Most studies on parameter estimation for HIV dynamic models have ignored pre-treatment viral load data hence utilizing only post-treatment viral load data. In this study we utilize pre-treatment viral load data to estimate parameters of the HIV dynamic model in the absence of therapy. By employing hierarchical Bayesian parameter estimation approach, we were able to get reasonably robust estimates of the model parameters. Using simulated data, the parameter estimation was done at both the individual and population levels with the implementation carried out via Markov Chain Monte Carlo methods.
Abstract. In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain , where is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.
Motivated by possible applications of Lyapunov techniques in the stability of stochastic networks, subgeometric ergodicity of Markov chains is investigated. In a nutshell, in this study we take a look at -ergodic general Markov chains, subgeometrically ergodic at rate , when the random-time Foster-Lyapunov drift conditions on a set of stopping times are satisfied.
We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs). We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.
Abstract. We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and show that the finiteness of the expectation, where τ △ is the hitting time on the coupling set △ and r is a subgeometric rate function, is equivalent to a sequence of Foster-Lyapunov drift conditions which imply subgeometric convergence in the Wassertein distance. We give an example for a 'family of nested drift conditions'.
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