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Finite Markov chains

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TLDR
This lecture reviews the theory of Markov chains and introduces some of the high quality routines for working with Markov Chains available in QuantEcon.jl.
Abstract
Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their own right You will find them in many of the workhorse models of economics and finance. In this lecture we review some of the theory of Markov chains. We will also introduce some of the high quality routines for working with Markov chains available in QuantEcon.jl. Prerequisite knowledge is basic probability and linear algebra.

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Book

Principles of Model Checking

TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Journal ArticleDOI

Learning to Predict by the Methods of Temporal Differences

Richard S. Sutton
- 01 Aug 1988 - 
TL;DR: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior – and proves their convergence and optimality for special cases and relation to supervised-learning methods.
Journal ArticleDOI

Markov Chains for Exploring Posterior Distributions

Luke Tierney
- 01 Dec 1994 - 
TL;DR: Several Markov chain methods are available for sampling from a posterior distribution as discussed by the authors, including Gibbs sampler and Metropolis algorithm, and several strategies for constructing hybrid algorithms, which can be used to guide the construction of more efficient algorithms.
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Anisotropic diffusion in image processing

TL;DR: This work states that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition, which means that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution.