4 votes

How can the Kalman filter be adapted to handle binary observations?

In principle, this is what nonlinear filtering does. Check this out, also under the name "hidden Markov model". Particle filters can be adapted to deal with this setup. In a nutshell, here is what ...
3 votes

Efficiency of the Baum-Welch Algorithm

Advantages: B-W converges to a local maximum of the likelihood function. Disadvantages: the convergence can be very slow. In general, maximizing the likelihood for an HMM is NP-hard, so one wouldn't ...
3 votes
Accepted

The reference on Markov chains uncovering the power of the subject in a better way for a working macro-economist

This may not be a viable route, but if your friend is familiar with Python, a hands-on course might be an effective way to explore Markov chains. The course designed by Sargent and Stachurski guides ...
2 votes

How can the Kalman filter be adapted to handle binary observations?

The Kalman filter is based on an assumption of Gaussian noise in both the observations and process. As I read your problem statement you have no observation noise. Given that, I don't think the KF is ...
1 vote
Accepted

Comprehensive reference for lumped or projected markov chains

The question of what properties are preserved has attracted a lot of attention in dynamics. I think the state of the art is by Mark Piraino, see 'projection of Gibbs states for Hölder potentials.' If ...
1 vote

How can the Kalman filter be adapted to handle binary observations?

What I would try when facing such a problem: 1°) Minimize $\lambda\int p'(t)^2\ dt +$ the sum of informations $\log (1/p(t_k))$ if heads at $t_k$, $\log (1/[1-p(t_k)])$ if tails. 2°) Chose $\lambda$ ...
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1 vote

What is hidden in Hidden Markov Models?

Suppose you want to predict the Stock or Forex market. After your first few failures, you'll come to the conclusion that this is nearly impossible. One reason is you don't know the mechanics of the ...

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