Sketch BFFG markov chain

chain.jl

xnew = sample(A[x, :]) 

struct TransitionKernel
   A::Matrix 
end
(kappa::TransitionKernel)(x) = kappa.A[x, :]

A = [0.5 0.5 0
     0 0.3 0.7
     1/3 1/3 1/3
]

kappa = TransitionKernel(A)

x = 2
kappa(x) == [0.0, 0.3,0.7] 


function backward(kappatilde::TransitionKernel, h)
  hout = kappatilde.A*h
  message = (hout, h)
  return message, hout
end


function forward(kappa::TransitionKernel, message, x)
    A = kappa.A
    hout, h = message
    samplefrom = A[x, :] .* h
    samplefrom ./ sum(samplefrom)
end



hT = [0, 0, 1]
message, hout = backward(kappatilde, hT)
...
...

x = sample(forward(kappa, message, x))