Multivariate Birth-Death Processes.

MultiBD

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

Installation

1. Install (if necessary) package dependencies and helpers:

install.packages(c("Rcpp", "RcppParallel", "BH", "devtools"))

2. Install MultiBD from github (until package becomes available via CRAN):

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. Birth(death)/birth-death processes and their computable transition probabilities with statistical applications. arXiv preprint arXiv:1603.03819, 2016.