Markov Chain Monte Carlo (MCMC) methods are often used to sample from intractable target distributions. Some MCMC variants aim to improve the performance by running a population of MCMC chains. In this paper, we investigate the use of techniques from Evolutionary Computation (EC) to design population-based MCMC algorithms that exchange useful information between the individual chains. We invest...

Let $\{s_n\}_{n\in \mathbb N}$ be a decreasing nonsummable sequence of positive reals. We investigate the weighted Birkhoff average $\frac {1}{S_n}\sum _{k=0}^{n-1}s_k\phi (T^kx)$ on an aperiodic irreducible subshift $\Sigma _{\bf A}$ finite type where

If {Xn} is a discrete-time ^-irreducible Markov chain on a measure space (#*, 3?) [4; p. 4], with «-step transition probabilities P"(x, A), it has been shown in [5] that there exists a subset ^R of 3F with the property that, for every Ae^R and 0-almost all x € W, the power series J^P(x, A)z" have the same radius of convergence R. Moreover, there is a countable partition of 2£ all of whose eleme...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

We consider discrete-time Markov chains with one coffin state and a finite set S of transient states, and are interested in the limiting behaviour of such a chain as time n tends to infinity, conditional on survival up to n. It is known that, when S is irreducible, the limiting conditional distribution of the chain equals the (unique) quasi-stationary distribution of the chain, while the latter...

Let A be an N ×N irreducible matrix with entries in {0, 1}. We define the topological Markov Dyck shift DA to be a nonsofic subshift consisting of the 2N brackets (1, . . . , (N , )1, . . . , )N with both standard bracket rule and Markov chain rule coming from A. The subshift is regarded as a subshift defined by the canonical generators S∗ 1 , . . . , S ∗ N , S1, . . . , SN of the Cuntz-Krieger...

An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with unit row sums. We show how the adoption of ...

One of the main difficulties faced when analyzing Markov chains modelling evolutionary algorithms is that their cardinality grows quite fast. A reasonable way to deal with this issue is to introduce an appropriate notion of a “coarse graining” or, in mathematical language, a quotient of such a Markov chain. The main topic of the current work is the construction of such a notion. We shell introd...

Abstract In an earlier paper (Hunter, 2002) it was shown that mean first passage times play an important role in determining bounds on the relative and absolute differences between the stationary probabilities in perturbed finite irreducible discrete time Markov chains. Further when two perturbations of the transition probabilities in a single row are carried out the differences between the sta...