# Questions tagged [markov-chain-montecarlo]

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.

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### What are good options for deriving probability distributions of transition matrices when data lacks the memoryless property of a Markov chain?

I have a dataset which I initially believed was suitable for running Markov chain simulations, in that there is a finite number of readily identifiable states that all population elements fall into ...
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### Monte Carlo for Dirichlet Multinomial Model

Problem I am trying to implement Markov Chain Monte Carlo for the Dirichlet Multinomial mixture, described in this reference (where one used the expectation maximization algorithm). The model is as ...
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• 101
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### Can we generate HPD regions from MCMC draws using convex hulls?

I thought of a procedure to generate high probability density regions with probability $1-\alpha$ from $n$ MCMC draws: Find the $\lfloor(1-\alpha)\cdot n\rfloor$ draws with the largest probability ...
• 2,536
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### Best method(s) to estimate the parameters of a stochastic process with a hybrid (i.e. switching) random input variable?

I'm looking for the best approach to and/or methods of solving the following inference problem. I have tried searching for similar questions but don't have enough knowledge on the various methods (...
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### Why don't we see Copula Models as much as Regression Models?

Is there any reason that don't see Copula Models as much as we see Regression Models (e.g. https://en.wikipedia.org/wiki/Vine_copula, https://en.wikipedia.org/wiki/Copula_(probability_theory)) ? I ...
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### Effective Sample Size for a cycle or mixture of kernels

The Effective Sample Size (ESS) of a univariate Markov Chain can be used to assess it performance. Is there a version of the ESS for when the Markov Kernel is a mixture $\alpha K_1 + (1-\alpha) K_2$ ...
• 1,458
1 vote
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### What is the relationship between model uncertianty and model parameter count?

I'm looking for references, information and/or existing theory behind the relationship between the uncertainty in a given model vs its complexity/parameter count. The situation I have in mind is using ...
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### How are copulas used in the real world?

I have been reading about copula models. Essentially, copula models seem to be a creative method for creating a joint probability distribution from several variables, in which each individual variable ...
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### What kind of bayesian approach should be used for expenditure reasearch?

I must find determinants of expenditure which using baysian approach. Dependent variable: LN education expenditure Independent variables: continuous: LN income, study year of mom, commuting time to ...
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### Why is my proportion estimate 0? (BEST MCMC Bayesian inference)

I am trying to run a simple Bayesian inference on my y1 vector as shown below. ...