Abstract. Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior) ensemble with a prescribed mean and covariance, consistent with the Kalman update. This includes several filters used in practice, such as the Ensemble Transform Kalman Filter (ETKF), the Ensemble Adjustment Kalman Filter (EAKF), and a filter by Whitaker and Hamill. We show that at every time index, as the number of ensemble members increases to infinity, the mean and covariance of an unbiased ensemble square root filter converge to those of the Kalman filter, in the case of a linear model and an initial distribution of which all moments exist. The convergence is in all L p , 1 ≤ p < ∞, and the convergence rate does not depend on the model or data dimensions. The result holds in infinitely dimensional Hilbert spaces as well.
Positive child health assessed using a quantitative PCHI was associated with QoL across the ELGAN cohort at school age. In the current study, the PCHI encompassed 11 outcomes assessed in ELGANs. Future research could include an enhanced panel of child health outcomes to support the use of PCHI as an indicator of positive child health.
Objective.To identify modifiable antecedents during pre-pregnancy and pregnancy windows associated with a positive child health at 10 years of age.Study design.Data on 889 children enrolled in the Extremely Low Gestational Age Newborn (ELGAN) study in 2002–2004 were analyzed for associations between potentially modifiable maternal antecedents during pre-pregnancy and pregnancy time windows and a previously described positive child health index (PCHI) score at 10 years of age. Stratification by race was also investigated for associations with investigated antecedents.Results.Factors associated with higher PCHI (more positive health) included greater gestational age, birth weight, multiple gestation, and medical interventions, including assisted reproduction, and cervical cerclage. Factors associated with lower PCHI included correlates of lower socioeconomic status, pre-pregnancy chronic medical disorders in the mother like pre-pregnancy BMI, maternal asthma. When stratified by race, variation in significant results was observed.Conclusions.Among children born extremely preterm, medical interventions and higher SES were associated with improved PCHI while chronic illness and high BMI in the mother is associated with lower PCHI at 10 years of age. Knowledge of such antecedent factors could inform efforts to develop interventions that promote positive child health outcomes in future pregnancies.
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