# Step-by-step hidden Markov chain log-likelihood calculation
**URL:** https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527
**Category:** Statistics
**Tags:** question
**Created:** [November 23, 2016, 3:12pm UTC](https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527 "2016-11-23T15:12:44Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [November 23, 2016, 3:12pm UTC](https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527/1 "2016-11-23T15:12:44Z")
I have a HMC for which the transition and observation matrices are time varying (and have some 0 elements).
I would like to calculate the log-likelihood (for Bayesian inference). Which library should I use? I looked at a few of them, but they seemed to have a high-level interface for constant matrices, and I need the low-level building blocks for updating, because of the time variation.
I need a numerically stable implementation, I can always program the algorithm from Rabiner’s tutorial, but would prefer not to do it if it has been done. Playing well with `AutoDiff.jl` would be a bonus (for NUTS/Hamiltonian MC).
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### Author:  [@jmxpearson](https://discourse.julialang.org/u/jmxpearson)
#### Post date: [November 24, 2016, 1:17pm UTC](https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527/2 "2016-11-24T13:17:19Z")
Not sure about AutoDiff.jl, but our code follows the conventions of Distributions.jl and will work with ForwarDiff.jl:
[https://github.com/jmxpearson/VinDsl.jl/blob/master/src/distributions/HMM.jl](https://github.com/jmxpearson/VinDsl.jl/blob/master/src/distributions/HMM.jl)
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### Author:  [@pint](https://discourse.julialang.org/u/pint)
#### Post date: [November 24, 2016, 1:47pm UTC](https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527/3 "2016-11-24T13:47:05Z")
something weird is going on with the logz member. you don’t set it in the constructor, but you use it later. maybe simply missing from new?
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### Author:  [@jmxpearson](https://discourse.julialang.org/u/jmxpearson)
#### Post date: [November 24, 2016, 2:14pm UTC](https://discourse.julialang.org/t/step-by-step-hidden-markov-chain-log-likelihood-calculation/527/4 "2016-11-24T14:14:47Z")
Thanks for that. Fixed now.