# Tag Info

• 106k
Accepted

### Writing MCMC Sampling Code by Hand

The code appears to be correct. Note however that the step ...
• 106k

### Estimating sigma in Bayesian inference

A completely flat inverse-Gamma, i.e. letting the shape and scale tend to zero, will often lead to the same problems in practice. Gelman's 2006 paper on prior distributions for variance parameters is ...
• 3,216
Accepted

### Sampling from an approximate distribution to estimate posterior mean

The issue with the question is that the expression$$\mathbb E[\theta_1|x]$$is not well-defined: either $(\theta_1,\theta_2)$ is considered a random vector with joint prior $\pi(\theta_1,\theta_2)$, ...
• 106k
Accepted

### What could lead to this misbehavior for the expected sample size (ESS)?

This is actually not an error - it is possible for the effective sample size to be larger than the actual sample size. This means that your MCMC samples provide more information about the parameter, ...
• 131

### Is there a Quasi-Monte Carlo variant of the Metropolis-Hastings algorithm?

The obvious question is: How do we need to compute the acceptance probability 𝛼? Or the different question is "Why do we need to compute the acceptance probability 𝛼?" If your point is to ...
• 78.7k

### Advice on sensitivity analysis for priors in Bayesian statistics

A reasonable place to start in this particular case is to recognize that the model is unidentified: tau1 and tau2 cannot be ...
• 9,940

• 9,007
1 vote
Accepted

### Jacobian and proposal ratio of Birth/death step in RJMCMC of Gaussian mixture model

For the birth step, we have to create $𝑤_{𝑗^∗}$ and $(μ_{𝑗^∗},σ_{𝑗^∗})$ pair and death step, pair of $𝑤_{𝑗^∗}$ and $(μ_{𝑗^∗},σ_{𝑗^∗})$ are deleted. Correct. However, the probability $A$ in (...
• 106k
1 vote

### Assumptions and setting for bayesian mixture model (for RJMCMC)

When considering a random variable distributed from a mixture model $$Y\sim\sum_{j=1}^k w_j f(y|\theta_j)\tag{1}$$ this random variable can be expressed as the marginal of a pair $(Y,Z)$ of random ...
• 106k
1 vote

### Why do we need to scale the variables in a Bayesian model?

In general, you do not need to scale the variables for a Bayesian model. This may be needed in some, specific, scenarios where you run into numerical issues with the sampling or optimization algorithm ...
• 138k
1 vote

### How can I pool Bayesian parameter estimates after multiple imputation?

Combine the samples from all the individual fits to the imputed data and then use the pooled posterior samples as you would a single fit (e.g. to compute expectations, quantiles, ...). As the number ...
• 2,572
1 vote

### Running Metropolis-Hastings algorithm with changing proposal kernel; each time the kernel is changing starting the algorithm afresh. Does it work?

If I understand the proposed algorithm correctly, we can prove that this doesn't generally sample from the target distribution by way of counter example. And while this algorithm will be a bit ...
• 21.1k
1 vote

### Is it OK to choose the MH proposal as the prior in a posterior simulation problem?

You can choose any distribution you want as a proposal distribution, including, of course, the prior distribution. But there's an interesting thing: Suppose the likelihood function \$L(\theta)=P(x|\...
• 131

Only top scored, non community-wiki answers of a minimum length are eligible