about HMM Evaluation question:

There are 3 methods to carry out HMM evaluation.

1) forward algorithm

2) backward algorithm

3) forward-backward algorithm

Sometimes, forward algorithm and backward algorithm may not give out the same result.

Can anybody (mathematician) help to explain it clearly?

I designed my data as: 2 hidden states, 3 observations, and the sequence if of length 4

1) initial state probability of state 1 and 2: 0.6, 0.4 sequentially

2) transition probability :

from state 1 to state 1: 0.7

from state 1 to state 2: 0.3

from state 2 to state 1: 0.4

from state 2 to state 2: 0.6

3) observation probability:

from state 1 to observation 1: 0.1

from state 1 to observation 2: 0.4

from state 1 to observation 3: 0.5

from state 2 to observation 1: 0.6

from state 2 to observation 2: 0.3

from state 2 to observation 3: 0.1

4) the observation sequence is known as: 0->1->2->

that is

observation 1 to observation 2 to observation 3 to observation 1

According to my implementation, forward algorithm got the probability as: 0.0090887999999999993

while backward algorithm got the probability as: 0.0090888000000000010

I'm wondering if this is the precision problem during the computation?

Or there are some other problems hidden in my wrong coding???

(Sorry that I didn't afford my coding at this moment,

I'm guessing Julius has its own HMM to have the above simple example computed)

The difference between two probabilities using my HMM looks like a precision issue,

but I'm just not certain about this.

Can anybody give a hand to confirm this?

Cheers

JIA