smsPOMDP

R package : solving POMDP problem When to stop managing or surveying cryptic threatened species ?

#smsPOMDP requires the previous intall of the package 'sarsop', available on github
list.of.packages <- c("sarsop")
new.packages <- list.of.packages[!(list.of.packages %in% utils::installed.packages()[,"Package"])]
if(length(new.packages)>0) {
  devtools::install_github("boettiger-lab/sarsop", host = "https://api.github.com")
}

devtools::install_github("conservation-decisions/smsPOMDP", host = "https://api.github.com")
library(smsPOMDP)

The main application of the package is also available: https://conservation-decisions.shinyapps.io/smsPOMDP/

We present our main application in the following article: https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.13501

Problem definition

Our problem is defined by a state space, states, representing the current state of the species (extant and extinct), an action space, actions representing the lead action (manage, survey and nothing), and an observation space, observations, representing the observation of the species (seen and not seen)

To solve the POMDP problem of: When to stop managing or surveying cryptic threatened species ?

Sumatran tiger example

Parameters

We need to fix the POMDP parameters

pen = 0.1 #local probability of extinction P(extinct/extant, survey or nothing)
p0 = 1-pen #local probability of persitance P(extant/extant, manage)
pem = 0.05816 #local probability of extinction if managed P(extinct/extant, manage)
pm = 1 - pem #local probability of persistance if managed P(extant/extant, manage)
d0 = 0.01 #local probability of detection P(present/extant, nothing)
dm = 0.78193 #local probability of detection if surveyed P(present/extant, manage)
d = 0.78193 #local probability of detection if surveyed P(present/extant, survey)
V = 175.133 #Estimated economic value of the species ($/yr)
Cm = 18.784 #Estimated cost of managing ($/yr)
Cs = 10.840 #Estimated cost of surveying ($/yr)

Buildind transition, observation and reward matrices calling smsPOMDP functions

The smsPOMDP package provides a set of functions which compute transition, observation and reward matrices

#transition, observation and reward matrices
Tr = tr(p0, pm, d0, d, V, Cm, Cs)
Ob = obs(p0, pm, d0, d, V, Cm, Cs)
Re = rew(p0, pm, d0, d, V, Cm, Cs)

Resolution of POMDP

You only need to call the 'graph' function, which will provide a decisions diagram

state_prior = c(1,0) #extant : 1, extinct : 0
graph(p0, pm, d0, d, V, Cm, Cs, state_prior)

state_prior = c(0.9,0.1) #extant : 0.9, extinct : 0.1
graph(p0, pm, d0, d, V, Cm, Cs, state_prior)

Simulation

A few more parameters to set and call the 'sim' function

#Initial belief state
state_prior = c(0.9,0.1) #extant : 0.9, extinct : 0.1

#Horizon of the simulation
Tmax = 20

sim(p0, pm, d0, d, V, Cm, Cs, state_prior, Tmax)

Running the app

This package provides a function which lanches an app, which eases the resolution of the problem for the users.

run_application()

Developer Notes

Unfortunately the appl source code of sarsop (https://github.com/boettiger-lab/sarsop) is a bit dated and not suitable for using as a shared library. It builds with lot of warnings and on Windows it only builds with MS Visual Studio. This package tries to make things as easy as possible for the user by bunding the appl executables and wrap them with system calls in R. This package also provides higher-level functions for POMDP analysis.