march.mc.bailey: Bailey Confidence Intervals for a Markov chain.
In march: Markov Chains

Description Usage Arguments Value Author(s) Examples

Compute the confidence intervals using Bailey's formula on a march.Mc object. See Bailey BJR (1980) Large sample simultaneous confidence intervals for the multinomial probabilities based ontransformation of the cell frequencies, Technometrics 22:583–589, for details.

1	march.mc.bailey(object, alpha)

`object`	the march.Model object on which compute the confidence intervals.
`alpha`	the significance level.

A list of half-length confidence intervals for each probability distribution of the Markov chain.

Berchtold André

# Compute the independence model for the pewee data.
Indep <- march.indep.construct(pewee)
# Display the model
print(Indep)
# Compute the half-length 95% confidence interval for each element of the distribution.
march.indep.bailey(Indep,alpha=0.05)

# Compute a second-order MTDg model for the pewee data.
MTD2g <- march.mtd.construct(pewee,2,mtdg=TRUE)
# Display the model
print(MTD2g)
# Compute the half-length 95% confidence interval for all parameters
# of the MTD2g model.
march.mtd.bailey(MTD2g,alpha=0.05)

Attaching package: ‘march’

The following object is masked from ‘package:datasets’:

    sleep

Independence

Probability distribution :
             1         2         3
[1,] 0.5207234 0.2690279 0.2102487

Frequency distribution :
       1   2   3
[1,] 691 357 279

Log-likelihood :  -1354.713 
Number of data :  1327 

CI for the independence model :
-------------------------------
Lower bound :                                  
[1,] 0.4871783 0.2400199 0.1837995

Upper bound :                                  
[1,] 0.5535219 0.2989918 0.2380544

MTDg(2)

High-order transition matrix : 
                 1          2           3
 1 1  : 0.77903206 0.14018681 0.080781136
 2 1  : 0.13930117 0.16671325 0.693985579
 3 1  : 0.05739149 0.86182737 0.080781136
 1 2  : 0.99217114 0.00000000 0.007828859
 2 2  : 0.35244025 0.02652644 0.621033302
 3 2  : 0.27053057 0.72164057 0.007828859
 1 3  : 0.98108026 0.01891974 0.000000000
 2 3  : 0.34134937 0.04544619 0.613204443
 3 3  : 0.25943969 0.74056031 0.000000000

Vector of weights : 
[1] 0.2783594 0.7216406

Transition matrix, lag 1 : 
          [,1]       [,2]      [,3]
[1,] 0.2061776 0.50361795 0.2902044
[2,] 0.9718750 0.00000000 0.0281250
[3,] 0.9320312 0.06796875 0.0000000

Transition matrix, lag 2 : 
          [,1]       [,2]      [,3]
[1,] 1.0000000 0.00000000 0.0000000
[2,] 0.1135048 0.03675853 0.8497367
[3,] 0.0000000 1.00000000 0.0000000

Log-likelihood :  -506.9897 
Number of data :  1325 

CI for the vector of weights :
------------------------------
Lower bound :
[1] 0.2508358 0.6927793

Upper bound :
[1] 0.3067313 0.7487037

CI for the transition matrix of lag 1 :
---------------------------------------
Lower bound :                                       
[1,] 0.0990426 0.5271286995 0.155463058
[2,] 0.8900302 0.0000000000 0.002526596
[3,] 0.8988861 0.0009018367 0.000000000

Upper bound :                                   
[1,] 0.2286619 0.69823106 0.3029479
[2,] 0.9946743 0.00000000 0.0977658
[3,] 0.9998680 0.08317881 0.0000000

CI for the transition matrix of lag 2 :
---------------------------------------
Lower bound :                                   
[1,] 0.9864792 0.00000000 0.0000000
[2,] 0.0752707 0.01524505 0.7813114
[3,] 0.0000000 0.97254293 0.0000000

Upper bound :                                  
[1,] 1.0000000 0.00000000 0.000000
[2,] 0.1718237 0.07476597 0.890179
[3,] 0.0000000 1.00000000 0.000000

CI for the high-order transition matrix :
-----------------------------------------
Lower bound :                                         
 [1,] 0.83490299 0.055116175 0.0135042633
 [2,] 0.08031026 0.109499774 0.6355514023
 [3,] 0.01354833 0.842468998 0.0242002473
 [4,] 0.97851464 0.000000000 0.0003512494
 [5,] 0.15774564 0.010661194 0.6663255810
 [6,] 0.08469987 0.779524152 0.0006646311
 [7,] 0.98095089 0.001843078 0.0000000000
 [8,] 0.13982619 0.011694653 0.6837781000
 [9,] 0.06317254 0.813872695 0.0000000000

Upper bound :                                      
 [1,] 0.91690331 0.12648388 0.05922240
 [2,] 0.18408849 0.22383621 0.77553442
 [3,] 0.08235226 0.94455281 0.10430655
 [4,] 0.99999657 0.00000000 0.01740802
 [5,] 0.29346204 0.07327272 0.80918604
 [6,] 0.21049435 0.90831329 0.03269990
 [7,] 1.00000000 0.01457606 0.00000000
 [8,] 0.27308773 0.07703349 0.82551382
 [9,] 0.18090011 0.93343447 0.00000000