Adds a bar representing state sequence.

Description

Add a colour coded horizontal bar representing the state sequence to a plot of (presumably time-series) data.

Usage

addStates(states, x=NULL,ybot = axTicks(2)[1],
          ytop=ybot + (axTicks(2)[2] - axTicks(2)[1])/5,dy  = ytop - ybot,
          greyscale = FALSE,leg = NA, J = length(unique(states)), time.scale = 1, 
          shiftx = 0)

Arguments

Author(s)

Soren Hojsgaard sorenh@math.aau.dk

See Also

addStates

Examples

  plot(rnorm(100),type='l')
  addStates(rep(c(1,2),each=50))  

  plot(seq(0.01,1,.01),rnorm(100),type='l')
  addStates(rep(c(1,2),each=50),seq(0.01,1,.01))  

Emission ensity function for a multivariate normal emission distribution

Description

Calculates the density of observations x for state j given the parameters in model. This is used for a multivariate Gaussian emission distribution of a HMM or HSMM and is a suitable prototype for user's to make their own custom distributions.

Usage

dmvnorm.hsmm(x, j, model)

Arguments

Details

This is used by hmm and hsmm to calculate densities for use in the E-step of the EM algorithm. It can also be used as a template for users wishing to building their own emission distributions

Value

A vector of probability densities.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

mstep.mvnorm, rmvnorm.hsmm

Examples

  J<-2
  initial <- rep(1/J,J)
  P <- matrix(c(.3,.5,.7,.5),nrow=J)
  b <- list(mu=list(c(-3,0),c(1,2)),sigma=list(diag(2),matrix(c(4,2,2,3), ncol=2)))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dmvnorm.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rmvnorm.hsmm)
  plot(train,xlim=c(0,100))
  h1 = hmmfit(train,model,mstep=mstep.mvnorm)

Emission density function for normal emission distribution

Description

Calculates the density of observations x for state j given the parameters in model. This is used for the Gaussian emission distribution of a HMM or HSMM and is a suitable prototype for user's to make their own custom distributions.

Usage

dnorm.hsmm(x, j, model)

Arguments

Details

This is used by hmm and hsmm to calculate densities for use in the E-step of the EM algorithm. It can also be used as a template for users wishing to building their own emission distributions

Value

A vector of probability densities.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Emission density function for Poisson emission distribution

Description

Calculates the density of observations x for state j given the parameters in model. This is used for a Poisson emission distribution of a HMM or HSMM and is a suitable prototype for user's to make their own custom distributions.

Usage

dpois.hsmm(x, j, model)

Arguments

Details

This is used by hmm and hsmm to calculate densities for use in the E-step of the EM algorithm. It can also be used as a template for users wishing to building their own emission distributions

Value

A vector of probability densities.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

mstep.pois, rpois.hsmm

Examples

  J<-3
  initial <- rep(1/J,J)
  P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
  b <- list(lambda=c(1,3,6))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dpois.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rpois.hsmm)
  plot(train,xlim=c(0,100))  
  h1 = hmmfit(train,model,mstep=mstep.pois)

Parameter estimation for the Gamma distribution

Description

Estimates parameters for the Gamma distribution using the Method of Maximum Likelihood, works with weighted data.

Usage

gammafit(x, wt = NULL)

Arguments

Value

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Choi, S. and Wette, R. (1969), Maximum likelihood estimation of the parameters of the gamma distribution and their bias, Technometrics, 11, 683-96-690.

Examples

  gammafit(rgamma(1000,shape=10,scale=13))

fit a hidden Markov model

Description

Estimates parameters of a HMM using the EM algorithm.

Usage

hmmfit(x,start.val,mstep=mstep.norm,lock.transition=FALSE,tol=1e-08,maxit=1000) 

Arguments

Value

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Jared O'Connell, Soren Hojsgaard (2011). Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R., Journal of Statistical Software, 39(4), 1-22., URL http://www.jstatsoft.org/v39/i04/.

Rabiner, L. (1989), A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, 77, 257-286.

See Also

predict.hmm

Examples

J<-3
initial <- rep(1/J,J)
P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
b <- list(mu=c(-3,0,2),sigma=c(2,1,.5))
model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dnorm.hsmm)
model

train <- simulate(model, nsim=300, seed=1234, rand.emis=rnorm.hsmm)
plot(train,xlim=c(0,100))

init0 <- rep(1/J,J)
P0 <- matrix(1/J,nrow=J,ncol=J)
b0 <- list(mu=c(-3,1,3),sigma=c(1,1,1))
startval <- hmmspec(init=init0, trans=P0,parms.emission=b0,dens.emission=dnorm.hsmm) 
h1 = hmmfit(train,startval,mstep=mstep.norm)

plot(h1$loglik,type='b',ylab='Log-likelihood',xlab='Iteration')
summary(h1)

#proportion of incorrect states
mean(train$s!=predict(h1,train)$s)

#simulate a new test set 
test <- simulate(model, nsim=c(100,200,300), seed=1234,rand.emis=rnorm.hsmm)
mean(test$s!=predict(h1,test)$s)

Specificatin of HMMs

Description

Creates a model specficiation for a hidden Markov model

Usage

hmmspec(init, trans, parms.emission, dens.emission, rand.emission=NULL,mstep=NULL)

Arguments

Value

A hmmspec object

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Jared O'Connell, Soren Hojsgaard (2011). Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R., Journal of Statistical Software, 39(4), 1-22., URL http://www.jstatsoft.org/v39/i04/.

Rabiner, L. (1989), A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, 77, 257-286.

See Also

simulate.hmmspec, simulate.hmmspec, hmmfit, predict.hmm

fit a hidden semi-Markov model

Description

Estimates parameters of a HSMM using the EM algorithm.

Usage

hsmmfit(x,model,mstep=NULL,M=NA,maxit=100,
        lock.transition=FALSE,lock.d=FALSE,graphical=FALSE)

Arguments

Value

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Jared O'Connell, Soren Hojsgaard (2011). Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R., Journal of Statistical Software, 39(4), 1-22., URL http://www.jstatsoft.org/v39/i04/.

Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003

See Also

hsmmspec,simulate.hsmmspec,predict.hsmm

Examples

J <- 3
init <- c(0,0,1)
P <- matrix(c(0,.1,.4,.5,0,.6,.5,.9,0),nrow=J)
B <- list(mu=c(10,15,20),sigma=c(2,1,1.5))
d <- list(lambda=c(10,30,60),shift=c(10,100,30),type='poisson')
model <- hsmmspec(init,P,parms.emission=B,sojourn=d,dens.emission=dnorm.hsmm)
train <- simulate(model,r=rnorm.hsmm,nsim=100,seed=123456)
plot(train,xlim=c(0,400))
start.poisson <- hsmmspec(init=rep(1/J,J),
  transition=matrix(c(0,.5,.5,.5,0,.5,.5,.5,0),nrow=J),
  parms.emission=list(mu=c(4,12,23),
		sigma=c(1,1,1)),
  sojourn=list(lambda=c(9,25,40),shift=c(5,95,45),type='poisson'),
 dens.emission=dnorm.hsmm)

M=500
# not run (takes some time)
# h.poisson <- hsmmfit(train,start.poisson,mstep=mstep.norm,M=M)
# plot(h.poisson$loglik,type='b',ylab='Log-likelihood',xlab='Iteration') ##has it converged?
# summary(h.poisson)
# predicted <- predict(h.poisson,train)  
# table(train$s,predicted$s) ##classification matrix
# mean(predicted$s!=train$s) ##misclassification rate

d <- cbind(dunif(1:M,0,50),dunif(1:M,100,175),dunif(1:M,50,130))
start.np <- hsmmspec(init=rep(1/J,J),
  transition=matrix(c(0,.5,.5,.5,0,.5,.5,.5,0),nrow=J),
  parms.emission=list(mu=c(4,12,23),
  sigma=c(1,1,1)),
  sojourn=list(d=d,type='nonparametric'),
  dens.emission=dnorm.hsmm)
# not run (takes some time)
# h.np <- hsmmfit(train,start.np,mstep=mstep.norm,M=M,graphical=TRUE)
# mean(predicted$s!=train$s) ##misclassification rate


#J <- 2
#init <- c(1, 0)
#P <- matrix(c(0, 1, 1, 0), nrow = J)
#B <- list(mu = list(c(2, 3), c(3, 4)), sigma = list(matrix(c(4, 2, 2, 3), ncol = 2), diag(2)))
#d <- list(shape = c(10, 25), scale = c(2, 2), type = "gamma")
#model <- hsmmspec(init, P, parms.emis = B, sojourn = d, dens.emis = dmvnorm.hsmm)
#train <- simulate(model, c(1000,100), seed = 123, rand.emis = rmvnorm.hsmm)

#yhat <- predict(model, train)
#mean(predict(model,train)$s==train$s)

Hidden semi-Markov model specification

Description

Creates a model specification of a hidden semi-Markov model.

