poisson_binomial <-
function(theta) {
N <- length(theta)
if (N == 0) return(c(1))
alpha <- matrix(-Inf, N+1, N+1)
alpha[1,1] <- 1
for(n in 1:N) {
tot = 0
alpha[n+1, tot+1] = alpha[n,tot+1]*(1-theta[n])
if (n > 1) {
for (tot in 1:(n-1)) {
alpha[n+1,tot+1] <- alpha[n,tot] * theta[n] + alpha[n, tot+1]*(1-theta[n])
}
}
tot = n
alpha[n+1,tot+1] = alpha[n,tot]*theta[n]
}
alpha[N+1,1:(N+1)]
}
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