Define a probability matrix by columns does not work well

[SergioMarreroMarrero]

When the transition probability matrix is defined by columns (each column sums one) aparently works well, but it does not interpret correctly the "recurrent class", "transient class". In fact , it interprets the "recurrent classes" as "transient classes" and vice versa.

[spedygiorgio]

Hi, could you please provide a reproducible example? Best

[SergioMarreroMarrero]

Hi, let the example of Gambler Ruin provided in the vignette. I modified the function you provided for generate this problem in such a way you can define how you want the vector probabilities (by row or by column):

gamblerRuinMarkovChain <- function(moneyMax = 10, prob = 0.5, byRow = TRUE){
  
  require(matlab)
  matr <- zeros(moneyMax + 1)
  states <- as.character(seq(from = 0, to = moneyMax, by = 1))
  rownames(matr) = states; colnames(matr) = states
  matr[1, 1] = 1; matr[moneyMax + 1, moneyMax +1] = 1
  
  for (i in 2:moneyMax) {matr[i, i - 1] = 1 - prob; matr[i, i + 1] = prob}
  
  
  
  if (byRow) {
  
    out <- new("markovchain",
               transitionMatrix = matr, byrow = byRow,
               name = paste("Gambler ruin", moneyMax, "dim", sep = " "))
  }else {
    
    out <- new("markovchain",
               transitionMatrix = t(matr), byrow = byRow,
               name = paste("Gambler ruin", moneyMax, "dim", sep = " "))
    
  }
    
  return(out)

}

## Run the function:
P_byRow <- gamblerRuinMarkovChain(byRow = TRUE)
## 1) Look what is inside P_byRow. 
P_byRow. 
## 2) Look at: summary(P_byRow)
summary(P_byRow)

P_byCol <- gamblerRuinMarkovChain(byRow = FALSE)
## 3) Look what is inside P_byCol.  At this point everything looks good!!
P_byCol
## 4) Look at: summary(P_byCol ). 
summary(P_byCol ) ## This does not look good.   The classes are exchanged !!

I hope my answer be enough.

Best !

Sergio

[spedygiorgio]

I will have a look by the end of the month. Best