MCMC from Scratch: A Practical Introduction to Markov Chain Monte Carlo

Price: $54.99
(as of Jan 22,2025 02:44:48 UTC – Details)

Publisher ‏ : ‎ Springer; 1st ed. 2022 edition (October 21, 2022)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 203 pages
ISBN-10 ‏ : ‎ 9811927146
ISBN-13 ‏ : ‎ 978-9811927140
Item Weight ‏ : ‎ 1.13 pounds
Dimensions ‏ : ‎ 6.14 x 0.63 x 9.29 inches

Markov Chain Monte Carlo (MCMC) is a powerful statistical technique used for sampling from complex probability distributions. In this post, we will provide a practical introduction to MCMC from scratch, covering the basic concepts and steps involved in implementing an MCMC algorithm.

First, let’s start with the basics. MCMC is a method for generating a sequence of random samples from a target probability distribution. It does this by constructing a Markov chain that has the desired distribution as its stationary distribution. In other words, the samples generated by the Markov chain will eventually converge to the target distribution.

The key idea behind MCMC is to simulate a Markov chain that explores the target distribution by transitioning from one state to another based on transition probabilities. The chain is constructed in such a way that the distribution of states visited by the chain converges to the target distribution as the number of iterations approaches infinity.

To implement an MCMC algorithm from scratch, the following steps are typically involved:

1. Choose a proposal distribution: The proposal distribution determines how the Markov chain transitions from one state to another. It should be easy to sample from and should have a high acceptance rate.

2. Initialize the Markov chain: Start the chain at a random initial state.

3. Generate a proposal state: Sample a new state from the proposal distribution.

4. Calculate the acceptance probability: Compute the acceptance probability based on the ratio of the target distribution at the proposed state and the current state.

5. Accept or reject the proposal: Accept the proposal with probability equal to the acceptance probability. If the proposal is rejected, stay at the current state.

6. Update the Markov chain: Move to the accepted state and repeat the process.

By iterating through these steps, the Markov chain will eventually converge to the target distribution, and the samples generated by the chain can be used for inference and estimation.

In conclusion, Markov Chain Monte Carlo is a versatile and powerful technique for sampling from complex probability distributions. By understanding the basic concepts and steps involved in implementing an MCMC algorithm from scratch, you can leverage this technique in various statistical and machine learning applications.
#MCMC #Scratch #Practical #Introduction #Markov #Chain #Monte #Carlo,machine learning: an applied mathematics introduction