R/mcmcdemUnif.R

In ctaglioni/demCMP: Functions for analysing demographic data with CMP distribution

#--------------------------------------------
# MCMC For model type: y_i = CMP(mu_i, nu_i)
# Uniform prior on nu_i
#--------------------------------------------
library(LaplacesDemon) # to use half t distribution
#---------------------------------
# First simple model, sd = half t
#---------------------------------

mcmc.dem.simple.unif <- function(y, iter, expo, gamma0 = rep(1,length(y)), nu0 = rep(1,length(y)),
                            lgamma0 = log(gamma0), lnu0 = log(nu0),
                            mu = 0, sigma = 10,
                            lnumin = -9, lnumax = 3){
  n <-length(y)
  gamma.mat <- matrix(NA, iter, n)
  nu.mat <- matrix(NA, iter, n)


  # Initialise

  gamma.mat[1,] <-gamma0
  nu.mat[1,] <- nu0

  # Acceptance

  gamma.nu.acc <- 0
  gamma.acc <- 0
  nu.acc <- 0

  # nu and gamma are updated with the exchange algorithm
  # for mu and eta Gibbs sampling
  # sigma and tau MH?
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    gamma.curr <- gamma.mat[i-1,]
    nu.curr <- nu.mat[i-1,]
    lgamma.curr<- log(gamma.curr)
    lnu.curr <- log(nu.curr)


    # generate candidates

    # candidate for c(gamma, nu):

    lgamma.cand <- rnorm(n, lgamma.curr, 0.1)
    lnu.cand <- runif(n, lnumin, lnumax)

    # Exchange algorithm for gamma and nu
    par.post<- c()
    for(k in 1:n){
      par.post[k] <- a.exch.unif(y[k], lgamma.curr[k], lnu.curr[k],
                            lgamma.cand[k], lnu.cand[k], expo[k], mu,
                            sigma)$test
    }

    gamma.mat[i,] <- ifelse(par.post, exp(lgamma.cand), exp(lgamma.curr))
    nu.mat[i,] <- ifelse(par.post, exp(lnu.cand), exp(lnu.curr))
    gamma.nu.acc <- ifelse(par.post, gamma.nu.acc+1, gamma.nu.acc)
    lgamma.curr <- ifelse(par.post, lgamma.cand, lgamma.curr)
    lnu.curr <- ifelse(par.post, lnu.cand, lnu.curr)

    # candidate for c(gamma, nu):

    lgamma.cand2 <- rnorm(n, lgamma.curr, 0.1)
    lnu.cand2 <- runif(n, lnumin, lnumax)

    # Exchange algorithm for gamma:
    par.post.g<- c()
    for(k in 1:n){
      par.post.g[k] <- a.exch.unif(y[k], lgamma.curr[k], lnu.curr[k],
                              lgamma.cand2[k], lnu.curr[k], expo[k],
                              mu, sigma)$test
    }

    gamma.mat[i,] <- ifelse(par.post.g, exp(lgamma.cand2), exp(lgamma.curr))
    gamma.acc <- ifelse(par.post.g, gamma.acc+1, gamma.acc)

    # Exchange algorithm for nu:
    par.post.n <- c()
    for(k in 1:n){
      par.post.n[k] <- a.exch.unif(y[k], lgamma.curr[k], lnu.curr[k],
                              lgamma.curr[k], lnu.cand2[k], expo[k],
                              mu, sigma)$test
    }

    nu.mat[i,] <- ifelse(par.post.n, exp(lnu.cand2), exp(lnu.curr))
    nu.acc <- ifelse(par.post.n, nu.acc+1, nu.acc)


  }

  return(list (parameters = list(gamma = gamma.mat, nu = nu.mat),
               acceptance = list(gamma.nu = gamma.nu.acc/iter,
                                 gamma = gamma.acc/iter,
                                 nu = nu.acc/iter))
  )
}

