The value of stateProbs() and getTrProbs() functions can't match with each other?

[xjtusjtu]

Hi Brett,

fitHaggis <- fitHMM(data = processedHaggis, nbStates = 2,
                    dist = list(step = "gamma", angle = "vm"),
                    Par0 = list(step = stepPar0, angle = anglePar0),
                    formula = ~ slope + I(slope^2),
                    estAngleMean = list(angle = TRUE))

Based on the code provided in "Guide to using momentuHMM.pdf - 2.2 HMM specification and fitting," I obtained the fitted model fitHaggis. Subsequently, I executed the stateProbs() and getTrProbs() functions. The results include the probability of the process being in different states at each time point and the transition probability matrix for each time step, as follows:

> sp <- stateProbs(fitHaggis)
> trProbs <- getTrProbs(fitHaggis)
> sp[1:5,]
          state 1      state 2
[1,] 7.191524e-01 2.808476e-01
[2,] 2.174842e-06 9.999978e-01
[3,] 1.141769e-01 8.858231e-01
[4,] 8.933096e-01 1.066904e-01
[5,] 1.000000e+00 4.473818e-08
> trProbs[,,1:5]
, , 1

           state 1   state 2
state 1 0.76818444 0.2318156
state 2 0.05158681 0.9484132

, , 2

           state 1   state 2
state 1 0.61340077 0.3865992
state 2 0.03605583 0.9639442

, , 3

           state 1   state 2
state 1 0.60749200 0.3925080
state 2 0.03961385 0.9603862

, , 4

          state 1   state 2
state 1 0.7311696 0.2688304
state 2 0.1072474 0.8927526

, , 5

          state 1   state 2
state 1 0.8384870 0.1615130
state 2 0.2341643 0.7658357

> sp[1,] %*% trProbs[,,1]
       state 1   state 2
[1,] 0.5669297 0.4330703
> sp[1,] %*% trProbs[,,2]
       state 1   state 2
[1,] 0.4512548 0.5487452

What confuses me is that sp[1,] %*% trProbs[,,1] is not equal to sp[2,]. Even if my indexing is incorrect, sp[1,] %*% trProbs[,,2] is also not equal to sp[2,].

If you know the reason for this, could you please enlighten me? Thank you very much!

[xjtusjtu]

The same issue arises where sp[3,] %*% trProbs[,,3] is not equal to sp[4,] and sp[3,] %*% trProbs[,,4] is not equal to sp[4,]. If there's any insight into why this is happening, I would greatly appreciate your explanation.

[xjtusjtu]

If I replace fitHaggis with example$m, the issue still persists.

m <- example$m
sp <- stateProbs(m)
trProbs <- getTrProbs(m)
sp[1:5,]
trProbs[,,1:5]
sp[1,] %*% trProbs[,,1]
sp[1,] %*% trProbs[,,2]

[bmcclintock]

Unless I'm missing something, the simple answer is that they shouldn't be equal. You should be able to verify this by examining the definitions/derivations of the state probabilities (i.e. "local" decoding based on the forward-backward algorithm) and the state transition probabilities in Zucchini et al. 2016 (or see this tutorial for abbreviated versions).

[xjtusjtu]

Thank you very much, brett. I'll read the material carefully!