This paper gives a brief introduction to Markov Chain Monte Carlo methods, which offer a general framework for calculating difficult integrals. We start with the basic theory of Markov chains and build up to a theorem that characterizes convergent chains. We then discuss the MetropolisHastings algorithm.

We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differ...

I show how to run an N-time-step Markov chain simulation in a circular fashion, so that the state at time 0 follows the state at time N ?1 in the same way as states at times t follow those at times t?1 for 0 < t < N. This wrap-around of the chain is achieved using a coupling procedure, and produces states that all have close to the equilibrium distribution of the Markov chain, under the assumpt...

which decreases as J gets larger. So the approximation will be more accurate as we obtain more samples. Here is an example of using Monte Carlo methods to integrate away weights in Bayesian neural networks. Let y(x) = f(x,w) for response y and input x, and let p(w) be the prior over the weights w. The posterior distribution of w given the data D is p(w|D) ∝ p(D|w)p(w) where p(D|w) is the likeli...

abstract in this paper, markov chain and dynamic programming were used to represent a suitable pattern for tax relief and tax evasion decrease based on tax earnings in iran from 2005 to 2009. results, by applying this model, showed that tax evasion were 6714 billion rials**. with 4% relief to tax payers and by calculating present value of the received tax, it was reduced to 3108 billion rials. ...

the probable lack of some arcs and nodes in the stochastic networks is considered in this paper, and its effect is shown as the arrival probability from a given source node to a given sink node. a discrete time markov chain with an absorbing state is established in a directed acyclic network. then, the probability of transition from the initial state to the absorbing state is computed. it is as...

background & aim: chronic diseases impact not only on patients but also on their family members’ lives. this study aims to determine dimensions of family dermatology life quality index (fdlqi) questionnaire by the use of classic and bayesian factor analysis (bfa) factor. methods & materials: in this study, fdlqi questionnaire distributed among 100 family members of dermatological patients. bfa ...

Finite, discrete-time Markov chain models of genetic algorithms have been used successfully in the past to understand the complex dynamics of a simple GA. Markov chains can exactly model the GA by accounting for all of the stochasticity introduced by various GA operators, such as initialization, selection, crossover, and mutation. Although such models quickly become unwieldy with increasing pop...

Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.