Usage

hsmmspec(init,transition,parms.emission,sojourn,dens.emission,
	rand.emission=NULL,mstep=NULL)

Arguments

Details

The sojourn argument provides a list containing the parameters for the available sojourn distributions. Available sojourn distributions are shifted Poisson, Gamma and non-parametric.

In the case of the Gamma distribution, sojourn is a list with vectors shape and scale (the Gamma parameters in dgamma), both of length J. Where J is the number of states. See reprocows for an example using Gamma sojourn distributions.

In the case of shifted Poisson, sojourn is list with vectors shift and lambda, both of length J. See hsmmfit for an example using shifted Poisson sojourn distributions.

In the case of non-parametric, sojourn is a list containing a M x J matrix. Where entry (i,j) is the probability of a sojourn of length i in state j. See hsmmfit for an example using shifted non-parametric sojourn distributions.

Value

An object of class hsmmspec

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Jared O'Connell, Soren Hojsgaard (2011). Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R., Journal of Statistical Software, 39(4), 1-22., URL http://www.jstatsoft.org/v39/i04/.

Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003

See Also

hsmmfit ,simulate.hsmmspec, predict.hsmm

Performs re-estimation (the M-step) for a multivariate normal emission distribution

Description

Re-estimates the parameters of a multivariate normal emission distribution as part of the EM algorithm for HMMs and HSMMs. This is called by the hmm and hsmm functions. It is a suitable prototype function for users wishing to design their own emission distributions.

Usage

mstep.mvnorm(x, wt)

Arguments

Details

Users may write functions that take the same arguments and return the same values for their own custom emission distributions.

Value

Returns the emission slot of a hmmspec or hsmmspec object

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

dmvnorm.hsmm, rmvnorm.hsmm

Examples

  J<-2
  initial <- rep(1/J,J)
  P <- matrix(c(.3,.5,.7,.5),nrow=J)
  b <- list(mu=list(c(-3,0),c(1,2)),sigma=list(diag(2),matrix(c(4,2,2,3), ncol=2)))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dmvnorm.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rmvnorm.hsmm)
  plot(train,xlim=c(0,100))
  h1 = hmmfit(train,model,mstep=mstep.mvnorm)

Performs re-estimation (the M-step) for a normal emission distribution

Description

Re-estimates the parameters of a normal emission distribution as part of the EM algorithm for HMMs and HSMMs. This is called by the hmm and hsmm functions. It is a suitable prototype function for users wishing to design their own emission distributions.

Usage

mstep.norm(x, wt)

Arguments

Details

Users may write functions that take the same arguments and return the same values for their own custom emission distributions.

Value

Returns the emission slot of a hmmspec or hsmmspec object

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Performs re-estimation (the M-step) for a Poisson emission distribution

Description

Re-estimates the parameters of a Poisson emission distribution as part of the EM algorithm for HMMs and HSMMs. This is called by the hmm and hsmm functions. It is a suitable prototype function for users wishing to design their own emission distributions.

Usage

mstep.pois(x, wt)

Arguments

Details

Users may write functions that take the same arguments and return the same values for their own custom emission distributions.

Value

Returns the emission slot of a hmmspec or hsmmspec object

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

rpois.hsmm, dpois.hsmm

Examples

  J<-3
  initial <- rep(1/J,J)
  P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
  b <- list(lambda=c(1,3,6))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dpois.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rpois.hsmm)
  plot(train,xlim=c(0,100))  
  h1 = hmmfit(train,model,mstep=mstep.pois)

Plot function for hsmms

Description

Displays the densities for the sojourn distributions of each state.

