sp: Calculate the conditional state probabilities.

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/sp.R

Description

Returns the probabilities that the underlying hidden state is equal to each of the possible state values, at each time point, given the observation sequence. Also can return the fitted conditional means, if requested, given that the observations are numeric.

Usage

1
sp(y, object = NULL, tpm, Rho, ispd=NULL, means = FALSE)

Arguments

y

The observations on the basis of which the probabilities of the underlying hidden states are to be calculated. May be a sequence of observations, or a list each component of which constitutes a (replicate) sequence of observations. If y is missing it is set equal to the y component of object, given that that object and that component exist. Otherwise an error is given.

object

An object of class hmm.discnp as returned by hmm().

tpm

The transition probability matrix for the underlying hidden Markov chain. Ignored if object is not NULL. Ignored if object is not NULL (in which case tpm is extracted from object).

Rho

The matrix of probabilities specifying the distribution of the observations, given the underlying state. The rows of this matrix correspond to the possible values of the observations, the columns to the states. Ignored if object is not NULL (in which case Rho is extracted from object).

ispd

Vector specifying the initial state probability distribution of the underlying hidden Markov chain. Ignored if object is not NULL (in which case ispd is extracted from object). If both object and ispd are NULL then ispd is calculated to be the stationary distribution of the chain as determined by tpm.

means

A logical scalar; if means is TRUE then the conditional expected value of the observations (given the observation sequence) is calculated at each time point. If means is TRUE and the observation values are not numeric, then an error is given.

Details

Then conditional mean value at time t is calculated as

SUM_k gamma_t(k)*mu_k

where gamma_t(k) is the conditional probability (given the observations) that the hidden Markov chain is in state k at time t, and mu_k is the expected value of an observation given that the chain is in state k.

Value

If means is TRUE then the returned value is a list with components

probs

The conditional probabilities of the states at each time point.

means

The conditional expectations of the observations at each time point.

Otherwise the returned value consists of probs as described above.

If there is a single vector of observations y then probs is a matrix whose rows correspond to the states of the hidden Markov chain, and whose columns correspond to the observation times. If the observations consist of a list of observation vectors, then probs is a list of such matrices, one for each vector of observations.

Likewise for the means component of the list returned when the argument means is TRUE.

Author(s)

Rolf Turner [email protected]

See Also

hmm(), mps(), viterbi(), pr(), fitted.hmm.discnp()

Examples

1
2
3
4
5
6
7
8
P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE)
R <- matrix(c(0.5,0,0.1,0.1,0.3,
              0.1,0.1,0,0.3,0.5),5,2)
set.seed(42)
y.num   <- sim.hmm(rep(300,20),P,R)
fit.num <- hmm(y.num,K=2,verb=TRUE)
cpe1    <- sp(object=fit.num,means=TRUE)    # Using the estimated parameters.
cpe2    <- sp(y.num,tpm=P,Rho=R,means=TRUE) # Using the ``true'' parameters.

Example output

hmm.discnp 0.2-4

     PLEASE NOTE:  The package has changed substantially 
     from the 0.0-x versions.  New functions have been 
     added and both the argument lists and the returned 
     values from old functions have new forms.  Please 
     read the ChangeLog and the documentation.


      Initial set-up completed ...

Repeating ...

