S U M M A R YIn most geophysical inverse problems the properties of interest are parametrized using a fixed number of unknowns. In some cases arguments can be used to bound the maximum number of parameters that need to be considered. In others the number of unknowns is set at some arbitrary value and regularization is used to encourage simple, non-extravagant models. In recent times variable or self-adaptive parametrizations have gained in popularity. Rarely, however, is the number of unknowns itself directly treated as an unknown. This situation leads to a transdimensional inverse problem, that is, one where the dimension of the parameter space is a variable to be solved for.This paper discusses trans-dimensional inverse problems from the Bayesian viewpoint. A particular type of Markov chain Monte Carlo (MCMC) sampling algorithm is highlighted which allows probabilistic sampling in variable dimension spaces. A quantity termed the evidence or marginal likelihood plays a key role in this type of problem. It is shown that once evidence calculations are performed, the results of complex variable dimension sampling algorithms can be replicated with simple and more familiar fixed dimensional MCMC sampling techniques. Numerical examples are used to illustrate the main points. The evidence can be difficult to calculate, especially in high-dimensional non-linear inverse problems. Nevertheless some general strategies are discussed and analytical expressions given for certain linear problems.
The nature and form of the urban environment is a critical determinant of the sustainability of our society, as it is responsible directly for a large proportion of consumed energy, and influences indirectly the patterns and modes of energy consumed in everyday activities. We examine the current state of research into the energy and greenhouse gas emissions attributable directly or indirectly to urban form. Specifically, we look at the embodied (construction) and operational energy attributable to the construction, maintenance and use of residential dwellings, and we review the literature on the relationship between urban structure and transport related energy consumption. While there is clear evidence from both intra and inter city comparisons that higher density, transit oriented cities have lower percapita transport energy use, the effect of housing density on residential (in-house) energy use is less clear. More detailed research is needed to examine the relationships between urban form and overall energy use. * Corresponding Author: peter.rickwood@gmail.com (ph: 02 9514 8606) 1 In this article, we discuss delivered energy, primary energy, and greenhouse gas emissions attributable to energy use. We asssume readers are aware of the relationship between these measures.
ObjectiveTo assess maternal and neonatal outcomes associated with increasing body mass index (BMI) and interpregnancy BMI changes in an Australian obstetric population.MethodsA retrospective cohort study from 2008 to 2013 was undertaken. BMI for 14 875 women was categorised as follows: underweight (≤18 kg/m2); normal weight (19–24 kg/m2); overweight (25–29 kg/m2); obese class I (30–34 kg/m2); obese class II (35–39 kg/m2) and obese class III (40+ kg/m2). BMI categories and maternal, neonatal and birthing outcomes were examined using logistic regression. Interpregnancy change in BMI and the risk of adverse outcomes in the subsequent pregnancy were also examined.ResultsWithin this cohort, 751 (5.1%) women were underweight, 7431 (50.0%) had normal BMI, 3748 (25.1%) were overweight, 1598 (10.8%) were obese class I, 737 (5.0%) were obese class II and 592 (4.0%) were obese class III. In bivariate adjusted models, obese women were at an increased risk of caesarean section, gestational diabetes, hypertensive disorders of pregnancy and neonatal morbidities including macrosomia, large for gestational age (LGA), hypoglycaemia, low 5 min Apgar score and respiratory distress. Multiparous women who experienced an interpregnancy increase of ≥3 BMI units had a higher adjusted OR (AOR) (CI) of the following adverse outcomes in their subsequent pregnancy: low 5-min Apgar score 3.242 (1.557 to 7.118); gestational diabetes mellitus (GDM) 3.258 (1.129 to 10.665) and hypertensive disorders of pregnancy 3.922 (1.243 to 14.760). These women were more likely to give birth vaginally 2.030 (1.417 to 2.913). Conversely, women whose parity changed from 0 to 1 and who experienced an interpregnancy increase of ≥3 BMI units had a higher AOR (CI) of caesarean section in their second pregnancy 1.806 (1.139 to 2.862).ConclusionsWomen who are overweight or obese have a significantly increased risk of various adverse outcomes. Interpregnancy weight gain, regardless of parity and baseline BMI, also increases various adverse outcomes. Effective weight management strategies are needed.
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