How to MCMC (or other simulation) given a non-stationary distribution?
Say I was given some directed graph that satisfies the Markov property, has a stationary distribution, $pi$, and I know the transition probabilities are functions of some unknown parameters $P_{ito j}=p(pmb{alpha})$, where $pmbalpha$ is a vector of unknown parameters (pardon my poor probability notation here). I know that I can use Markov Chain Monte Carlo to simulate the stationary distribution, $pi$, to calculate the posterior for $pmbalpha$. However, I am curious if MCMC can still be used to get the posterior if you were given some non-stationary distribution instead? By non-stationary, I mean non-equilibrium distribution here.
In example, let $t>0$ be time and $T$ be the time it takes for the graph to reach the equilibrium (stationary) state. Now say your experiment/data takes too long to reach equilibrium and you can only sample the data at some time $t_0<T$. Can you still use that distribution to get the posterior and thereby infer $pi$?
stochastic-processes markov-chains machine-learning markov-process monte-carlo
asked Dec 26 '18 at 17:20
MasterYoda
94829
add a comment |
Say I was given some directed graph that satisfies the Markov property, has a stationary distribution, $pi$, and I know the transition probabilities are functions of some unknown parameters $P_{ito j}=p(pmb{alpha})$, where $pmbalpha$ is a vector of unknown parameters (pardon my poor probability notation here). I know that I can use Markov Chain Monte Carlo to simulate the stationary distribution, $pi$, to calculate the posterior for $pmbalpha$. However, I am curious if MCMC can still be used to get the posterior if you were given some non-stationary distribution instead? By non-stationary, I mean non-equilibrium distribution here.
In example, let $t>0$ be time and $T$ be the time it takes for the graph to reach the equilibrium (stationary) state. Now say your experiment/data takes too long to reach equilibrium and you can only sample the data at some time $t_0<T$. Can you still use that distribution to get the posterior and thereby infer $pi$?
stochastic-processes markov-chains machine-learning markov-process monte-carlo
asked Dec 26 '18 at 17:20
MasterYoda
94829
add a comment |
Say I was given some directed graph that satisfies the Markov property, has a stationary distribution, $pi$, and I know the transition probabilities are functions of some unknown parameters $P_{ito j}=p(pmb{alpha})$, where $pmbalpha$ is a vector of unknown parameters (pardon my poor probability notation here). I know that I can use Markov Chain Monte Carlo to simulate the stationary distribution, $pi$, to calculate the posterior for $pmbalpha$. However, I am curious if MCMC can still be used to get the posterior if you were given some non-stationary distribution instead? By non-stationary, I mean non-equilibrium distribution here.
In example, let $t>0$ be time and $T$ be the time it takes for the graph to reach the equilibrium (stationary) state. Now say your experiment/data takes too long to reach equilibrium and you can only sample the data at some time $t_0<T$. Can you still use that distribution to get the posterior and thereby infer $pi$?
stochastic-processes markov-chains machine-learning markov-process monte-carlo
asked Dec 26 '18 at 17:20
MasterYoda
94829
Say I was given some directed graph that satisfies the Markov property, has a stationary distribution, $pi$, and I know the transition probabilities are functions of some unknown parameters $P_{ito j}=p(pmb{alpha})$, where $pmbalpha$ is a vector of unknown parameters (pardon my poor probability notation here). I know that I can use Markov Chain Monte Carlo to simulate the stationary distribution, $pi$, to calculate the posterior for $pmbalpha$. However, I am curious if MCMC can still be used to get the posterior if you were given some non-stationary distribution instead? By non-stationary, I mean non-equilibrium distribution here.
In example, let $t>0$ be time and $T$ be the time it takes for the graph to reach the equilibrium (stationary) state. Now say your experiment/data takes too long to reach equilibrium and you can only sample the data at some time $t_0<T$. Can you still use that distribution to get the posterior and thereby infer $pi$?
stochastic-processes markov-chains machine-learning markov-process monte-carlo
stochastic-processes markov-chains machine-learning markov-process monte-carlo
asked Dec 26 '18 at 17:20
MasterYoda
94829
asked Dec 26 '18 at 17:20
MasterYoda
94829
asked Dec 26 '18 at 17:20
MasterYoda
94829
asked Dec 26 '18 at 17:20
MasterYoda
94829
asked Dec 26 '18 at 17:20
MasterYoda
94829
94829
add a comment |
add a comment |
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