#-------------------------------------
# Model assuming IG prior on Variance
# (i.e. Gibbs sampling for sigma and tau as conjugate model)
#-------------------------------------

mcmc.dem.IG.unif <- function(y, iter, expo, lambda0 = rep(0,length(y)), omega0 = rep(0,length(y)),
                        mu0 = 0, sigma0 = 0.1,
                        alpha0 = 0, beta0 = 0.1,
                        sh.sigma0 = 0.001, sc.sigma0 = 0.001,
                        mean.lambda.cand = 0, sd.lambda.cand = 1,
                        model.upd, ommin = 0.0001, ommax = 5){

  n <- length(y)
  # Space for storing values
  lambda.mat <- matrix(NA, iter, n)
  omega.mat <- matrix(NA, iter, n)
  mu.vec <- c()
  sigma.vec <- c()

  # Initialise

  lambda.mat[1,]<- lambda0
  omega.mat[1,] <- omega0
  mu.vec[1] <- mu0
  sigma.vec[1] <- sigma0

  # Acceptance

  acceptance <- 0

  # Begin loop
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    lambda.curr <- lambda.mat[(i-1),]
    omega.curr <- omega.mat[(i-1),]
    #
    # Parameters for Gibbs sampling

    # Update mu
    # mean
    num.alpha <- alpha0 / beta0^2 + sum(lambda.mat[(i-1),])/(sigma.vec[(i-1)])^2
    den.alpha <- (1 / beta0^2 + n / (sigma.vec[(i-1)])^2)
    alpha <-  num.alpha / den.alpha
    # sd
    beta <- sqrt(1 / (1 / beta0^2 + n / (sigma.vec[(i-1)])^2))
    #
    mu.vec[i] <- rnorm(1, alpha, beta)

    # Update sigma
    # shape
    sh.sigma <- sh.sigma0 + n / 2
    # scale
    sc.sigma <- sc.sigma0 + 0.5 * sum((lambda.mat[(i-1),] - mu.vec[i])^2)
    #
    sigma.vec[i] <- sqrt(1 / rgamma(1, shape = sh.sigma, scale = sc.sigma))

    mu.curr <- mu.vec[i]
    sigma.curr <- sigma.vec[i]

    # candidate for lambda and omega:
    # by default standard normal or if model.upd == "RW" it is a random walk step
    # or with hyperparameters if Gibbs
    if(model.upd=="RW"){
      mean.lambda.cand <- lambda.mat[(i-1),]
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    } else{
      mean.lambda.cand <- mean.lambda.cand
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    }


    #
    lambda.cand<- rnorm(n, mean.lambda.cand, sd.lambda.cand)



    # Exchange algorithm for lambda and omega
    par.post <- c()
    for(k in 1:n){
      par.post[k] <- a.exch.unif(y[k], lambda.curr[k], omega.curr[k],
                            lambda.cand[k], omega.cand[k],
                            expo[k], mu.curr, sigma.curr, ommin, ommax)$test
    }

    lambda.mat[i,] <- ifelse(par.post, lambda.cand, lambda.curr)
    omega.mat[i,] <- ifelse(par.post, omega.cand, omega.curr)
    acceptance <- ifelse(par.post, acceptance + 1, acceptance)

  }

  return(list (parameters = list(gamma = exp(lambda.mat), nu = exp(omega.mat),
                                 mu = mu.vec, sigma = sigma.vec),
               acceptance = acceptance/iter)
  )
}

#-------------------------------------
# Model assuming IG prior on Variance separate updating
# (i.e. Gibbs sampling for sigma and tau as conjugate model)
#-------------------------------------

mcmc.dem.IG.sep.unif <- function(y, iter, expo, lambda0 = rep(0,length(y)), omega0 = rep(0,length(y)),
                            mu0 = 0, sigma0 = 0.1,
                            alpha0 = 0, beta0 = 0.1,
                            sh.sigma0 = 0.001, sc.sigma0 = 0.001,
                            mean.lambda.cand = 0, sd.lambda.cand = 1,
                            model.upd, ommin = 0.001, ommax = 10){

  n <- length(y)
  # Space for storing values
  lambda.mat <- matrix(NA, iter, n)
  omega.mat <- matrix(NA, iter, n)
  mu.vec <- c()
  sigma.vec <- c()

