回复： Bayesian Hidden Markov Models

Dear Oscar,
 
I have used the the following codes to perform a Bayesian HMM for the exchange
rate data.
But, one intresting result is that the model fits a 6-state HMM with a common
variance.
This is very hard to understand. Because, from the plot graph, we could see
there are obviously differents with high and low volatility.
 
So, could you please help me to take a look at this? Attached is the exchange
rate data.
I am really grateful for your help and time.
 
Best Regards,
 
James LAN
 
 
#input exchange rate data
exrt<-read.table(file="exrt.txt",header=F)
plot(exrt$V2)
library(RJaCGH)
y<-exrt$V2
Pos<- 1:length(y)
Chrom <- rep(1, length(y))
res<-RJaCGH(y=y, Pos=Pos, Chrom=Chrom)
summary(res)
Q.NH(summary(res)[[1]]$beta, x=0)
Summary for ARRAY  array1:
Distribution of the number of hidden states:
1 2 3 4 5 6
0 0 0 0 0 1
Model with  6  states:
Distribution of the posterior means of hidden states:
            10%    25%    50%    75%    90%
Loss-1   -0.298 -0.284 -0.284 -0.279 -0.279
Loss-2   -0.144 -0.142 -0.142 -0.135 -0.135
Normal-1 -0.045 -0.043 -0.043 -0.040 -0.040
Normal-2 -0.004 -0.003 -0.003  0.000  0.000
Normal-3  0.047  0.056  0.056  0.059  0.059
Gain      0.177  0.197  0.197  0.198  0.198
Distribution of the posterior variances of hidden states:
           10%   25%   50%   75%   90%
Loss-1   0.001 0.001 0.001 0.001 0.001
Loss-2   0.001 0.001 0.001 0.001 0.001
Normal-1 0.001 0.001 0.001 0.001 0.001
Normal-2 0.001 0.001 0.001 0.001 0.001
Normal-3 0.001 0.001 0.001 0.001 0.001
Gain     0.001 0.001 0.001 0.001 0.001
Parameters of the transition functions:
         Loss-1 Loss-2 Normal-1 Normal-2 Normal-3  Gain
Loss-1    0.000  0.217    0.192    1.229    0.185 0.857
Loss-2    2.104  0.000    0.305    2.190    0.132 1.424
Normal-1  2.728  1.472    0.000    4.606    0.293 2.423
Normal-2  5.919  4.746    5.518    0.000    5.067 5.834
Normal-3  2.295  0.537    0.115    4.329    0.000 2.514
Gain      1.519  0.247    0.036    1.263    0.132 0.000
================================================

Q.NH(summary(res)[[1]]$beta, x=0)

              Loss-1      Loss-2    Normal-1    Normal-2    Normal-3
Loss-1   0.239381248 0.192598942 0.197535790 0.070058386 0.198853168
Loss-2   0.039503637 0.323847484 0.238632024 0.036241348 0.283843424
Normal-1 0.030559504 0.107234801 0.467453369 0.004669696 0.348627295
Normal-2 0.002624349 0.008474303 0.003915585 0.975979222 0.006151494
Normal-3 0.037727330 0.218834862 0.333794793 0.004936521 0.374412381
Gain     0.053064705 0.189481114 0.233947328 0.068592117 0.212423356
                Gain
Loss-1   0.101572465
Loss-2   0.077932083
Normal-1 0.041455335
Normal-2 0.002855048
Normal-3 0.030294113
Gain     0.242491380


???? Oscar Rueda [via R] <ml-node+s789695n4431468h14 at n4.nabble.com>
???? monkeylan <lanjinchi at yahoo.com.cn>
????? 2012?2?29?, ???, ?? 9:21
??: Re: Bayesian Hidden Markov Models


Dear James,

The distances are normalized between zero and 1, so in your case all of them
will be zero. You can check that with

res$Dist.for.model

And do

Q.NH(summary(res)[[1]]$beta, x=0)

To obtain the common transition matrix.