EM step 1:
     Log-likelihood: -7922.866
     Percent decrease in log-likelihood: 17.25897
     Root-SS of change in coef.: 0.340697
     Max. abs. change in coef.: 0.185699
EM step 2:
     Log-likelihood: -7917.113
     Percent decrease in log-likelihood: 0.072616
     Root-SS of change in coef.: 0.013783
     Max. abs. change in coef.: 0.008103
EM step 3:
     Log-likelihood: -7909.047
     Percent decrease in log-likelihood: 0.101882
     Root-SS of change in coef.: 0.016665
     Max. abs. change in coef.: 0.009646
EM step 4:
     Log-likelihood: -7898.733
     Percent decrease in log-likelihood: 0.130401
     Root-SS of change in coef.: 0.019277
     Max. abs. change in coef.: 0.010782
EM step 5:
     Log-likelihood: -7886.88
     Percent decrease in log-likelihood: 0.150066
     Root-SS of change in coef.: 0.021213
     Max. abs. change in coef.: 0.011464
EM step 6:
     Log-likelihood: -7874.711
     Percent decrease in log-likelihood: 0.154298
     Root-SS of change in coef.: 0.022131
     Max. abs. change in coef.: 0.012537
EM step 7:
     Log-likelihood: -7863.551
     Percent decrease in log-likelihood: 0.141708
     Root-SS of change in coef.: 0.021841
     Max. abs. change in coef.: 0.012981
EM step 8:
     Log-likelihood: -7854.365
     Percent decrease in log-likelihood: 0.116818
     Root-SS of change in coef.: 0.020382
     Max. abs. change in coef.: 0.012675
EM step 9:
     Log-likelihood: -7847.49
     Percent decrease in log-likelihood: 0.08753
     Root-SS of change in coef.: 0.018058
     Max. abs. change in coef.: 0.01169
EM step 10:
     Log-likelihood: -7842.7
     Percent decrease in log-likelihood: 0.061046
     Root-SS of change in coef.: 0.015343
     Max. abs. change in coef.: 0.010273
EM step 11:
     Log-likelihood: -7839.478
     Percent decrease in log-likelihood: 0.041087
     Root-SS of change in coef.: 0.012707
     Max. abs. change in coef.: 0.008723
EM step 12:
     Log-likelihood: -7837.289
     Percent decrease in log-likelihood: 0.027915
     Root-SS of change in coef.: 0.01047
     Max. abs. change in coef.: 0.007278
EM step 13:
     Log-likelihood: -7835.724
     Percent decrease in log-likelihood: 0.019977
     Root-SS of change in coef.: 0.008765
     Max. abs. change in coef.: 0.006068
EM step 14:
     Log-likelihood: -7834.514
     Percent decrease in log-likelihood: 0.01543
     Root-SS of change in coef.: 0.00757
     Max. abs. change in coef.: 0.005124
EM step 15:
     Log-likelihood: -7833.508
     Percent decrease in log-likelihood: 0.012846
     Root-SS of change in coef.: 0.006781
     Max. abs. change in coef.: 0.004422
EM step 16:
     Log-likelihood: -7832.621
     Percent decrease in log-likelihood: 0.011321
     Root-SS of change in coef.: 0.006273
     Max. abs. change in coef.: 0.003916
EM step 17:
     Log-likelihood: -7831.811
     Percent decrease in log-likelihood: 0.010342
     Root-SS of change in coef.: 0.005939
     Max. abs. change in coef.: 0.003557
EM step 18:
     Log-likelihood: -7831.056
     Percent decrease in log-likelihood: 0.009639
     Root-SS of change in coef.: 0.005707
     Max. abs. change in coef.: 0.003302
EM step 19:
     Log-likelihood: -7830.346
     Percent decrease in log-likelihood: 0.009075
     Root-SS of change in coef.: 0.00553
     Max. abs. change in coef.: 0.003118
EM step 20:
     Log-likelihood: -7829.674
     Percent decrease in log-likelihood: 0.008583
     Root-SS of change in coef.: 0.005381
     Max. abs. change in coef.: 0.002982
EM step 21:
     Log-likelihood: -7829.037
     Percent decrease in log-likelihood: 0.00813
     Root-SS of change in coef.: 0.005247
     Max. abs. change in coef.: 0.002877
EM step 22:
     Log-likelihood: -7828.434
     Percent decrease in log-likelihood: 0.007699
     Root-SS of change in coef.: 0.005118
     Max. abs. change in coef.: 0.002791
EM step 23:
     Log-likelihood: -7827.864
     Percent decrease in log-likelihood: 0.007281
     Root-SS of change in coef.: 0.00499
     Max. abs. change in coef.: 0.002716
EM step 24:
     Log-likelihood: -7827.326
     Percent decrease in log-likelihood: 0.006875
     Root-SS of change in coef.: 0.004861
     Max. abs. change in coef.: 0.002646
EM step 25:
     Log-likelihood: -7826.819
     Percent decrease in log-likelihood: 0.006479