  # Initialise

  lambda.mat[1,]<- lambda0
  omega.mat[1,] <- omega0
  mu.vec[1] <- mu0
  sigma.vec[1] <- sigma0

  # Acceptance

  acceptance.lambda <- 0
  acceptance.omega <- 0

  # Begin loop
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    lambda.curr <- lambda.mat[(i-1),]
    omega.curr <- omega.mat[(i-1),]
    #
    # Parameters for Gibbs sampling

    # Update mu
    # mean
    num.alpha <- alpha0 / beta0^2 + sum(lambda.mat[(i-1),])/(sigma.vec[(i-1)])^2
    den.alpha <- (1 / beta0^2 + n / (sigma.vec[(i-1)])^2)
    alpha <-  num.alpha / den.alpha
    # sd
    beta <- sqrt(1 / (1 / beta0^2 + n / (sigma.vec[(i-1)])^2))
    #
    mu.vec[i] <- rnorm(1, alpha, beta)

    # Update sigma
    # shape
    sh.sigma <- sh.sigma0 + n / 2
    # scale
    sc.sigma <- sc.sigma0 + 0.5 * sum((lambda.mat[(i-1),] - mu.vec[i])^2)
    #
    sigma.vec[i] <- sqrt(1 / rgamma(1, shape = sh.sigma, scale = sc.sigma))


    mu.curr <- mu.vec[i]
    sigma.curr <- sigma.vec[i]

    # candidate for lambda and omega:
    # by default standard normal or if model.upd == "RW" it is a random walk step
    # or with hyperparameters if Gibbs

    if(model.upd=="RW"){
      mean.lambda.cand <- lambda.mat[(i-1),]
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    } else{
      mean.lambda.cand <- mean.lambda.cand
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    }


    #
    lambda.cand<- rnorm(n, mean.lambda.cand, sd.lambda.cand)

    # Exchange algorithm for lambda
    par.post.lambda <- c()
    for(k in 1:n){
      par.post.lambda[k] <- a.exch.unif(y[k], lambda.curr[k], omega.curr[k],
                                   lambda.cand[k], omega.curr[k],
                                   expo[k], mu.curr, sigma, ommin, ommax)$test
    }

    lambda.mat[i,] <- ifelse(par.post.lambda, lambda.cand, lambda.curr)
    acceptance.lambda <- ifelse(par.post.lambda, acceptance.lambda + 1, acceptance.lambda)


    # Exchange algorithm for omega

    par.post.omega <- c()
    for(k in 1:n){
      par.post.omega[k] <- a.exch.unif(y[k], lambda.curr[k], omega.curr[k],
                                  lambda.curr[k], omega.cand[k],
                                  expo[k], mu.curr, sigma, ommin, ommax)$test
    }

    omega.mat[i,] <- ifelse(par.post.omega, omega.cand, omega.curr)
    acceptance.omega <- ifelse(par.post.omega, acceptance.omega + 1, acceptance.omega)

  }


  return(list (parameters = list(gamma = exp(lambda.mat), nu = exp(omega.mat),
                                 mu = mu.vec, sigma = sigma.vec),
               acceptance = list(gamma=acceptance.lambda/iter,
                                 nu = acceptance.omega/iter)))
}

#---------------------------------------------
#
mcmc.dem.IG.un <- function(y, iter, expo, lambda0 = rep(0,length(y)), omega0 = 0,
                           mu0 = 0, sigma0 = 0.1, eta0 = 0, tau0 = 0.5,
                           alpha0 = 0, beta0 = 0.1, delta0 = 0, xi0 = 0.1,
                           sh.sigma0 = 0.001, sh.tau0 = 0.001,
                           sc.sigma0 = 0.001, sc.tau0 = 0.001,
                           mean.lambda.cand = 0, mean.omega.cand = 0,
                           sd.lambda.cand = 1, sd.omega.cand = 1,
                           model.upd){

  n <- length(y)
  # Space for storing values
  lambda.mat <- matrix(NA, iter, n)
  omega.vec <- c()
  mu.vec <- c()
  sigma.vec <- c()
  eta.vec <- c()
  tau.vec <- c()

