# Generate observations given a model Function used to generate simulated observations given a hidden Markov model. ```r generateObservations(hmm, length) ``` ## Arguments - `hmm`: a list with the necessary variables to define a hidden Markov model. - `length`: the number of observations will be generated. ## Returns A `"list"` that contains the generated observations and the hidden state that generated it. - **X**: a vector representing the path of hidden states. - **Y**: generated observations. HMM and PHMM return a vector. GHMM returns a matrix. ## Examples ```r ## Values for a hidden Markov model with categorical observations # Set the model parameters n <- c("First","Second") m <- c("A","T","C","G") A <- matrix(c(0.8,0.2, 0.1,0.9), nrow = 2, byrow = TRUE) B <- matrix(c(0.2, 0.2, 0.3, 0.3, 0.4, 0.4, 0.1, 0.1), nrow = 2, byrow = TRUE) Pi <- c(0.5, 0.5) params <- list( "Model" = "HMM", "StateNames" = n, "ObservationNames" = m, "A" = A, "B" = B, "Pi" = Pi) HMM <- verifyModel(params) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM, length) # Observed data head(observationSequence$Y) # Hidden states path head(observationSequence$X) ## Values for a hidden Markov model with discrete observations n <- c("Low","Normal","High") A <- matrix(c(0.5, 0.3,0.2, 0.2, 0.6, 0.2, 0.1, 0.3, 0.6), ncol=length(n), byrow=TRUE) B <- c(2600, # First distribution with mean 2600 2700, # Second distribution with mean 2700 2800) # Third distribution with mean 2800 Pi <- rep(1/length(n), length(n)) HMM.discrete <- verifyModel(list("Model"="PHMM", "StateNames" = n, "A" = A, "B" = B, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.discrete, length) # Observed data head(observationSequence$Y) # Hidden states path head(observationSequence$X) ## Values for a hidden Markov model with continuous observations # Number of hidden states = 3 # Univariate gaussian mixture model N = c("Low","Normal", "High") A <- matrix(c(0.5, 0.3,0.2, 0.2, 0.6, 0.2, 0.1, 0.3, 0.6), ncol= length(N), byrow = TRUE) Mu <- matrix(c(0, 50, 100), ncol = length(N)) Sigma <- array(c(144, 400, 100), dim = c(1,1,length(N))) Pi <- rep(1/length(N), length(N)) HMM.cont.univariate <- verifyModel(list( "Model"="GHMM", "StateNames" = N, "A" = A, "Mu" = Mu, "Sigma" = Sigma, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.cont.univariate, length) # Observed data observationSequence$Y[,1:6] # Hidden states path head(observationSequence$X) ## Values for a hidden Markov model with continuous observations # Number of hidden states = 2 # Multivariate gaussian mixture model # Observed vector with dimensionality of 3 N = c("X1","X2") M <- 3 # Same number of dimensions Sigma <- array(0, dim =c(M,M,length(N))) Sigma[,,1] <- matrix(c(1.0,0.8,0.8, 0.8,1.0,0.8, 0.8,0.8,1.0), ncol = M, byrow = TRUE) Sigma[,,2] <- matrix(c(1.0,0.4,0.6, 0.4,1.0,0.8, 0.6,0.8,1.0), ncol = M, byrow = TRUE) Mu <- matrix(c(0, 5, 10, 0, 5, 10), nrow = M, byrow = TRUE) A <- matrix(c(0.6, 0.4, 0.3, 0.7), ncol = length(N), byrow = TRUE) Pi <- c(0.5, 0.5) HMM.cont.multi <- verifyModel(list( "Model" = "GHMM", "StateNames" = N, "A" = A, "Mu" = Mu, "Sigma" = Sigma, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.cont.multi, length) # Observed data observationSequence$Y[,1:6] # Hidden states path head(observationSequence$X) ```

generateObservations function