Approximating Euclidean by Imprecise Markov Decision Processes

Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite models. In this paper we address two questions: first, we investigate what kind of approximation guarantees are obtained when the Euclidean process is approximated by finite state approximations induced by increasingly fine partitions of the continuous state space. We show that for cost functions over finite time horizons the approximations become arbitrarily precise. Second, we use imprecise Markov decision process approximations as a tool to analyse and validate cost functions and strategies obtained by reinforcement learning. We find that, on the one hand, our new theoretical results validate basic design choices of a previously proposed reinforcement learning approach. On the other hand, the imprecise Markov decision process approximations reveal some inaccuracies in the learned cost functions

The evolution of socioeconomic status-related inequalities in maternal health care utilization: evidence from Zimbabwe, 1994-2011

Background: Inequalities in maternal health care are pervasive in the developing world, a fact that has led to questions about the extent of these disparities across socioeconomic groups. Despite a growing literature on maternal health across Sub-Saharan African countries, relatively little is known about the evolution of these inequalities over time for specific countries. This study sought to quantify and explain the observed differences in prenatal care use and professional delivery assistance in Zimbabwe. Methods: The empirical analysis uses four rounds of the nationwide Zimbabwe Demographic and Health Survey administered in 1994, 1999, 2005/06 and 2010/11. Two binary indicators were used as measures of maternal health care utilization; (1) the receipt of four or more antenatal care visits and (2) receiving professional delivery assistance for the most recent pregnancy. We measure inequalities in maternal health care use using the Erreygers corrected concentration index. A decomposition analysis was conducted to determine the underlying drivers of the measured disparities. Results: The computed concentration indices for professional delivery assistance and prenatal care reveal a mostly pro-rich distribution of inequalities between 1994 and 2011. Particularly, the concentration index [95% confidence interval] for the receipt of prenatal care was 0.111 [0.056, 0.171] in 2005/06 and 0.094 [0.057, 0.138] in 2010/11. For professional delivery assistance, the concentration index stood at 0.286 [0.244, 0.329] in 2005/06 and 0.324 [0.283, 0.366] in 2010/11. The pro-rich inequality was also increasing in both rural and urban areas over time. The decomposition exercise revealed that wealth, education, religion and information access were the underlying drivers of the observed inequalities in maternal health care. Conclusions: In Zimbabwe, socioeconomic disparities in maternal health care use are mostly pro-rich and have widened over time regardless of the location of residence. Overall, we established that inequalities in wealth and education are amongst the top drivers of the observed disparities in maternal health care. These findings suggest that addressing inequalities in maternal health care utilization requires coordinated public policies targeting the more poor and vulnerable segments of the population in Zimbabwe

Decomposing socio-economic inequalities in leisure-time physical inactivity: the case of Spanish children

BACKGROUND: Physical inactivity is associated with an increased risk of all-cause mortality and entails a substantial economic burden for health systems. Also, the analysis of inequality in lifestyles for young populations may contribute to reduce health inequalities during adulthood. This paper examines the income-related inequality regarding leisure-time physical inactivity in Spanish children. METHODS: In this cross-sectional study based on the Spanish National Health Survey for 2011-12, concentration indices are estimated to measure socioeconomic inequalities in leisure-time physical inactivity. A decomposition analysis is performed to determine the factors that explain income-related inequalities. RESULTS: There is a significant socioeconomic gradient favouring the better-off associated with leisure-time physical inactivity amongst Spanish children, which is more pronounced in the case of girls. Income shows the highest contribution to total inequality, followed by education of the head of the household. The contribution of several factors (education, place of residence, age) significantly differs by gender. CONCLUSIONS: There is an important inequity in the distribution of leisure-time physical inactivity. Public policies aimed at promoting physical activity for children should prioritize the action into the most disadvantaged subgroups of the population. As the influence of determinants of health styles significantly differ by gender, this study points out the need of addressing the research on income-related inequalities in health habits from a gender perspective