bs: Backwards sampling algorithm for Hidden Markov Models

In jmhewitt/dsdive: Discrete Space Models for Dive Trajectories of Animals

Description

Implementation of backwards sampling algorithm described in Appendix A of Rao and Teh (2013).

Usage

bs(a, B, L)

Arguments

a	collection of forward filtering distributions
B	collection of uniformized single-step transition matrices
L	likelihood matrix where each column is the probability distribution for the state at each of the discrete transitions

References

Rao, Vinayak, and Yee Whye Teh. "Fast MCMC sampling for Markov jump processes and extensions." The Journal of Machine Learning Research 14.1 (2013): 3295-3320.

Examples

data('dive.sim')
attach(dive.sim)
attach(dive.sim$params)

# uniformized transition rate
r.unif = max(outer(lambda, 2 * depth.bins$halfwidth, '/'))

# single-step transition matrix
m = dsdive.tx.matrix.uniformized(depth.bins = depth.bins, beta = beta, 
                                 lambda = lambda, s0 = 2, 
                                 rate.uniformized = r.unif)

# number of states
k = nrow(m)

# number of transitions
N = 10

# list of transition matrices
B = lapply(1:N, function(i) m)

# starting and ending coordinates
x0 = 5
xN = 10

# encode likelihood information
L = matrix(0, nrow = k, ncol = N+1)
L[x0,1] = 1                           # fixed starting location
L[xN,N+1] = 1                         # fixed ending location
L[,-c(1,N+1)] = 1/k                   # free transitions
L[x0,2] = 0                           # force a transition by 2nd step
L = sweep(L, 2, colSums(L), '/')      # restandardize likelihood

# forward filter
a = ff(B = B, L = L)

# backwards sample
set.seed(2019)
y = bs(a = a, B = B, L = L)

# execute forward filtering and backwards sampling via wrapper
set.seed(2019)
x = ffbs(B = B, L = L)

# sampling steps are identical
identical(x,y)

detach(dive.sim$params)
detach(dive.sim)

jmhewitt/dsdive documentation built on May 29, 2020, 5:18 p.m.