A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Semiparametric estimation of count regression models

This paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity. We use the generalized Laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a Poisson mixture model. We establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated, censored, and zero-inflated count regression models. Monte Carlo evidence shows that the finite sample behavior of the estimator is quite good. The paper applies the method to a model of individual shopping behavior. © 1999 Elsevier Science S.A. All rights reserved.

An evaluation of crowd counting methods, features and regression models

Existing crowd counting algorithms rely on holistic, local or histogram based features to capture crowd properties. Regression is then employed to estimate the crowd size. Insufficient testing across multiple datasets has made it difficult to compare and contrast different methodologies. This paper presents an evaluation across multiple datasets to compare holistic, local and histogram based methods, and to compare various image features and regression models. A K-fold cross validation protocol is followed to evaluate the performance across five public datasets: UCSD, PETS 2009, Fudan, Mall and Grand Central datasets. Image features are categorised into five types: size, shape, edges, keypoints and textures. The regression models evaluated are: Gaussian process regression (GPR), linear regression, K nearest neighbours (KNN) and neural networks (NN). The results demonstrate that local features outperform equivalent holistic and histogram based features; optimal performance is observed using all image features except for textures; and that GPR outperforms linear, KNN and NN regression

A national satellite-based land-use regression model for air pollution exposure assessment in Australia

Land-use regression (LUR) is a technique that can improve the accuracy of air pollution exposure assessment in epidemiological studies. Most LUR models are developed for single cities, which places limitations on their applicability to other locations. We sought to develop a model to predict nitrogen dioxide (NO2) concentrations with national coverage of Australia by using satellite observations of tropospheric NO2 columns combined with other predictor variables. We used a generalised estimating equation (GEE) model to predict annual and monthly average ambient NO2 concentrations measured by a national monitoring network from 2006 through 2011. The best annual model explained 81% of spatial variation in NO2 (absolute RMS error=1.4 ppb), while the best monthly model explained 76% (absolute RMS error=1.9 ppb). We applied our models to predict NO2 concentrations at the ~350,000 census mesh blocks across the country (a mesh block is the smallest spatial unit in the Australian census). National population-weighted average concentrations ranged from 7.3 ppb (2006) to 6.3 ppb (2011). We found that a simple approach using tropospheric NO2 column data yielded models with slightly better predictive ability than those produced using a more involved approach that required simulation of surface-to-column ratios. The models were capable of capturing within-urban variability in NO2, and offer the ability to estimate ambient NO2 concentrations at monthly and annual time scales across Australia from 2006–2011. We are making our model predictions freely available for research.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

Long-term outcomes following Medtronic Open Pivot valved conduit

Aortic root replacement is a complex procedure, though subsequent modifications of the original Bentall procedure have made surgery more reproducible. The study aim was to examine the outcomes of a modified Bentall procedure, using the Medtronic Open PivotTM valved conduit. Whilst short-term data on the conduit and long-term data on the valve itself are available, little is known of the long-term results with the valved conduit. Patients undergoing aortic root replacement between February 1999 and February 2010, using the Medtronic Open Pivot valved conduit were identified from the prospectively collected Cardiothoracic Register at The Prince Charles Hospital, Brisbane, Australia. All patients were followed up echocardiographically and clinically. The primary end-point was death, and a Cox proportional model was used to identify factors associated.with survival. Secondary end-points were valve-related morbidity (as defined by STS guidelines) and postoperative morbidity. Predictors of morbidity were identified using logistic regression. A total of 246 patients (mean age 50 years) was included in the study. The overall mortality was 12%, with actuarial 10-year survival 79% and a 10-year estimate of valve-related death of 0.04 (95% CI: 0.004, 0.07). Preoperative myocardial infarction (p = 0.004, HR 4.74), urgency of operation (p = 0.038, HR 2.8) and 10% incremental decreases in ejection fraction (p = 0.046, HR 0.69) were predictive of mortality. Survival was also affected by the valve gradients, with a unit increase in peak gradient reducing mortality (p = 0.021, HR 0.93). Valve-related morbidity occurred in 11 patients. Urgent surgery (p <0.001, OR 4.12), aortic dissection (p = 0.015, OR 3.35), calcific aortic stenosis (p = 0.016, OR 2.35) and Marfan syndrome (p 0.009, OR 3.75) were predictive of postoperative morbidity. The reoperation rate was 1.2%. The Medtronic Open Pivot valved conduit is a safe and durable option for aortic root replacement, and is associated with low morbidity and 10-year survival of 79%. However, further studies are required to determine the effect of valve gradient on survival.

