Transforming morning to afternoon using linear regression techniques

Visual localization in outdoor environments is often hampered by the natural variation in appearance caused by such things as weather phenomena, diurnal fluctuations in lighting, and seasonal changes. Such changes are global across an environment and, in the case of global light changes and seasonal variation, the change in appearance occurs in a regular, cyclic manner. Visual localization could be greatly improved if it were possible to predict the appearance of a particular location at a particular time, based on the appearance of the location in the past and knowledge of the nature of appearance change over time. In this paper, we investigate whether global appearance changes in an environment can be learned sufficiently to improve visual localization performance. We use time of day as a test case, and generate transformations between morning and afternoon using sample images from a training set. We demonstrate the learned transformation can be generalized from training data and show the resulting visual localization on a test set is improved relative to raw image comparison. The improvement in localization remains when the area is revisited several weeks later.

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.

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.

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.

Efficient estimation for rank-based regression with clustered data

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration.

Quantile regression for longitudinal data with a working correlation model

This paper proposes a linear quantile regression analysis method for longitudinal data that combines the between- and within-subject estimating functions, which incorporates the correlations between repeated measurements. Therefore, the proposed method results in more efficient parameter estimation relative to the estimating functions based on an independence working model. To reduce computational burdens, the induced smoothing method is introduced to obtain parameter estimates and their variances. Under some regularity conditions, the estimators derived by the induced smoothing method are consistent and have asymptotically normal distributions. A number of simulation studies are carried out to evaluate the performance of the proposed method. The results indicate that the efficiency gain for the proposed method is substantial especially when strong within correlations exist. Finally, a dataset from the audiology growth research is used to illustrate the proposed methodology.

Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.