana <- metropdir(obj = lupost.banana, dobj = gr.banana, initial = c(0,1),lchain = 2000, sd.prop=1.25, steplen=0.01,s=1.5,B=0.03) msjd(out.metdir.banana\$batch) ## End(Not run) ```