Introduction to Probability · 免费预览
梅特罗波利斯-黑斯廷斯算法与吉布斯采样
通过构造平稳分布为目标分布的马尔可夫链来对难以采样的分布进行采样：采用接受-拒绝规则的 Metropolis-Hastings 方法，以及基于完全条件分布的 Gibbs 采样。
1. The problem MCMC solves
The problem MCMC solves
2. Metropolis-Hastings
Metropolis-Hastings
3. Gibbs sampling
Gibbs sampling
4. Using the samples honestly
Using the samples honestly
5. The Metropolis acceptance rule
In Metropolis-Hastings with symmetric proposals, a move from i to j with f(j) = 6 and f(i) = 2 is proposed. What happens?
6. Why detailed balance matters here
What does verifying detailed balance for the Metropolis chain immediately imply?
7. Downhill acceptance
Metropolis with symmetric proposals proposes a move with target values f(i) = 8 and f(j) = 2. With what probability is it accepted? Enter a decimal like 0.25.
8. Stationary by construction
A Metropolis chain ran 10000 steps visiting state A 6000 times and state B 4000 times. The target ratio f(A)/f(B) is estimated as what? Enter like 1.5.
9. A Gibbs step
In Gibbs sampling for a joint distribution of X and Y, one full sweep consists of drawing X from its conditional given the current Y, then Y from its conditional given the new X. How many random draws per sweep for two variables? Enter an integer.
10. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.