  # Initialise

  lambda.mat[1,]<- lambda0
  omega.vec[1] <- omega0
  mu.vec[1] <- mu0
  sigma.vec[1] <- sigma0
  eta.vec[1] <- eta0
  tau.vec[1] <- tau0

  # Acceptance

  acceptance.lambda <- 0
  acceptance.omega <- 0

  # Begin loop
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    lambda.curr <- lambda.mat[(i-1),]
    omega.curr <- omega.vec[(i-1)]
    #
    # Parameters for Gibbs sampling

    # Update mu
    # mean
    num.alpha <- alpha0 / beta0^2 + sum(lambda.mat[(i-1),])/(sigma.vec[(i-1)])^2
    den.alpha <- (1 / beta0^2 + n / (sigma.vec[(i-1)])^2)
    alpha <-  num.alpha / den.alpha
    # sd
    beta <- sqrt(1 / (1 / beta0^2 + n / (sigma.vec[(i-1)])^2))
    #
    mu.vec[i] <- rnorm(1, alpha, beta)

    # Update sigma
    # shape
    sh.sigma <- sh.sigma0 + n / 2
    # scale
    sc.sigma <- sc.sigma0 + 0.5 * sum((lambda.mat[(i-1),] - mu.vec[i])^2)
    #
    sigma.vec[i] <- sqrt(1 / rgamma(1, shape = sh.sigma, scale = sc.sigma))

    # Update eta
    # mean
    num.delta <- delta0 / xi0^2 + sum(omega.vec[(i-1)])/(tau.vec[(i-1)])^2
    den.delta <- 1 / xi0^2 + n / (tau.vec[(i-1)])^2
    delta <-  num.delta / den.delta
    # sd
    xi <- sqrt(1 / (1 / xi0^2 + n / (tau.vec[(i-1)])^2 ))
    #
    eta.vec[i] <- rnorm(1, delta, xi)

    # Update tau
    # shape
    sh.tau <- sh.tau0 + n / 2
    # scale
    sc.tau <- sc.tau0 + 0.5 * sum((omega.vec[(i-1)] - eta.vec[i])^2)
    #
    tau.vec[i] <- sqrt(1 / rgamma(1, shape = sh.tau, scale = sc.tau))

    mu.curr <- mu.vec[i]
    sigma.curr <- sigma.vec[i]
    eta.curr <- eta.vec[i]
    tau.curr <- tau.vec[i]

    # candidate for lambda and omega:
    # by default standard normal or if model.upd == "RW" it is a random walk step
    # or with hyperparameters if Gibbs
    if(model.upd=="RW"){
      mean.lambda.cand <- lambda.mat[(i-1),]
      mean.omega.cand <- omega.vec[(i-1)]
      sd.lambda.cand <- sd.lambda.cand
      sd.omega.cand <- sd.omega.cand
    } else if(model.upd=="Gibbs"){
      mean.lambda.cand <- mu.curr
      mean.omega.cand <- eta.curr
      sd.lambda.cand <- sigma.curr
      sd.omega.cand <- tau.curr
    } else{
      mean.lambda.cand <- mean.lambda.cand
      mean.omega.cand <- mean.omega.cand
      sd.lambda.cand <- sd.lambda.cand
      sd.omega.cand <- sd.omega.cand
    }


    #
    lambda.cand<- rnorm(n, mean.lambda.cand, sd.lambda.cand)
    omega.cand <- rnorm(1, mean.omega.cand, sd.omega.cand)


    # Exchange algorithm for lambda and omega
    par.post.lambda <- c()
    for(k in 1:n){
      par.post.lambda[k] <- a.exch(y[k], lambda.curr[k], omega.curr,
                                   lambda.cand[k], omega.curr,
                                   expo[k], mu.curr, sigma.curr,
                                   eta.curr, tau.curr)$test
    }

    lambda.mat[i,] <- ifelse(par.post.lambda, lambda.cand, lambda.curr)
    acceptance.lambda <- ifelse(par.post.lambda, acceptance.lambda + 1, acceptance.lambda)
    lambda.curr <- lambda.mat[i,]

    par.post.omega <- c()
    par.post.omega <- a.exch1(y, lambda.curr, omega.curr,
                              lambda.curr, omega.cand,
                              expo, mu.curr, sigma.curr,
                              eta.curr, tau.curr)$test
    if(par.post.omega){
      omega.vec[i] <- omega.cand
      acceptance.omega <- acceptance.omega + 1
    } else {
      omega.vec[i] <- omega.curr
      acceptance.omega <- acceptance.omega
    }

  }

  return(list (parameters = list(gamma = exp(lambda.mat), nu = exp(omega.vec),
                                 mu = mu.vec, sigma = sigma.vec,
                                 eta = eta.vec, tau = tau.vec),
               acceptance = list(gamma=acceptance.lambda/iter,
                                 nu=acceptance.omega/iter))
  )
}


#------------------------------------
# No omega only nu
#------------------------------------


mcmc.dem.simple.unif2 <- function(y, iter, expo, gamma0 = rep(1,length(y)), nu0 = rep(1,length(y)),
                                 lgamma0 = log(gamma0),
                                 mu = 0, sigma = 10,
                                 numin = 0.0001, lnumax = 10,
                                 model.upd){
  n <-length(y)
  gamma.mat <- matrix(NA, iter, n)
  nu.mat <- matrix(NA, iter, n)
  
  
  # Initialise
  
  gamma.mat[1,] <-gamma0
  nu.mat[1,] <- nu0
  
  gamma.nu.n <- length(c(gamma0, nu0))
  
  # Acceptance
  
  gamma.nu.acc <- 0
  gamma.acc <- 0
  nu.acc <- 0
  
  # nu and gamma are updated with the exchange algorithm
  # for mu and eta Gibbs sampling
  # sigma and tau MH?
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    gamma.curr <- gamma.mat[i-1,]
    nu.curr <- nu.mat[i-1,]
    lgamma.curr<- log(gamma.curr)
    
    # generate candidates
    
    # candidate for c(gamma, nu):
    if(model.upd == "Norm-Unif"){
    lgamma.cand <- rnorm(n, lgamma.curr, 0.1)
    nu.cand <- runif(n, numin, numax)
    } else if (model.upd == "MVNorm"){
      
      if(i < 500){
        VarCov <- diag(1, gamma.nu.n)
      } else {
        Varlgamma <- apply(gamma.mat[(i-200):(i-1),], 2, var)
        Varnu <- apply(nu.mat[(i-200):(i-1),], 2, var)
        Covlgammanu <- 
        VarCov <- 
      }
      
      gamma.nu.cand <- rmvnorm(n = gamma.nu.n, 
                               mean = c(gamma.mat[i-1,], nu.mat[i-1,]), 
                               sigma = VarCov)
    }
    
    # Exchange algorithm for gamma and nu
    par.post<- c()
    for(k in 1:n){
      par.post[k] <- a.exch.unif2(y[k], lgamma.curr[k], nu.curr[k],
                                 lgamma.cand[k], nu.cand[k], expo[k], mu,
                                 sigma)$test
    }
    
    gamma.mat[i,] <- ifelse(par.post, exp(lgamma.cand), exp(lgamma.curr))
    nu.mat[i,] <- ifelse(par.post, nu.cand, nu.curr))
    gamma.nu.acc <- ifelse(par.post, gamma.nu.acc+1, gamma.nu.acc)
    lgamma.curr <- ifelse(par.post, lgamma.cand, lgamma.curr)
    lnu.curr <- ifelse(par.post, nu.cand, nu.curr)