Usage

## S3 method for class 'hsmm'
plot(x, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Plot function for hsmm data

Description

Produces a plot of the observed sequences, and displays a coloured bar signifying the hidden states (if available)

Usage

## S3 method for class 'hsmm.data'
plot(x, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

addStates

Examples

  J<-3
  initial <- rep(1/J,J)
  P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
  b <- list(mu=c(-3,0,2),sigma=c(2,1,.5))
  model <- hmmspec(init=initial, trans=P, parms.emission=b, dens.emission=dnorm.hsmm)
  
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rnorm.hsmm)
  plot(train,xlim=c(0,100))

Prediction function for hmm

Description

Predicts the underlying state sequence for an observed sequence newdata given a hmm model

Usage

## S3 method for class 'hmm'
predict(object, newdata,method = "viterbi", ...)

Arguments

Details

If method="viterbi", this technique applies the Viterbi algorithm for HMMs, producing the most likely sequence of states given the observed data. If method="smoothed", then the individually most likely (or smoothed) state sequence is produced, along with a matrix with the respective probabilities for each state.

Value

Returns a hsmm.data object, suitable for plotting.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Rabiner, L. (1989), A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, 77, 257-286.

See Also

hmmfit,hmmspec

Examples

##See examples in 'hmmfit'

Prediction function for hmmspec

Description

Predicts the underlying state sequence for an observed sequence newdata given a hmmspec model

Usage

## S3 method for class 'hmmspec'
predict(object, newdata,method = "viterbi", ...)

Arguments

Details

If method="viterbi", this technique applies the Viterbi algorithm for HMMs, producing the most likely sequence of states given the observed data. If method="smoothed", then the individually most likely (or smoothed) state sequence is produced, along with a matrix with the respective probabilities for each state. This function differs from predict.hmm in that it takes the output from hmmspec ie. this is useful when users already know their parameters and wish to make predictions.

Value

Returns a hsmm.data object, suitable for plotting.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Rabiner, L. (1989), A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, 77, 257-286.

See Also

hmmspec

Examples

     J<-3
     initial <- rep(1/J,J)
     P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
     b <- list(mu=c(-3,0,2),sigma=c(2,1,.5))
     model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dnorm.hsmm)    
     train <- simulate(model, nsim=300, seed=1234, rand.emis=rnorm.hsmm)
     mean(predict(model,train)$s!=train$s) #error rate when true model is known

Prediction for hsmms

Description

Predicts the underlying state sequence for an observed sequence newdata given a hsmm model

Usage

## S3 method for class 'hsmm'
predict(object, newdata, method = "viterbi", ...)

Arguments

Details

If method="viterbi", this technique applies the Viterbi algorithm for HSMMs, producing the most likely sequence of states given the observed data. If method="smoothed", then the individually most likely (or smoothed) state sequence is produced, along with a matrix with the respective probabilities for each state.

Value

Returns a hsmm.data object, suitable for plotting.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003

See Also

hsmmfit,predict.hsmmspec

Examples

##See 'hsmmfit' for examples

Prediction for hsmmspec

Description

Predicts the underlying state sequence for an observed sequence newdata given a hsmm model

Usage

## S3 method for class 'hsmmspec'
predict(object, newdata, method = "viterbi",M=NA, ...)

Arguments

Details

If method="viterbi", this technique applies the Viterbi algorithm for HSMMs, producing the most likely sequence of states given the observed data. If method="smoothed", then the individually most likely (or smoothed) state sequence is produced, along with a matrix with the respective probabilities for each state. This method is different to predict.hsmm in that it takes the output from hsmmspec as input ie. it is useful for people who already know their model parameters.

Value

Returns a hsmm.data object, suitable for plotting.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003

See Also

hsmmspec, predict.hsmm

Examples

J <- 3
init <- c(0,0,1)
P <- matrix(c(0,.1,.4,.5,0,.6,.5,.9,0),nrow=J)
B <- list(mu=c(10,15,20),sigma=c(2,1,1.5))
d <- list(lambda=c(10,30,60),shift=c(10,100,30),type='poisson')
model <- hsmmspec(init,P,parms.emission=B,sojourn=d,dens.emission=dnorm.hsmm)
train <- simulate(model,r=rnorm.hsmm,nsim=100,seed=123456)
mean(predict(model,train,M=500)$s!=train$s) #error rate when true model is known

Print method for hmm objects

Description

Prints the slots of a hmm object

Usage

## S3 method for class 'hmm'
print(x, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Print function for hmmspec

Description

Prints the parameters contained in the object

Usage

## S3 method for class 'hmmspec'
print(x, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Print function for hsmmspec

Description

Prints the parameters contained in the object

Usage

## S3 method for class 'hsmmspec'
print(x, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Artificial insemination times for seven cows

Description

This is an auxilliary data set to the cows data set containing times of artificial insemination for respective cows. Only the day of insemination was recorded so time of day is always midday.