     Root-SS of change in coef.: 0.00473
     Max. abs. change in coef.: 0.00258
EM step 26:
     Log-likelihood: -7826.342
     Percent decrease in log-likelihood: 0.006091
     Root-SS of change in coef.: 0.004596
     Max. abs. change in coef.: 0.002514
EM step 27:
     Log-likelihood: -7825.895
     Percent decrease in log-likelihood: 0.005714
     Root-SS of change in coef.: 0.00446
     Max. abs. change in coef.: 0.002447
EM step 28:
     Log-likelihood: -7825.476
     Percent decrease in log-likelihood: 0.005348
     Root-SS of change in coef.: 0.004322
     Max. abs. change in coef.: 0.00238
EM step 29:
     Log-likelihood: -7825.086
     Percent decrease in log-likelihood: 0.004993
     Root-SS of change in coef.: 0.004182
     Max. abs. change in coef.: 0.002311
EM step 30:
     Log-likelihood: -7824.722
     Percent decrease in log-likelihood: 0.00465
     Root-SS of change in coef.: 0.004041
     Max. abs. change in coef.: 0.00224
EM step 31:
     Log-likelihood: -7824.384
     Percent decrease in log-likelihood: 0.004321
     Root-SS of change in coef.: 0.003899
     Max. abs. change in coef.: 0.002169
EM step 32:
     Log-likelihood: -7824.07
     Percent decrease in log-likelihood: 0.004006
     Root-SS of change in coef.: 0.003757
     Max. abs. change in coef.: 0.002097
EM step 33:
     Log-likelihood: -7823.781
     Percent decrease in log-likelihood: 0.003705
     Root-SS of change in coef.: 0.003616
     Max. abs. change in coef.: 0.002024
EM step 34:
     Log-likelihood: -7823.513
     Percent decrease in log-likelihood: 0.00342
     Root-SS of change in coef.: 0.003476
     Max. abs. change in coef.: 0.001951
EM step 35:
     Log-likelihood: -7823.267
     Percent decrease in log-likelihood: 0.003149
     Root-SS of change in coef.: 0.003337
     Max. abs. change in coef.: 0.001877
EM step 36:
     Log-likelihood: -7823.04
     Percent decrease in log-likelihood: 0.002895
     Root-SS of change in coef.: 0.003201
     Max. abs. change in coef.: 0.001805
EM step 37:
     Log-likelihood: -7822.832
     Percent decrease in log-likelihood: 0.002656
     Root-SS of change in coef.: 0.003066
     Max. abs. change in coef.: 0.001732
EM step 38:
     Log-likelihood: -7822.642
     Percent decrease in log-likelihood: 0.002432
     Root-SS of change in coef.: 0.002935
     Max. abs. change in coef.: 0.001661
EM step 39:
     Log-likelihood: -7822.468
     Percent decrease in log-likelihood: 0.002224
     Root-SS of change in coef.: 0.002806
     Max. abs. change in coef.: 0.001591
EM step 40:
     Log-likelihood: -7822.309
     Percent decrease in log-likelihood: 0.00203
     Root-SS of change in coef.: 0.002681
     Max. abs. change in coef.: 0.001522
EM step 41:
     Log-likelihood: -7822.165
     Percent decrease in log-likelihood: 0.00185
     Root-SS of change in coef.: 0.002559
     Max. abs. change in coef.: 0.001455
EM step 42:
     Log-likelihood: -7822.033
     Percent decrease in log-likelihood: 0.001684
     Root-SS of change in coef.: 0.002441
     Max. abs. change in coef.: 0.001389
EM step 43:
     Log-likelihood: -7821.913
     Percent decrease in log-likelihood: 0.001531
     Root-SS of change in coef.: 0.002327
     Max. abs. change in coef.: 0.001326
EM step 44:
     Log-likelihood: -7821.804
     Percent decrease in log-likelihood: 0.001391
     Root-SS of change in coef.: 0.002216
     Max. abs. change in coef.: 0.001264
EM step 45:
     Log-likelihood: -7821.706
     Percent decrease in log-likelihood: 0.001262
     Root-SS of change in coef.: 0.00211
     Max. abs. change in coef.: 0.001205
EM step 46:
     Log-likelihood: -7821.616
     Percent decrease in log-likelihood: 0.001144
     Root-SS of change in coef.: 0.002007
     Max. abs. change in coef.: 0.001147
EM step 47:
     Log-likelihood: -7821.535
     Percent decrease in log-likelihood: 0.001036
     Root-SS of change in coef.: 0.001909
     Max. abs. change in coef.: 0.001092
EM step 48:
     Log-likelihood: -7821.462
     Percent decrease in log-likelihood: 0.000938
     Root-SS of change in coef.: 0.001814
     Max. abs. change in coef.: 0.001038
EM step 49:
     Log-likelihood: -7821.395
     Percent decrease in log-likelihood: 0.000849
     Root-SS of change in coef.: 0.001724
     Max. abs. change in coef.: 0.000987
EM step 50:
     Log-likelihood: -7821.335
     Percent decrease in log-likelihood: 0.000769
     Root-SS of change in coef.: 0.001638
     Max. abs. change in coef.: 0.000938
EM step 51:
     Log-likelihood: -7821.281
     Percent decrease in log-likelihood: 0.000695
     Root-SS of change in coef.: 0.001555
     Max. abs. change in coef.: 0.000891
EM step 52:
     Log-likelihood: -7821.232
     Percent decrease in log-likelihood: 0.000629
     Root-SS of change in coef.: 0.001476
     Max. abs. change in coef.: 0.000847
EM step 53:
     Log-likelihood: -7821.187
     Percent decrease in log-likelihood: 0.000569
     Root-SS of change in coef.: 0.001401
     Max. abs. change in coef.: 0.000804
EM step 54:
     Log-likelihood: -7821.147
     Percent decrease in log-likelihood: 0.000515
     Root-SS of change in coef.: 0.001329
     Max. abs. change in coef.: 0.000763
EM step 55:
     Log-likelihood: -7821.11
     Percent decrease in log-likelihood: 0.000466
     Root-SS of change in coef.: 0.001261
     Max. abs. change in coef.: 0.000724
EM step 56:
     Log-likelihood: -7821.077
     Percent decrease in log-likelihood: 0.000422
     Root-SS of change in coef.: 0.001196
     Max. abs. change in coef.: 0.000688
EM step 57:
     Log-likelihood: -7821.048
     Percent decrease in log-likelihood: 0.000382
     Root-SS of change in coef.: 0.001135
     Max. abs. change in coef.: 0.000652
EM step 58:
     Log-likelihood: -7821.021
     Percent decrease in log-likelihood: 0.000346
     Root-SS of change in coef.: 0.001076
     Max. abs. change in coef.: 0.000619
EM step 59:
     Log-likelihood: -7820.996
     Percent decrease in log-likelihood: 0.000314
     Root-SS of change in coef.: 0.001021
     Max. abs. change in coef.: 0.000587
EM step 60:
     Log-likelihood: -7820.974
     Percent decrease in log-likelihood: 0.000285
     Root-SS of change in coef.: 0.000969
     Max. abs. change in coef.: 0.000557
EM step 61:
     Log-likelihood: -7820.953
     Percent decrease in log-likelihood: 0.000259
     Root-SS of change in coef.: 0.000919
     Max. abs. change in coef.: 0.000529
EM step 62:
     Log-likelihood: -7820.935
     Percent decrease in log-likelihood: 0.000235
     Root-SS of change in coef.: 0.000872
     Max. abs. change in coef.: 0.000502
EM step 63:
     Log-likelihood: -7820.918
     Percent decrease in log-likelihood: 0.000214
     Root-SS of change in coef.: 0.000827
     Max. abs. change in coef.: 0.000476
EM step 64:
     Log-likelihood: -7820.903
     Percent decrease in log-likelihood: 0.000195
     Root-SS of change in coef.: 0.000785
     Max. abs. change in coef.: 0.000452
EM step 65:
     Log-likelihood: -7820.889
     Percent decrease in log-likelihood: 0.000178
     Root-SS of change in coef.: 0.000745
     Max. abs. change in coef.: 0.000429
EM step 66:
     Log-likelihood: -7820.877
     Percent decrease in log-likelihood: 0.000162
     Root-SS of change in coef.: 0.000707
     Max. abs. change in coef.: 0.000407
EM step 67:
     Log-likelihood: -7820.865
     Percent decrease in log-likelihood: 0.000148
     Root-SS of change in coef.: 0.000671
     Max. abs. change in coef.: 0.000386
EM step 68:
     Log-likelihood: -7820.854
     Percent decrease in log-likelihood: 0.000136
     Root-SS of change in coef.: 0.000637
     Max. abs. change in coef.: 0.000367
EM step 69:
     Log-likelihood: -7820.845
     Percent decrease in log-likelihood: 0.000124
     Root-SS of change in coef.: 0.000605
     Max. abs. change in coef.: 0.000349
EM step 70:
     Log-likelihood: -7820.836
     Percent decrease in log-likelihood: 0.000114
     Root-SS of change in coef.: 0.000575
     Max. abs. change in coef.: 0.000331
EM step 71:
     Log-likelihood: -7820.828
     Percent decrease in log-likelihood: 0.000105
     Root-SS of change in coef.: 0.000546
     Max. abs. change in coef.: 0.000314
EM step 72:
     Log-likelihood: -7820.82
     Percent decrease in log-likelihood: 9.6e-05
     Root-SS of change in coef.: 0.000519
     Max. abs. change in coef.: 0.000299
Warning message:
In check.yval(y, Rho) : Matrix "Rho" has no row names.  Assuming that the
 rows of Rho correspond to the sorted unique values of "y".

hmm.discnp documentation built on May 29, 2017, 12:28 p.m.

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