All Questions
Tagged with simulation bayesian
110
questions
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12
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Recycling MCMC samples for another data set from the same distribution
Suppose I'm given $\theta_0$ and I want to sample data from a density $f(Y|\theta_0)$ and then sample from the posterior of $\theta|Y$ (given, obviously, some prior). I want to do this lots of times, ...
- 41.6k
5
votes
1
answer
42
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ABC (Approximate Bayesian Computation) Sampling, Simulating data from Complex models
In ABC sampling methods, Rejection, MCMC and SMC, when we sample potential parameter values from the prior/proposal, we then use those parameters on our model and simulate data values. This can be ...
- 63
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119
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How to compute Expected Squared Jump Distance (ESJD) of a Metropolis-Hastings algorithm
The Expected Squared Jump Distance (ESJD) seems to be defined slightly differently in various papers, which makes this very confusing. For instance, Definition 2.2 of Optimal Scaling of Random-Walk ...
- 2,236
1
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18
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Entries of the matrix variate generalized inverse Gaussian
I'm currently dealing with a Gibbs sampler of the matrix variate generalized inverse Gaussian distribution. In order to check the correctness of the Gibbs sampler, I'd like to know what are the ...
- 19.5k
1
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1
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37
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In what sense do Bayesian models simulate observation?
Could you verify that i understand the author correctly here? New to Bayes.
[...] These assumptions [the prior and the likelihood] also allow us to simulate the observations that the model implies. ...
- 111
0
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1
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89
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Acceptance-Reject to generate a distribution proportionate to Inverse Gamma and truncate Cauchy distribution
Assume $Y_{ij} \sim N(\mu_i,\sigma^2)$, $\mu_i \sim N(\eta,\tau^2)$ for $i=1,2$ $j=1,\cdots,n_i$ and prior $\pi(\eta,\tau^2,\sigma^2) \propto Ca^+(\tau^2,0,b_{\tau}) \times Ca^+(\sigma^2,0,b_{\sigma})$...
- 33
5
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1
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201
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Sampling from the posterior with a constraint on the posterior mean
Background
Under certain assumptions we know that being given the posterior mean and a family of conditional distributions, we can uniquely determine the joint distribution. I quote one of the ...
- 540
2
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0
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73
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Bayesian calibration of computer simulations - Likelihood function calculation
I am starting to study Bayesian calibrations of computer models. I am not a statistician and just starting to learn so bear with me if I do not use the correct terminology.
The general approach is ...
- 121
2
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0
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217
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Why is it easy for the Gibbs sampler to take long time to converge to target distribution?
This is related to Gelman's Bayesian Data Analysis 3rd Edition pg 300 first paragraph of Section 12.4. The book says the following.
"An inherent inefficiency in the Gibbs sampler and Metropolis
...
- 1,445
1
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146
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R statistics: compare bayesian bootstrap to frequentist bootstrap for statistics: univariate odds ratio for small sample [closed]
Greetings to the community, I am seeking assistance in finding a solution to the challenges I am facing.
OBJECTIVES:
I aim to estimate the univariate odds ratio for a binary exposure in a population. ...
- 11
0
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75
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How to use Gibbs sampler to simulate normal-normal hierarchical models?
This is related to Gelman's BDA 3rd Edition Chapter 11, Sec 3. The book says the following.
"The Gibbs sampler is the simplest of the Markov chain simulation algorithms, and it is our first ...
- 1,445
0
votes
0
answers
26
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How to simulate multivariate posterior distribution with a flat prior in general?
If I know that the posterior $p(\theta_1,\dots,\theta_m|y)$ can be written $p(\theta_1|\theta_2,\dots,\theta_m,y)p(\theta_2|\theta_3,\dots,\theta_m|y)\dots p(\theta_m|y)$ where $p(\cdot|y)$ in each ...
- 1,445
1
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0
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57
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Why is my 95% CI from a simulation being either 100% or 0%?
So what I intended doing with the code is to simulate dataset with the outcome being number of parasites that died (yi) out of every n=50 parasites on the host. There are 2 treatment groups (control ...
- 11
0
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0
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22
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Identify name of sampling / simulation strategy
From what I've learned, it seems like in order to simulate draws from a distribution $X \sim p(X)$ one can take advantage of the fact that $p(X) = \int p(X, z)p(z)dz$ and use the following strategy:
...
- 387
1
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11
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circularness of imputing draws via regression in MCAR
Suppose we have covariates $X$ and outcome $Y$. Part of $X$ is missing under MCAR. I am reading Rubin's Missing Data book. I do not see why the following statement making sense intuitively. Let $x,y$ ...
- 1,445