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Results tagged with markov-chain-montecarlo
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user 53332
Markov Chain Monte Carlo (MCMC) refers to a class of simulation methods for generating samples from a complex target distribution by generating random numbers from a Markov Chain whose stationary distribution is the target distribution. MCMC methods are typically used when more direct methods for random number generation (e.g. inversion method) are infeasible. The very first MCMC method was the Metropolis (et al.) algorithm, later expanded by Hastings.
9
votes
1
answer
407
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Using a black box MCMC algorithm as a proposal distribution
Let's say I have some MCMC algorithm implemented as a function, black_box(x), which generates samples from $P(x)$ when run in a chain. I would now like to sample from $P(x)G(x)$. Is it possible to use …
- 285
1
vote
0
answers
109
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Gibbs within Collapsed Gibbs?
I have a model with variables $X_{1}, X_{2}, X_{3}, X_{4}$. I would like to sample it within a larger MCMC chain using:
$(X_{1}, X_{2}) \sim P(X_{1}, X_{2})$
$(X_{3}, X_{4}) \sim P(X_{3}, X_{4} \mid …
- 285
0
votes
0
answers
119
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Gibbs within Metropolis
Consider a model with two parameters, $\alpha$ and $\beta$. We want to sample these two parameters conditioning on two data points, $d_1$ and $d_2$. Is it possible to use an algorithm like this:
1) S …
- 285
1
vote
1
answer
455
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MCMC sampling with sum constraints
I'm interested in sampling a collection of variables with a sum constraint on them. For a simplified example:
Prior:
$X \sim \mathcal{N}(0, 1)$
$Y \sim \mathcal{N}(0, 1)$
Observation:
$X + Y = 1$ …
- 285
2
votes
0
answers
208
views
Gibbs sample from AR(1) of exogenous input
I am trying to fit a model where there is a sequence of exogenous "shocks", $X_1, X_2, ..., X_T$, and a AR(1) of these shocks explain $Y_1, Y_2, ..., Y_T$. Specifically,
Data (known):
$X_1, X_2, ... …
- 285