Usage

reproai

Format

reproai is a dataframe with 12 rows and id being the cow's id and days.from.calving recording the number of days from calving when insemination occurred.

Source

Danish Cattle Research Centre

References

Peters, A. and Ball, P. (1995), "Reproduction in Cattle," 2nd ed.

Reproductive data from seven dairy cows

Description

This data set contains hourly observations on progesterone and an activity index at hourly intervals since calving on seven dairy cows.

Usage

reprocows

Format

reprocows is a data frame containing 13040 rows. id is the cow ID, progesterone is a measurement of the hormone in ng/L taken from a milk sample, activity is a relative measure of activity calculated from a pedometer.

There are a large number of missing values as progesterone is measured only at milking time (and at a farm manager's discretion). Missing values in activity occur due to hardware problems can occur with pedometers.

Source

Danish Cattle Research Centre

References

Peters, A. and Ball, P. (1995), "Reproduction in Cattle," 2nd ed.

Examples

data(reprocows)
data(reproai)
data(reproppa)
tm = 1600

J <- 3
init <- c(1,0,0)
trans <- matrix(c(0,0,0,1,0,1,0,1,0),nrow=J)
emis <- list(mu=c(0,2.5,0),sigma=c(1,1,1))

N <- as.numeric(table(reprocows$id))
train <- list(x=reprocows$activity,N=N)
class(train) <- "hsmm.data"
tmp <- gammafit(reproppa * 24)
M <- max(N)

d <- cbind(dgamma(1:M,shape=tmp$shape,scale=tmp$scale),
 # ppa sojourn directly estimated from ppa data set
dunif(1:M,4,30),
 # oestrus between 4 and 30 hours
dunif(1:M,15*24,40*24))
 #not-oestrus between 15 and 40 days

startval <- hsmmspec(init,trans,parms.emission=emis,list(d=d,type='gamma'),
  dens.emission=dnorm.hsmm)
#not run (takes some time)
#h.activity <- hsmmfit(train,startval,mstep=mstep.norm,maxit=10,M=M,lock.transition=TRUE)
  

Observed lengths of post-partum anoestrus for 73 dairy cows

Description

This data set contains the observed length of post-partum anoestrus (in days) for 73 dairy cattle.

Usage

reproppa

Format

reproppa a vector containing 73 integers.

Source

Danish Cattle Research Centre

References

Peters, A. and Ball, P. (1995), "Reproduction in Cattle," 2nd ed.

Random number generation from a multivariate normal distributed emission distribution

Description

This generates values from a multivariate normal distributed emission state j given parameters in model.

Usage

rmvnorm.hsmm(j, model)

Arguments

Details

This is essentially a wrapper for rnorm. Users may build functions with the same arguments and return values so they can use their own custom emission distributions.

Value

A single value from the emission distribution.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

dmvnorm.hsmm, mstep.mvnorm

Examples

  J<-2
  initial <- rep(1/J,J)
  P <- matrix(c(.3,.5,.7,.5),nrow=J)
  b <- list(mu=list(c(-3,0),c(1,2)),sigma=list(diag(2),matrix(c(4,2,2,3), ncol=2)))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dmvnorm.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rmvnorm.hsmm)
  plot(train,xlim=c(0,100))
  h1 = hmmfit(train,model,mstep=mstep.mvnorm)

Random number generation from a normally distributed emission distribution

Description

This generates values from a normally distributed emission state j given parameters in model.

Usage

rnorm.hsmm(j, model)

Arguments

Details

This is essentially a wrapper for rnorm. Users may build functions with the same arguments and return values so they can use their own custom emission distributions.

Value

A single value from the emission distribution.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Random number generation from a Poisson distributed emission distribution

Description

This generates values from a Poisson distributed emission state j given parameters in model.

