How deeply does Causal AI cover markov chain monte carlo?

Explains accept/reject chains and limiting convergence, then applies MCMC within a causal inference workflow.

Markov chain monte carlo

As explained in Causal AI

Markov chain Monte Carlo is a family of sampling algorithms that generate a Markov chain whose limiting distribution is a target probability distribution.

Markov chain Monte Carlo (MCMC) performs probabilistic inference by generating a chain of outcomes: each accepted outcome depends on the previous one, and the chain’s distribution eventually converges to a target distribution. section 2.2.5

For causal questions, MCMC follows model transformation. An intervention modifies the causal generative model, conditioning adds observed information, and probabilistic inference then generates samples from the resulting distribution. section 11.6.2

A practical MCMC workflow is:

Transform the causal model with the required intervention, such as setting a variable with Pyro’s do function. section 11.6.2
Condition on observations when the query requires them. section 11.6.2
Run an MCMC algorithm to generate samples from the transformed or conditioned distribution. section 2.2.5 section 11.6.2

Online gaming intervention

An online gaming model targets P(IE = 0) and P(IE = 0 | E = 1). The intervention E = 0 is applied to the model; for the conditional query, E = 1 is also observed. MCMC then generates samples for each target distribution. section 11.6.2

Hamiltonian Monte Carlo (HMC) is a popular MCMC variant that avoids requiring users to implement the generator. Pyro and PyMC provide HMC and other MCMC algorithms. section 2.2.5

How Causal AI covers it

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Also explained in

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Machine Learning Algorithms in DepthMarkov chain Monte Carlo is a Monte Carlo methodology that samples a Markov chain to approximate a target probability distribution, typically a posterior distribution.

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Related concepts

metropolis-hastings samplingincludes · Metropolis-Hastings sampling is a Markov chain Monte Carlo method that proposes state changes and accepts or rejects them probabilistically to generate samples from a target distribution.
stochastic variational inferencealternative to · Stochastic variational inference is a variational inference technique that optimizes an objective using stochastic estimates, often computed from randomly sampled data subsets.
variational inferencealternative to · Variational inference is an approximate inference technique that optimizes a tractable family of probability distributions to approximate a target distribution, often a posterior.
posterior probabilityuses · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
Markov chainuses · A Markov chain is a stochastic process of states whose transition probabilities depend on the current state rather than the full preceding history.
gibbs samplingincludes · Gibbs sampling is a Markov chain Monte Carlo technique that repeatedly samples each variable from its conditional distribution given the others.

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