  }
  
  return(list (parameters = list(gamma = gamma.mat, nu = nu.mat),
               acceptance = list(gamma.nu = gamma.nu.acc/iter,
                                 gamma = gamma.acc/iter,
                                 nu = nu.acc/iter))
  )
}

#-------------------------------------
# Model assuming IG prior on Variance
# (i.e. Gibbs sampling for sigma and tau as conjugate model)
#-------------------------------------

mcmc.dem.IG.unif <- function(y, iter, expo, lambda0 = rep(0,length(y)), omega0 = rep(0,length(y)),
                             mu0 = 0, sigma0 = 0.1,
                             alpha0 = 0, beta0 = 0.1,
                             sh.sigma0 = 0.001, sc.sigma0 = 0.001,
                             mean.lambda.cand = 0, sd.lambda.cand = 1,
                             model.upd, ommin = 0.0001, ommax = 5){
  
  n <- length(y)
  # Space for storing values
  lambda.mat <- matrix(NA, iter, n)
  omega.mat <- matrix(NA, iter, n)
  mu.vec <- c()
  sigma.vec <- c()
  
  # Initialise
  
  lambda.mat[1,]<- lambda0
  omega.mat[1,] <- omega0
  mu.vec[1] <- mu0
  sigma.vec[1] <- sigma0
  
  # Acceptance
  
  acceptance <- 0
  
  # Begin loop
  for(i in 2:iter){
    if(i%%(0.1*iter)==0) print(i)
    lambda.curr <- lambda.mat[(i-1),]
    omega.curr <- omega.mat[(i-1),]
    #
    # Parameters for Gibbs sampling
    
    # Update mu
    # mean
    num.alpha <- alpha0 / beta0^2 + sum(lambda.mat[(i-1),])/(sigma.vec[(i-1)])^2
    den.alpha <- (1 / beta0^2 + n / (sigma.vec[(i-1)])^2)
    alpha <-  num.alpha / den.alpha
    # sd
    beta <- sqrt(1 / (1 / beta0^2 + n / (sigma.vec[(i-1)])^2))
    #
    mu.vec[i] <- rnorm(1, alpha, beta)
    
    # Update sigma
    # shape
    sh.sigma <- sh.sigma0 + n / 2
    # scale
    sc.sigma <- sc.sigma0 + 0.5 * sum((lambda.mat[(i-1),] - mu.vec[i])^2)
    #
    sigma.vec[i] <- sqrt(1 / rgamma(1, shape = sh.sigma, scale = sc.sigma))
    
    mu.curr <- mu.vec[i]
    sigma.curr <- sigma.vec[i]
    
    # candidate for lambda and omega:
    # by default standard normal or if model.upd == "RW" it is a random walk step
    # or with hyperparameters if Gibbs
    if(model.upd=="RW"){
      mean.lambda.cand <- lambda.mat[(i-1),]
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    } else{
      mean.lambda.cand <- mean.lambda.cand
      sd.lambda.cand <- sd.lambda.cand
      omega.cand <- log(runif(n, ommin, ommax))
    }
    
    
    #
    lambda.cand<- rnorm(n, mean.lambda.cand, sd.lambda.cand)
    
    
    
    # Exchange algorithm for lambda and omega
    par.post <- c()
    for(k in 1:n){
      par.post[k] <- a.exch.unif(y[k], lambda.curr[k], omega.curr[k],
                                 lambda.cand[k], omega.cand[k],
                                 expo[k], mu.curr, sigma.curr, ommin, ommax)$test
    }
    
    lambda.mat[i,] <- ifelse(par.post, lambda.cand, lambda.curr)
    omega.mat[i,] <- ifelse(par.post, omega.cand, omega.curr)
    acceptance <- ifelse(par.post, acceptance + 1, acceptance)
    
  }
  
  return(list (parameters = list(gamma = exp(lambda.mat), nu = exp(omega.mat),
                                 mu = mu.vec, sigma = sigma.vec),
               acceptance = acceptance/iter)
  )
}

#-------------------------------------