Usage

rpois.hsmm(j, model)

Arguments

Details

This is essentially a wrapper for rpois. Users may build functions with the same arguments and return values so they can use their own custom emission distributions.

Value

A single value from the emission distribution.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

See Also

mstep.pois, dpois.hsmm

Examples

  J<-3
  initial <- rep(1/J,J)
  P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
  b <- list(lambda=c(1,3,6))
  model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dpois.hsmm)
  model
  train <- simulate(model, nsim=300, seed=1234, rand.emis=rpois.hsmm)
  plot(train,xlim=c(0,100))  
  h1 = hmmfit(train,model,mstep=mstep.pois)

Markov chain simulation

Description

Simulates a Markov chain

Usage

sim.mc(init, transition, N)

Arguments

Value

A vector of integers representing the state sequence.

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Examples

  p <- matrix(c(.1,.3,.6,rep(1/3,3),0,.5,.5),ncol=3,byrow=TRUE)
  init <- rep(1/3,3)
  sim.mc(init,p,10)  
  
  

Simulation of hidden Markov models

Description

Simulates data from a hidden Markov model

Usage

## S3 method for class 'hmmspec'
simulate(object, nsim, seed = NULL, rand.emission=NULL,...)

Arguments

Details

If nsim is a single integer then a HMM of that length is produced. If nsim is a vector of integers, then length(nsim) sequences are generated with respective lengths.

Value

An object of class hmmdata

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Rabiner, L. (1989), A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, 77, 257-286.

See Also

hmmspec, link{predict.hmm}

Examples

J<-3
initial <- rep(1/J,J)
P <- matrix(c(.8,.5,.1,0.05,.2,.5,.15,.3,.4),nrow=J)
b <- list(mu=c(-3,0,2),sigma=c(2,1,.5))
model <- hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dnorm.hsmm)
train <- simulate(model, nsim=100, seed=1234, rand.emis=rnorm.hsmm)
plot(train)

Simulation for HSMMs

Description

Simulates values for a specified hidden semi-Markov model

Usage

## S3 method for class 'hsmmspec'
simulate(object, nsim, seed = NULL,rand.emission=NULL,...)

Arguments

Details

If nsim is a single integer then a HSMM of that length is produced. If nsim is a vector of integers, then length(nsim) sequences are generated with respective lengths. Note thate length is the number of states visited, each state will have a sojourn time typically >1 so the vector will be longer than nsim

Value

An object of class hmmdata

Author(s)

Jared O'Connell jaredoconnell@gmail.com

References

Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003

See Also

hsmmfit, hsmmspec, predict.hsmm

Examples

J <- 3
init <- c(0,0,1)
P <- matrix(c(0,.1,.4,.5,0,.6,.5,.9,0),nrow=J)
B <- list(mu=c(10,15,20),sigma=c(2,1,1.5))
d <- list(lambda=c(10,30,60),shift=c(10,100,30),type='poisson')
model <- hsmmspec(init,P,parms.emission=B,sojourn=d,dens.emission=dnorm.hsmm)
train <- simulate(model,rand.emis=rnorm.hsmm,nsim=100,seed=123456)
plot(train,xlim=c(0,400))

Smoothing a discrete time series.

Description

The smooth.discrete() function provides a simple smoothing of a time series of discrete values measured at equidistant times. Under the hood of smooth.discrete() is a hidden Markov model.

Usage

smooth.discrete(y, init = NULL, trans = NULL, parms.emission = 0.5, 
                method = "viterbi", details = 0, ...)

Arguments

Details

The parameters are estimated using the Baum-Welch algorithm (a special case of the EM-algorithm).

Value

A list with the following components:

Author(s)

S<c3><b8>ren H<c3><b8>jsgaard <sorenh at math.aau.dk>

See Also

hmmspec, hmmfit

Examples

## Please see the vignette

Summary method for hmm objects

Description

Prints the estimated parameters of a hmm object

Usage

## S3 method for class 'hmm'
summary(object, ...)

Arguments

Value

An object of class 'summary.hmm'

Author(s)

Jared O'Connell jaredoconnell@gmail.com

Summary function for hsmm

Description

Returns a summary object for a hsmm object

Usage

## S3 method for class 'hsmm'
summary(object, ...)

Arguments

Author(s)

Jared O'Connell jaredoconnell@gmail.com