Gibbs sampling
Why Cross Validated Stack Exchange recommends it
Stats Stack Exchange users link it as a quick introduction to Gibbs sampling and as a reference when they implement the bivariate normal example or ask how its full conditionals are derived.
Recommended by 2 people across 2 different months, 2016 to 2021.
What it is
A short mini-lecture by Jarad Niemi explaining Gibbs sampling, including a worked bivariate normal example where each variable is sampled from its full conditional distribution. It is an 8-minute screen lecture aimed at students new to MCMC.
What people said
Recommends Xi'an · 2016-06 · Cross Validated Stack Exchange · on “Gibbs sampling and conditional distribution”
If you do not know about Gibbs sampling, you should invest into an introduction to the topic. See for instance this mini-lecture [this video] . Or this longer one [LINK] about MCMC. About minute 34 for reaching Gibbs sampling.
Recommends mjake · 2020-08 · Cross Validated Stack Exchange · on “Deriving full conditionals from joint distributions?”
In this link ( [this video] ), the author derives the conditional distributions from the joint; but I got lost in the mechanics of what happened, the process was overly simplified. The topic of the video was on Gibbs Sampling, the derivation of full conditionals was not the subject but a supporting part of the video. When I try to prove that his conditional distributions are accurate and I write the full joint PDF, divided a single variable PDF, I get a messy equation that is not easy to simplify. $$\theta ~ N_2\left(\mu= \begin{bmatrix} 0\\0\end{bmatrix}, cov = \begin{bmatrix}1 &0.9 \\ 0.9 & 1 \end{bmatrix}\right)$$ $$\theta_1|\theta_2 \sim N(\mu= 0.9\theta_2, \sigma= 1-0.9^2)$$ $$\theta_2|\thet
Cites jbuddy_13 · 2020-06 · Cross Validated Stack Exchange · on “python gibbs sampler for bivariate normal distribution, failing to converge”
I've been trying to understand Gibbs sampling for some time. Recently, I saw a video that made a good deal of sense. [this video] The author used Gibbs sampling to converge on the mean values (theta_1 and theta_2) of a bivariate normal distribution, using the process as follows: init: Initialize theta_2 to a random value. Loop: sample theta_1 conditioned on theta_2 as N~(p(theta_2), [1-p**2]) sample theta_2 conditioned on theta_1 as N~(p(theta_1), [1-p**2]) (repeat until convergence.) I tried this on my own and ran into an issue: import matplotlib.pyplot as plt from scipy.stats import multivariate_normal rv = multivariate_normal(mean=[0.5, -0.2], cov=[[1, 0.9], [0.9, 1]]) rv.mean >>> array([ 0.5,
Cites stats_noob · 2021-09 · Cross Validated Stack Exchange · on “Details of the Metropolis-Hastings Algorithm”
Clarifying the Metropolis-Hastings Algorithm: 1) Metropolis-Hastings: In Bayes Law : P(thetha|data = [P(data|thetha) * P(thetha)] / P(Data) In the continuous case: P(Data) = integral of [ P(Data|thetha) * P(thetha)] for all values of thetha Suppose we say "integral of [ P(Data|thetha) * P(thetha)] " = Z . Z is some constant. Then: P (thetha | data ) = [P (Data | thetha) * P (thetha)] / Z For initialization, take a random sample from : P (thetha | data ) . This random sample is divided by Z (as a formality). Call this sample as x-i. Now, define a "candidate distribution" as "g" - e.g. "g" is a normal distribution with a mean of 0 and variance of 1000. Sample some number from "g". Call this sa