Pao-Lu Hsu (Xu, Bao-lu): The Grandparent of Probability and Statistics in China

The years 1910-1911 are auspicious years in Chinese mathematics with the births of Pao-Lu Hsu, Luo-Keng Hua and Shiing-Shen Chern. These three began the development of modern mathematics in China: Hsu in probability and statistics, Hua in number theory, and Chern in differential geometry. We here review some facts about the life of P.-L. Hsu which have been uncovered recently, and then discuss some of his contributions. We have drawn heavily on three papers in the 1979 Annals of Statistics (volume 7, pages 467-483) by T. W. Anderson, K. L. Chung and E. L. Lehmann, as well as an article by Jiang Ze-Han and Duan Xue-Fu in Hsu's collected papers.Comment: Published in at http://dx.doi.org/10.1214/12-STS387 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Competitive exclusion for chemostat equations with variable yields

In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. The model was studied by Fiedler and Hsu [J. Math. Biol. (2009) 59:233-253]. These authors prove the nonexistence of periodic orbits, by means of a multi-dimensional Bendixon-Dulac criterion. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu [SIAM J. Appl. Math. (1978) 34:760-763] and by Wolkowicz and Lu [SIAM J. Appl. Math. (1997) 57:1019-1043] in the case when growth rates are proportional to food uptakes

Primary health service use by mothers and children from London-Middlesex, Ontario

Primary health service use (P-HSU) may be influenced by predisposing and enabling factors measured at individual- and contextual-levels but is equitable when driven by need factors. Objectives: 1) Estimate the effect of residential location on maternal and child P-HSU; 2) Assess P-HSU inequity by determining whether the effects of need factors on P-HSU are dependent on predisposing and enabling factors; 3) Describe perceived unmet healthcare needs in the maternal-child population observed to have inequitable P-HSU. Methodology: The sample of 1451 mother-child pairs was from a prenatal cohort recruited from London, Ontario between 2002 and 2004, with follow-up until children were toddler/preschooler-aged. Individual-level data were linked by residential address to contextual-level data sourced from Statistics Canada. Two multilevel logistic regression models were built to assess the multilevel characteristics associated with P-HSU by mothers and children, and interactions of need factors with covariates were tested to assess P-HSU inequity. The prevalence of perceived unmet healthcare need was described, and a discussion on limitations of its measurement in the literature was performed. Results: P-HSU varied between neighbourhoods but only for mothers (p=0.02). Maternal obesity’s effect on P-HSU was different for rural mothers living in low-income households (OR=0.26, pConclusion:Results indicate that differences in maternal P-HSU exist between neighbourhoods, partially explained by urban/rural residence. Several enabling factors modified the effect of need factors on both maternal and child P-HSU, providing evidence for inequitable P-HSU. This research has the potential to inform Canadian healthcare policy with regards to contextual effects, P-HSU inequity, and perceived unmet healthcare needs in mothers and children

Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-It\^o integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.Comment: To appear in "Electronic Communications in Probability

Cross-sectional associations of depressive symptom severity and functioning with health service use by older people in low-and-middle income countries

Background: Comprehensive understanding of the determinants of health service use (HSU) by older people with depression is essential for health service planning for an ageing global population. This study aimed to determine the extent to which depressive symptom severity and functioning are associated with HSU by older people with depression in low and middle income countries (LMICs). Methods: A cross-sectional analysis of the 10/66 Dementia Research Group population-based surveys dataset. Participants (n = 4590) were those aged 65 or older, in the clinical range for depressive symptoms (defined as scoring four or more on the EURO-D), living in 13 urban and/or rural catchment areas in nine LMICs. Associations were calculated using Poisson regression and random-effects meta-analysis. Results: After adjustment for confounding variables, (EURO-D) depressive symptom severity was significantly associated with “any community HSU” (Pooled Prevalence Ratios = 1.02; 95% CI = 1.01–1.03) but not hospital admission. Conversely, after adjustment, (WHODAS-II) functioning was significantly associated with hospital admission (Pooled PR = 1.14; 95% CI = 1.02–1.26) but not “any community HSU”. Conclusions: Depressive symptom severity does not explain a large proportion of the variance in HSU by older people with depression in LMICs. The association of functioning with this HSU is worthy of further investigation. In LMICs, variables related to accessibility may be more important correlates of HSU than variables directly related to health problems