Reduction of Markov Chains using a Value-of-Information-Based Approach

In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative Kullback-Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the `optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.Comment: Submitted to Entrop

Analyze This! A Cosmological Constraint Package for CMBEASY

We introduce a Markov Chain Monte Carlo simulation and data analysis package that extends the CMBEASY software. We have taken special care in implementing an adaptive step algorithm for the Markov Chain Monte Carlo in order to improve convergence. Data analysis routines are provided which allow to test models of the Universe against measurements of the cosmic microwave background, supernovae Ia and large scale structure. We present constraints on cosmological parameters derived from these measurements for a $\Lambda$CDM cosmology and discuss the impact of the different observational data sets on the parameters. The package is publicly available as part of the CMBEASY software at www.cmbeasy.org.Comment: Published version, JCAP style, 16 pages, 7 figures. The software is available at http://www.cmbeasy.or