Search results for "Markov chain"

Dynamics in stochastic evolutionary models

2014

First published: 01 February 2016 We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict, and illustrate the theory with the fall of the Qing dynasty and the rise of communism in China. We are especially indebted to Juan Block for his many comments and suggestions. We would also like to thank Drew Fudenberg, Kevin Hasker, Matt Jackson, Peyton Young, and five anonymous referees. We are grateful to NSF Grant SES-08-51315 and to the MIUR PRIN 20103S5RN3 for financial support.

Cost Effectiveness of Peginterferon ??-2a Plus Ribavirin versus Interferon ??-2b Plus Ribavirin as Initial Therapy for Treatment-Naive Chronic Hepati…

2004

Introduction: In adults with previously untreated chronic hepatitis C (CHC), the combination of peginterferon α-2a plus ribavirin produces a higher rate of sustained virological response (SVR) than interferon α-2b plus ribavirin, but it is still unproven whether this increase is cost effective. The objective of this study was to determine if the gain in SVR with peginterferon α-2a plus ribavirin is worth the incremental cost. Methods: We constructed a Markov model of disease progression in which cohorts of patients received peginterferon α-2a plus ribavirin or interferon α-2b plus ribavirin for 48 weeks (hepatitis C virus [HCV] genotype 1 and non-1 patients with fibrosis) or 24 weeks (genot…

Cost-effectiveness of screening for colorectal cancer in France using a guaiac test versus an immunochemical test

2010

Objectives: The aim of this study was to compare the cost and the effectiveness of two biennial fecal occult blood screening tests for colorectal cancer: a guaiac nonrehydrated test (G-FOBT) and an immunochemical test (I-FOBT) with the absence of screening.Methods: A Markov model was developed to compare these strategies in a general population of subjects aged 50 to 74 over a 20-year period.Results: Compared with the absence of screening, G-FOBT and I-FOBT were associated with a decrease in colorectal cancer mortality of 17.4 percent and 25.2 percent, respectively. With regard to cost-effectiveness, expressed as cost per life-year gained, I-FOBT was the most effective and most costly alter…

Cost-effectiveness of sofosbuvir plus ribavirin with or without pegylated interferon for the treatment of chronic hepatitis C in Italy.

2015

Objective:Across Italy up to 7.3% of the population is infected with hepatitis C virus (HCV), with long-term complications resulting in high medical costs and significant morbidity and mortality. Current treatment options have limitations due to side effects, interferon intolerability and ineligibility, long treatment durations and low sustained virological response (SVR) rates, especially for the most severe patients). Sofosbuvir is the first nucleotide polymerase inhibitor with pan-genotypic activity. Sofosbuvir, administered with ribavirin (RBV) and with or without pegylated interferon (PEG-INF), resulted in >90% SVR across treatment-naïve (TN) genotype (GT) 1-6 patients. It is also t…

Recursion at the crossroads of sequence modeling, random trees, stochastic algorithms and martingales

2013

This monograph synthesizes several studies spanning from dynamical systems in the statistical analysis of sequences, to analysis of algorithms in random trees and discrete stochastic processes. These works find applications in various fields ranging from biological sequences to linear regression models, branching processes, through functional statistics and estimates of risk indicators for insurances. All the established results use, in one way or another, the recursive property of the structure under study, by highlighting invariants such as martingales, which are at the heart of this monograph, as tools as well as objects of study.

Gradient walks and $p$-harmonic functions

2017

Validating Habitual and Goal-Directed Decision-Making Performance Online in Healthy Older Adults

2021

Everyday decision-making is supported by a dual-system of control comprised of parallel goal-directed and habitual systems. Over the past decade, the two-stage Markov decision task has become popularized for its ability to dissociate between goal-directed and habitual decision-making. While a handful of studies have implemented decision-making tasks online, only one study has validated the task by comparing in-person and web-based performance on the two-stage task in children and young adults. To date, no study has validated the dissociation of goal-directed and habitual behaviors in older adults online. Here, we implemented and validated a web-based version of the two-stage Markov task usi…

Can the adaptive Metropolis algorithm collapse without the covariance lower bound?

2011

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …