mcmc's questions - Chinese 1answer

952 mcmc questions.

I'm using MCMC to simulation the distribution of some parameters in a Bayesian hierarchical model, which has the following form: $$\gamma_{ik} \sim Ber(\omega_{ik}).$$ Then I make a logit-...

I'm trying to fit this simple varying intercept model with brms: Weight ~ Height + (1|Gender) However sampling is slow (>10mins), effective sample size is low, autocorrelation is large. Although the ...

I am trying to interpret the regression coefficients of a covariate in a Bayesian linear regression problem. More specifically, I am trying to determine if the regression coefficient have an important ...

I am a new user to WINBUGS. I am running a model with 2 chains. When my model has finished running I have the following posterior density plot of my parameter: The plot only shows one distribution (i....

I am currently in the process of implementing a model for soccer result prediction in JAGS. Actually, I have implemented several, but I have reached my most difficult challenge yet: A model described ...

When running MCMC sampling, a common measure of performance is the effective sample size (ESS). There are lots of different ways to estimate the ESS from samples e.g. https://arxiv.org/abs/1011.0175. ...

For numerical Bayesian inference we have Posterior~Prior*Likelihood. In MCMC we do not need to calculate the denominator in Bayes rule. My question is that can I multiply the Likelihood by a large ...

I am trying to estimate a Bayesian Hierarchical model using the random-walk Metropolis-Hastings algorithm. While in a non-Hierarchical model, the algorithm is staight-forward, I am not sure I am ...

I'm reading about Markov chains and I'm starting to bump into these drift conditions, and their relationship with a chain's ergodic properties. The drift condition is that there exists a "scale ...

Lets say I have $n$ posterior samples of $\theta_1$ and $\theta_2$. I suppose that any region $R$ which contains exactly $(1-\alpha)n$ of the points will be an approximate $(1-\alpha)\times100$ ...

I believe MCMC could be utilized to estimate the MAP. At least there is an option in packages like PyMC. I just started reading about Bayesian Optimization, but the first thing that hit me was that ...

I am interested in generating samples from a density $\pi(\theta)$ to construct a histogram for $\pi(\theta)$ and to use these samples to generate samples of $f(\theta)$ for some function $f$. I may ...

I have a BSTS model and need the forecast for the entire period. For example, My training set is between 2008 to 2016 and my testing is 2017 Jan to 2018 Jan. Now I need the predicted values for 2008 ...

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Background We want to sample from some intractable density $\pi(\theta)$. Using an MCMC algorithm, we generate a sample of draws $\{\theta_i\}_{i=1}^N$ from a Markov chain that has $\pi(\theta)$ as ...

I need to generate samples from a pdf given by $\frac{f_Z(z)\cdot 1_{Z \in B}}{P(Z \in B)}$ where $Z \in \mathbb{R}^d$ is a normal random vector with independent components. $Z \in B$ is a set that is ...

I am still new to Bayesian forecasting, so I am hoping to get some clarification on a simple concept (by the sounds of it). Suppose that we are interested in forecasting some time series one-step ...

In the book Introducing Monte Carlo Methods by Casella and Robert, there's a sentence with which I'm having some trouble to understand. «If the domain explored in $q$ [proposal] is too small, ...

I am using the following model in WINBUGS to run a hierarchical Bayesian regression where the beta are my covariates: If I modify this model by adding the ...

Maybe the concept, why it's used, and an example.

Slice Sampling asks to draw uniformly from $f^{-1}]y,+\infty[$. Wikipedia page However, how can we be sure that a uniform defined over the set $f^{-1}]y,+\infty[$ is in fact proper? If I had to ...

I'd like to implement a version of Metropolis-adjusted Langevin sampling, but I'm unsure how to go about tuning the parameters of the proposal density. My understanding is that in MALA, a proposal ...

I'm working with a 6-dimensional Bayesian model, and the affine-invariant sampler implemented in emcee. Four of those parameters are discrete, while the other two ...

In many of the papers on particle filter I've read (e.g. Douc, Moulines and Olsson, 2007), stochastic volatility is a common example to show that a newly-proposed filter is working. At the same time, ...

I'm estimating 15 parameters of my model using a Bayesian approach and a Markov Chain Monte Carlo (MCMC) method. My data after running a MCMC chain of 100000 samples is therefore a 100000×15 table of ...

I am new to Bayesian analysis and using the following WINBUGS example to understand Bayesian hierarchical modeling: This is a 'mixed' model with both fixed effects (covariates given by 'beta' terms) ...

