# [R] HMM Package parameter estimation

Rolf Turner rolf.turner at xtra.co.nz
Tue Apr 16 11:53:59 CEST 2013

```I think it's your starting values for the initial state probability
distribution,
i.e. c(1,1,1)/3 that cause the problem.  They seem to drop you into some
sort of local maximum/stationary point, a long way from the global maximum.

Try, e.g. c(4,2,1)/7; this gives me:

hmmFit\$hmm\$emissionProbs
symbols
states         1          2
1 0.9385018 0.06149819
2 0.7883591 0.21164092
3 0.2279287 0.77207131

hmmFit\$hmm\$transProbs
to
from         1         2         3
1 0.6925055 0.1239590 0.1835355
2 0.2537700 0.5780679 0.1681621
3 0.2455462 0.1190872 0.6353666

which look to be in "reasonable" agreement with the "true" values.
Note though that states 2 and 3 have been swapped.  This happens.

cheers,

Rolf Turner

On 16/04/13 13:13, Richard Philip wrote:
> Hi,
>
> I am having difficulties estimating the parameters of a HMM using the HMM
> package. I have simulated a sequence of observations from a known HMM. When
> I estimate the parameters of a HMM using these simulated observations the
> parameters are not at all close to the known ones. I realise the estimated
> parameters are not going to be exactly the same as the known/true
> parameters, but these are nowhere close. Below is my code used. Any ideas
> or possible suggestions regarding this issue would be greatly appreciated?
>
>
> library(HMM)
>
> ## DECLARE PARAMETERS OF THE KNOWN MODEL
> states = c(1,2,3)
> symbols = c(1,2)
> startProb = c(0.5,0.25,0.25)
> transProb = matrix(c(0.8,0.05,0.15,0.2,0.6,0.2,0.2,0.3,0.5),3,3,TRUE)
> emissionProb =  matrix(c(0.9,0.1,0.2,0.8,0.7,0.3), 3,2,TRUE)
>
> # CREATE THE KNOWN MODEL
> hmmTrue = initHMM(states, symbols, startProb, transProb , emissionProb)
>
> # SIMULATE 1000 OBSERVATIONS OF THE KNOWN MODEL
> observation = simHMM(hmmTrue, 1000)
> obs = observation\$observation
>
> #ESTIMATE A MODEL USING THE OBSERVATIONS GENERATED FROM THE KNOWN MODEL
> hmmInit = initHMM(states, symbols, c(1/3,1/3,1/3))
> hmmFit = baumWelch(hmmInit, obs)
>
>
> #The parameters of hmmTrue and hmmFit are not at all alike, why is this?

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