Who explains Bayesian inference with Hamiltonian Monte Carlo?
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I recently found an amazing and useful explanation of Bayesian inference with Hamiltonian Monte Carlo by M. N. Neyshabur (2015, ArXiv), in his excellent blog post “Implementing Hamiltonian Monte Carlo: An Update on the Concept and its Impact”. In this post, he provides a step-by-step tutorial on how to implement Hamiltonian Monte Carlo for Bayesian inference in Python. I followed his instructions step by step, and as you can see, my implementation is exactly the same as Neyshabur’s.
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For those who might not know, BIBO (Bayesian Inference with Batches of Samples) is a method for constructing estimates (or “hypothetical conclusions”) of unknown parameters (in Bayesian terms) using batches of samples from a dataset. The method works by using a Monte Carlo method to draw from a posterior probability distribution, which is the probability of the unknown parameters given observed data. The samples are drawn from the posterior probability distribution, weighted by their posterior probabilities. One method of estimating
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Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo algorithm that relies on Hamiltonian dynamics to keep track of the state of the underlying process. In HMC, a Hamiltonian is constructed to minimize a non-differentiable cost function while taking into account the current step’s probability, using a variant of the rejection sampling algorithm. For an algorithm that takes a stochastic differential equation (SDE) as input, the Hamiltonian dynamics generate a Markov chain of trajectories with corresponding samples. At each step, the Hamiltonian dynamics generate the next state
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Bayesian inference is a powerful technique used to analyze and model data in a variety of scientific and engineering fields. One of the most commonly used tools in Bayesian inference is Hamiltonian Monte Carlo (HMC). HMC is a powerful tool used to approximate the full posterior distribution in high-dimensional problems. here are the findings It is an optimal numerical algorithm used for computing posterior distributions when the number of parameters is large. HMC’s method, developed by John Le Cam in 1982, was named after a character from La Belle et La Bête, a French fairy tale. HMC has
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I was amazed to read in my professor’s lecture that students need assistance with this important concept of Bayesian inference. click for more Why? The explanation was inadequate. My heart started racing with excitement. The answer was clear — I had to write it down on paper and share with my friends. After weeks of preparation, here is what I wrote for my professor: Bayesian inference is the scientific theory that guides decision-making. It predicts that probabilities of an event happening in the future depend on both the present and past events. In practice, this
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Bayesian inference is the central topic in statistics. The theory of Bayes’ theorem and posterior distributions is the cornerstone of the field. The theory has many implications. For example, Bayesian methods are used to model complex, stochastic models and to analyze data from them. In our field, we use the theory of Bayesian inference to perform data analysis, modeling, and prediction. This topic, however, requires some understanding of Hamiltonian Monte Carlo (HMC). HMC is a statistical method for sampling from probability distributions that are intractable for analytic computation