I'm using the affine-invariant sampler from emcee to draw samples from a $p$ dimensional posterior, using $M$ parallel chains ($M>10$). Since my model is p-dimensional with $p>1$, I'm also ...

I am new to Bayesian analysis and using the following WINBUGS example to understand Bayesian hierarchical modeling: I have 2 questions: 1) For the fixed effects terms, i.e., the beta0 and beta1 ...

I am drawing a sample Y of size n from a p-dimensional Normal ($\mu, \Sigma$). Typically, p is 5. I have $\bar{Y}$ and $V = YY'$, the sum of squares. Now I want to draw samples from this $\bar{Y}$, ...

After reading this blog post about Bayesian structural time series models, I wanted to look at implementing this in the context of a problem I'd previously used ARIMA for. I have some data with some ...

I'm wondering if a MCMC algorithm, in a Gibbs or a Metropolis-Hastings style, work for a State-Space model. Would I also be able to learn about the state variable and not just the parameters? I've ...

I am quite new to the using Graphical Models, so pardon me for the naivety. My intention is to have some fun for the weekend and impress my friends on Monday. I am trying to understand MCMC and ...

I recently encounter such an interesting question. For example, if I have want to create a model using x to predict y. A part of ...

MCMC Geweke diagnostic

2 answers, 2.839 views mcmc diagnostic
I'm running a Metropolis sampler (C++) and want to use the previous samples to estimate the convergence rate. One easy to implement diagnostic I found is the Geweke diagnostic, which computes the ...

I have a simple question about model comparison: Let's say you fit two models using MCMC: Model A and model B, where model B is model A minus one parameter. You want to assess whether dropping the ...

I'm using the Delayed Rejection Adaptive Metropolis (DRAM) algorithm (Haario et al., 2006) for some Bayesian inference and trying to get an intuition for it so I can be sure to use it properly. So far ...

I'm trying to understand how to estimate the parameter vector $\mathbf{\theta} = (\theta_1,\theta_2, \theta_3)$ of a model using the MH algorithm. I am given a joint posterior density: $p(\mathbf{\...

From what I have read Hamiltonian Monte Carlo is the "goto" MCMC method when your problem is high dimensional. Practically speaking, how many dimensions 10's, 100'...

I have been noticing that in many practical applications, MCMC-based methods are used to estimate a parameter even though the posterior is analytical (for example because the priors were conjugate). ...

The minimum multi-variate effective sample size (minESS) is defined in the R package mcmcse (where the function is implemented) ...

Basically, the title of the question. I'm wondering if it is reasonable to use the mESS (defined here) to estimate the autocorrelation time $\tau$ as: $$\tau = \frac{N}{mESS}$$ where $N$ is the size ...

Consider performing inference via a standard Gibbs sampler for a standard Gaussian Mixture Model (GMM) with $k$ components that are Gaussians $$\mathcal{N}(\mu_{k}, \sigma^{2}_{k})$$ where we assume ...

A 3-state Markov chain $X = \{x_i : i \in \{1, \cdots, N\}\}$ is observed, and its transition matrix $P$ is assumed to be of the form $$ \begin{pmatrix} (1-a)^2 & 2a(1-a) & a^2 \\ b(1-a) &...

To my understanding Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) have very similar aims. Below I describe my understanding of these methods and how I perceive the ...

The following plots are trace plots of 3 variables for MCMC results of a hierarchical Bayes probit model. The plots are fairly linear and seem to grow (or decline) without bound. This looks like a ...

Consider a posterior density that involves two parameters: $\beta_1$ and $\beta_2$ given by $f(\beta)$ where $\beta = [\beta_1, \beta_2]^T$. We run a MCMC sampler to sample from the posterior and ...

Consider a coin with bias $p$. We generate a random sample $x_1, \dots, x_n \sim \text{Bernoulli}(p)$, but we do not observe results of these coin tosses. Instead, for each $x_i$, we observe a set of ...

I am trying to understand how fitting a model using MCMC works. Is there a loss function that is optimized? Or is it simply a case of more draws from the distribution amount to a more complete ...

I am trying to sample from a posterior having many modes particularly far from each others using MCMC. It appears that in most cases, only one of these modes contains the 95% hpd I am looking for. I ...

I was browsing the github repo for Pymc and found this notebook: Variational Inference: Bayesian Neural Networks The author extols the virtues of bayesian/probabilistic programming but then goes on ...

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