Identifying risk factors and protective factors for venous leg ulcer recurrence using a theoretical approach : a longitudinal study

Background The high recurrence rate of chronic venous leg ulcers has a significant impact on an individual’s quality of life and healthcare costs. Objectives This study aimed to identify risk and protective factors for recurrence of venous leg ulcers using a theoretical approach by applying a framework of self and family management of chronic conditions to underpin the study. Design Secondary analysis of combined data collected from three previous prospective longitudinal studies. Setting The contributing studies’ participants were recruited from two metropolitan hospital outpatient wound clinics and three community-based wound clinics. Participants Data were available on a sample of 250 adults, with a leg ulcer of primarily venous aetiology, who were followed after ulcer healing for a median follow-up time of 17 months after healing (range: 3 to 36 months). Methods Data from the three studies were combined. The original participant data were collected through medical records and self-reported questionnaires upon healing and every 3 months thereafter. A Cox proportion-hazards regression analysis was undertaken to determine the influential factors on leg ulcer recurrence based on the proposed conceptual framework. Results The median time to recurrence was 42 weeks (95% CI 31.9–52.0), with an incidence of 22% (54 of 250 participants) recurrence within three months of healing, 39% (91 of 235 participants) for those who were followed for six months, 57% (111 of 193) by 12 months, 73% (53 of 72) by two years and 78% (41 of 52) of those who were followed up for three years. A Cox proportional-hazards regression model revealed that the risk factors for recurrence included a history of deep vein thrombosis (HR 1.7, 95% CI 1.07–2.67, p=0.024), history of multiple previous leg ulcers (HR 4.4, 95% CI 1.84–10.5, p=0.001), and longer duration (in weeks) of previous ulcer (HR 1.01, 95% CI 1.003–1.01, p<0.001); while the protective factors were elevating legs for at least 30 minutes per day (HR 0.33, 95% CI 0.19–0.56, p<0.001), higher levels of self-efficacy (HR 0.95, 95% CI 0.92–0.99, p=0.016), and walking around for at least three hours/day (HR 0.66, 95% CI 0.44–0.98, p=0.040). Conclusions Results from this study provide a comprehensive examination of risk and protective factors associated with leg ulcer recurrence based on the chronic disease self and family management framework. These results in turn provide essential steps towards developing and testing interventions to promote optimal prevention strategies for venous leg ulcer recurrence.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.

Discovery and replication of gene influences on brain structure using LASSO regression

We implemented least absolute shrinkage and selection operator (LASSO) regression to evaluate gene effects in genome-wide association studies (GWAS) of brain images, using an MRI-derived temporal lobe volume measure from 729 subjects scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Sparse groups of SNPs in individual genes were selected by LASSO, which identifies efficient sets of variants influencing the data. These SNPs were considered jointly when assessing their association with neuroimaging measures. We discovered 22 genes that passed genome-wide significance for influencing temporal lobe volume. This was a substantially greater number of significant genes compared to those found with standard, univariate GWAS. These top genes are all expressed in the brain and include genes previously related to brain function or neuropsychiatric disorders such as MACROD2, SORCS2, GRIN2B, MAGI2, NPAS3, CLSTN2, GABRG3, NRXN3, PRKAG2, GAS7, RBFOX1, ADARB2, CHD4, and CDH13. The top genes we identified with this method also displayed significant and widespread post hoc effects on voxelwise, tensor-based morphometry (TBM) maps of the temporal lobes. The most significantly associated gene was an autism susceptibility gene known as MACROD2.We were able to successfully replicate the effect of the MACROD2 gene in an independent cohort of 564 young, Australian healthy adult twins and siblings scanned with MRI (mean age: 23.8±2.2 SD years). Our approach powerfully complements univariate techniques in detecting influences of genes on the living brain.

Rank regression for analyzing ordinal qualitative data for treatment comparison

Ordinal qualitative data are often collected for phenotypical measurements in plant pathology and other biological sciences. Statistical methods, such as t tests or analysis of variance, are usually used to analyze ordinal data when comparing two groups or multiple groups. However, the underlying assumptions such as normality and homogeneous variances are often violated for qualitative data. To this end, we investigated an alternative methodology, rank regression, for analyzing the ordinal data. The rank-based methods are essentially based on pairwise comparisons and, therefore, can deal with qualitative data naturally. They require neither normality assumption nor data transformation. Apart from robustness against outliers and high efficiency, the rank regression can also incorporate covariate effects in the same way as the ordinary regression. By reanalyzing a data set from a wheat Fusarium crown rot study, we illustrated the use of the rank regression methodology and demonstrated that the rank regression models appear to be more appropriate and sensible for analyzing nonnormal data and data with outliers.