Lecture

Markov Chain Monte Carlo: Sampling and Convergence

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In course

MGT-484: Applied probability & stochastic processes

This course focuses on dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We will also study applications in queuing theory, finance, project management, etc. ...

Description

This lecture covers the concept of Markov Chain Monte Carlo (MCMC) for sampling from high-dimensional distributions. It explains the challenges of sampling when the normalization constant is unknown and introduces the Metropolis-Hastings algorithm. The lecture discusses the construction of a Markov chain with a desired stationary distribution, detailed balance conditions, and convergence properties. It also explores the application of MCMC in practice for optimizing functions and sampling from complex distributions.

Instructor

Negar Kiyavash

Teaching & PhD PhD Students Mohammad Shahverdikondori, Badri Mohammad Reza, Arefe Boushehrian, Sepehr Elahi, Mohammadsadegh Khorasani, Mohammadsaeed Masiha, Amir Mohammad Aboueimehrizi Past EPFL PhD Students Sina Akbari, Ehsan Mokhtarian, Yaroslav Kivva, Fateme Jamshidi Courses Causal inference MGT-416 Students will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory andapplication will be balanced, with students working directly with networ

Official source

Related concepts (32)

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Stratified sampling

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population.

Convenience sampling

Convenience sampling (also known as grab sampling, accidental sampling, or opportunity sampling) is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand. This type of sampling is most useful for pilot testing. Convenience sampling is not often recommended for research due to the possibility of sampling error and lack of representation of the population. But it can be handy depending on the situation. In some situations, convenience sampling is the only possible option.

Sampling error

In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. It can produced biased results. Since the sample does not include all members of the population, statistics of the sample (often known as estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters). The difference between the sample statistic and population parameter is considered the sampling error.

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