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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