Cheers,
Oscar


On 29/2/12 03:59, "monkeylan" <[hidden email]> wrote:

Dear Oscar,
 
I am extremely grateful to your help and detailed explanation of the use of
RJaCGH package.
But, when runing the sample codes you listed, another issue I am a little
confused is as following:
After runing summary(res), I have got the estimation of the random matrix
Beta:

Parameters of the transition functions:
       Normal  Gain
Normal  0.000 4.258
Gain    2.001 0.000
 
But, the transition probabilty matrix Q based on the aboving Beta is more
concerned in my modeling.
Here, I am not sure how can I get the  matrix Q. I did try the Q.NH
functions.However, Shoud I set the distance parameter x be 1 or 0? I am not
sure.
 
 If 1( according to my own understanding), the following result seems not
reseanable.
 
tran<-matrix(c(0,2.001,4.528,0),2,2)
Q.NH(beta=tran, x=1)
     [,1] [,2]
[1,]  0.5  0.5
[2,]  0.5  0.5
 
Many thanks for your further help and time.
 
James Allan

--- 12?2?28????, Oscar Rueda [via R]
<[hidden email]> ???


???: Oscar Rueda [via R] <[hidden email]>
??: Re: Bayesian Hidden Markov Models
???: "monkeylan" <[hidden email]>
??: 2012?2?28?,??,??7:02


Dear James,

Basically you just need the values (y) and the positions (in your case it
would be the index of the times series). The chromosome argument does not
apply to your case so it can be a vector of ones.
If the positions are at the same distance between (equally spaced) then the
model will be homogeneous.

So for example something like this would be enough:

library(RJaCGH)
y <- c(rnorm(100,0,1), rnorm(20, 2, 1), rnorm(50, 0, 1))
Pos <- 1:length(y)
Chrom <- rep(1, length(y))
res <- RJaCGH(y=y, Pos=Pos, Chrom=Chrom)
summary(res)

However, it uses a Reversible Jump algorithm and therefore jumps between
models with different hidden states. I would suggest you take a look at the
vignette that comes with the package or the paper that is referenced there
for specific details of the model it fits.


Hope it helps,
Oscar
 


On 28/2/12 04:52, "monkeylan" <[hidden email]> wrote:

Dear Doctor Oscar,
 
Sorry for not noticing that you are the author of the RJaCGH package.

But I noticed that hidden Markov model in your package is with
non-homogeneous
transition probabilities. Here in my work, the HMM is just a first-order
homogeneous Markov chain, i.e. the  transition  matrix is constant.
 
So, Could you please tell me how can I adjust the R functions in your
package
to implement my analysis?
 
Best Regards,
 
James Allan


--- 12?2?27????, Oscar Rueda [via R]
<[hidden email]> ???


???: Oscar Rueda [via R] <[hidden email]>
??: Re: Bayesian Hidden Markov Models
???: "monkeylan" <[hidden email]>
??: 2012?2?27?,??,??6:05


Dear James,
Although designed for the analysis of copy number CGH microarrays, RJaCGH
uses a Bayesian HMM model.

Cheers,
Oscar


On 27/2/12 08:32, "monkeylan" <[hidden email]> wrote:

Dear R buddies,

Recently, I attempt to model the US/RMB Exchange rate log-return time
series
with a *Hidden Markov model (first order Markov Chain & mixed Normal
distributions). *

I have applied the RHmm package to accomplish this task, but the results
are
not so satisfying.
So, I would like to try a *Bayesian method *for the parameter estimation of
the Hidden Markov model.

Could anyone kindly tell me which R package can perform Bayesian estimation
of the model?

Many thanks for your help and time.

Best Regards,
James Allan


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Postdoctoral Research Fellow, Breast Cancer Functional Genomics.
Cancer Research UK Cambridge Research Institute.
Li Ka Shing Centre, Robinson Way.
Cambridge CB2 0RE
England




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This e-mail (including any attachments) is intended for the above-named
person(s). If you are not the intended recipient, notify the sender
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any purpose.

We may monitor all incoming and outgoing emails in line with current
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free from any virus, but it remains your responsibility to ensure that viruses
do not adversely affect you.
Cancer Research UK
Registered in England and Wales
Company Registered Number: 4325234.
Registered Charity Number: 1089464 and Scotland SC041666
Registered Office Address: Angel Building, 407 St John Street, London EC1V
4AD.