Contents
What can MCMC be used for?
MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals, for example in Bayesian statistics, computational physics, computational biology and computational linguistics.
Is MCMC always Bayesian?
MCMC methods are generally used on Bayesian models which have subtle differences to more standard models. As most statistical courses are still taught using classical or frequentist methods we need to describe the differences before going on to consider MCMC methods.
What is the inference problem?
The inference problem in databases occur when sensitive information can be disclosed from non- sensitive data and metadata (see Figure 1). Metadata may refer to database constraints, like database dependencies and integrity constraints, or outside information, like do- main knowledge and query correlations.
How are Markov chain Monte Carlo algorithms used in Bayesian inference?
In this article we introduce the main family of algorithms, known collectively as Markov Chain Monte Carlo (MCMC), that allow us to approximate the posterior distribution as calculated by Bayes’ Theorem. In particular, we consider the Metropolis Algorithm, which is easily stated and relatively straightforward to understand.
When did Bayesian inference via MCMC become popular?
Baysian inference via MCMC was the bandwagon of the nineties in statistics. It usage exploded after 1990 (Google Ngram is seriously distorted because it looks only at books, not scientific papers, but Google Trends only goes back to 2004 after the popularity had already peaked).
How does PyMC3 carry out Bayesian inference in Python?
PyMC3 is a Python library (currently in beta) that carries out “Probabilistic Programming”. That is, we can define a probabilistic model and then carry out Bayesian inference on the model, using various flavours of Markov Chain Monte Carlo. In this sense it is similar to the JAGS and Stan packages.
How is MCMC used in the real world?
As an aside, MCMC is not just for carrying out Bayesian Statistics. It is also widely used in computational physics and computational biology as it can be applied generally to the approximation of any high dimensional integral. Markov Chain Monte Carlo Algorithms