# iact: Integrated Auto correlation times of a Markov Chain In dirmcmc: Directional Metropolis Hastings Algorithm

## Description

This function calculates the Integrated Auto Correlation Times of a Markov Chain.

## Usage

 `1` ```iact(x) ```

## Arguments

 `x` chain (one dimension)

## Details

The Integrated Auto Correlation Times of a Markov Chain X is defined as:

1 + 2 ∑ Γ_i

, where

Γ

indicates the estimated autocorrelation terms of the chain. These are estimated using the sample correlation matrix from the lagged chain. This measure is intended for one dimensional chains or single component of a multivariate chains.

## Value

Integrated ACT of the chain.

## Author(s)

Abhirup Mallik, malli066@umn.edu

`msjd` for mean squared jumping distance, `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) iact(out.metdir.banana\$batch[,1]) ## End(Not run) ```