Multivariate Birth-Death Processes.

MultiBD

MultiBD is an R package for direct likelihood-based inference of multivariate birth-death processes.

Installation

1. Install CRAN release version:

install.packages("MultiBD")

2. Install the bleeding-edge version of MultiBD from github:

devtools::install_github("msuchard/MultiBD")

Short example

library(MultiBD)
data(Eyam)

loglik_sir <- function(param, data) {
  alpha <- exp(param[1]) # Rates must be non-negative
  beta  <- exp(param[2])
  
  # Set-up SIR model
  drates1 <- function(a, b) { 0 }
  brates2 <- function(a, b) { 0 }
  drates2 <- function(a, b) { alpha * b     }
  trans12 <- function(a, b) { beta  * a * b }
  
  sum(sapply(1:(nrow(data) - 1), # Sum across all time steps k
             function(k) {
               log(
                 dbd_prob(  # Compute the transition probability matrix
                   t  = data$time[k + 1] - data$time[k], # Time increment
                   a0 = data$S[k], b0 = data$I[k],       # From: S(t_k), I(t_k)                                      
                   drates1, brates2, drates2, trans12,
                   a = data$S[k + 1], B = data$S[k] + data$I[k] - data$S[k + 1],
                   computeMode = 4, nblocks = 80         # Compute using 4 threads
                 )[1, data$I[k + 1] + 1]                 # To: S(t_(k+1)), I(t_(k+1))
               )
             }))
}

loglik_sir(log(c(3.204, 0.019)), Eyam) # Evaluate at mode

Vignettes

1. Simple MCMC under SIR
2. SIR model and proposed branching approximation

License

MultiBD is licensed under Apache License 2.0

Development status

Beta

Acknowledgements

• This project is supported in part through the National Science Foundation grant DMS 1264153 and National Institutes of Health grant R01 AI107034.

References

1. Ho LST, Xu J, Crawford FW, Minin VN, Suchard MA (2018). Birth/birth-death processes and their computable transition probabilities with biological applications. Journal of Mathematical Biology 76(4) 911-944.
2. Ho LST, Crawford FW, Suchard MA (2018). Direct likelihood-based inference for discretely observed stochastic compartmental models of infectious disease. Annals of Applied Statistics. In press.