Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Interaction between FTO gene variants and lifestyle factors on metabolic traits in an Asian Indian population

Background Lifestyle factors such as diet and physical activity have been shown to modify the association between fat mass and obesity–associated (FTO) gene variants and metabolic traits in several populations; however, there are no gene-lifestyle interaction studies, to date, among Asian Indians living in India. In this study, we examined whether dietary factors and physical activity modified the association between two FTO single nucleotide polymorphisms (rs8050136 and rs11076023) (SNPs) and obesity traits and type 2 diabetes (T2D). Methods The study included 734 unrelated T2D and 884 normal glucose-tolerant (NGT) participants randomly selected from the urban component of the Chennai Urban Rural Epidemiology Study (CURES). Dietary intakes were assessed using a validated interviewer administered semi-quantitative food frequency questionnaire (FFQ). Physical activity was based upon the self-report. Interaction analyses were performed by including the interaction terms in the linear/logistic regression model. Results There was a significant interaction between SNP rs8050136 and carbohydrate intake (% energy) (Pinteraction = 0.04), where the ‘A’ allele carriers had 2.46 times increased risk of obesity than those with ‘CC’ genotype (P = 3.0 × 10−5) among individuals in the highest tertile of carbohydrate intake (% energy, 71 %). A significant interaction was also observed between SNP rs11076023 and dietary fibre intake (Pinteraction = 0.0008), where individuals with AA genotype who are in the 3rd tertile of dietary fibre intake had 1.62 cm lower waist circumference than those with ‘T’ allele carriers (P = 0.02). Furthermore, among those who were physically inactive, the ‘A’ allele carriers of the SNP rs8050136 had 1.89 times increased risk of obesity than those with ‘CC’ genotype (P = 4.0 × 10−5). Conclusions This is the first study to provide evidence for a gene-diet and gene-physical activity interaction on obesity and T2D in an Asian Indian population. Our findings suggest that the association between FTO SNPs and obesity might be influenced by carbohydrate and dietary fibre intake and physical inactivity. Further understanding of how FTO gene influences obesity and T2D through dietary and exercise interventions is warranted to advance the development of behavioral intervention and personalised lifestyle strategies, which could reduce the risk of metabolic diseases in this Asian Indian population.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Analysis of feeding strategies for small-scale dairy systems in central Mexico using linear programming

A limitation of small-scale dairy systems in central Mexico is that traditional feeding strategies are less effective when nutrient availability varies through the year. In the present work, a linear programming (LP) model that maximizes income over feed cost was developed, and used to evaluate two strategies: the traditional one used by the small-scale dairy producers in Michoacan State, based on fresh lucerne, maize grain and maize straw; and an alternative strategy proposed by the LIP model, based on ryegrass hay, maize silage and maize grain. Biological and economic efficiency for both strategies were evaluated. Results obtained with the traditional strategy agree with previously published work. The alternative strategy did not improve upon the performance of the traditional strategy because of low metabolizable protein content of the maize silage considered by the model. However, the Study recommends improvement of forage quality to increase the efficiency of small-scale dairy systems, rather than looking for concentrate supplementation.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

A parametric model for the interval censored survival times of Acacia mangium plantation in a spacing trial

Survival times for the Acacia mangium plantation in the Segaliud Lokan Project, Sabah, East Malaysia were analysed based on 20 permanent sample plots (PSPs) established in 1988 as a spacing experiment. The PSPs were established following a complete randomized block design with five levels of spacing randomly assigned to units within four blocks at different sites. The survival times of trees in years are of interest. Since the inventories were only conducted annually, the actual survival time for each tree was not observed. Hence, the data set comprises censored survival times. Initial analysis of the survival of the Acacia mangium plantation suggested there is block by spacing interaction; a Weibull model gives a reasonable fit to the replicate survival times within each PSP; but a standard Weibull regression model is inappropriate because the shape parameter differs between PSPs. In this paper we investigate the form of the non-constant Weibull shape parameter. Parsimonious models for the Weibull survival times have been derived using maximum likelihood methods. The factor selection for the parameters is based on a backward elimination procedure. The models are compared using likelihood ratio statistics. The results suggest that both Weibull parameters depend on spacing and block.

Bayesian decision procedures for binary and continuous bivariate dose-escalation studies

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on binary measures of undesirable events and continuous measures of therapeutic benefit. The methods generalize earlier approaches where undesirable events and therapeutic benefit are both binary. A logistic regression model is used to model the binary responses, while a linear regression model is used to model the continuous responses. Prior distributions for the unknown model parameters are suggested. A gain function is discussed and an optional safety constraint is included. Copyright (C) 2006 John Wiley & Sons, Ltd.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Bergmann's rule and body size in mammals

Aim: To describe the geographical pattern of mean body size of the non-volant mammals of the Nearctic and Neotropics and evaluate the influence of five environmental variables that are likely to affect body size gradients. Location: The Western Hemisphere. Methods: We calculated mean body size (average log mass) values in 110 × 110 km cells covering the continental Nearctic and Neotropics. We also generated cell averages for mean annual temperature, range in elevation, their interaction, actual evapotranspiration, and the global vegetation index and its coefficient of variation. Associations between mean body size and environmental variables were tested with simple correlations and ordinary least squares multiple regression, complemented with spatial autocorrelation analyses and split-line regression. We evaluated the relative support for each multiple-regression model using AIC. Results: Mean body size increases to the north in the Nearctic and is negatively correlated with temperature. In contrast, across the Neotropics mammals are largest in the tropical and subtropical lowlands and smaller in the Andes, generating a positive correlation with temperature. Finally, body size and temperature are nonlinearly related in both regions, and split-line linear regression found temperature thresholds marking clear shifts in these relationships (Nearctic 10.9 °C; Neotropics 12.6 °C). The increase in body sizes with decreasing temperature is strongest in the northern Nearctic, whereas a decrease in body size in mountains dominates the body size gradients in the warmer parts of both regions. Main conclusions: We confirm previous work finding strong broad-scale Bergmann trends in cold macroclimates but not in warmer areas. For the latter regions (i.e. the southern Nearctic and the Neotropics), our analyses also suggest that both local and broad-scale patterns of mammal body size variation are influenced in part by the strong mesoscale climatic gradients existing in mountainous areas. A likely explanation is that reduced habitat sizes in mountains limit the presence of larger-sized mammals.

Investigation of the factors influencing the survival of Bifidobacterium longum in model acidic solutions and fruit juices

The survival of Bifidobacterium longum NCIMB 8809 was studied during refrigerated storage for 6 weeks in model solutions, based on which a mathematical model was constructed describing cell survival as a function of pH, citric acid, protein and dietary fibre. A Central Composite Design (CCD) was developed studying the influence of four factors at three levels, i.e., pH (3.2–4), citric acid (2–15 g/l), protein (0–10 g/l), and dietary fibre (0–8 g/l). In total, 31 experimental runs were carried out. Analysis of variance (ANOVA) of the regression model demonstrated that the model fitted well the data. From the regression coefficients it was deduced that all four factors had a statistically significant (P < 0.05) negative effect on the log decrease [log10N0 week−log10N6 week], with the pH and citric acid being the most influential ones. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate and strawberry. The highest cell survival (less than 0.4 log decrease) after 6 weeks of storage was observed in orange and pineapple, both of which had a pH of about 3.8. Although the pH of grapefruit and blackcurrant was similar (pH ∼3.2), the log decrease of the former was ∼0.5 log, whereas of the latter was ∼0.7 log. One reason for this could be the fact that grapefruit contained a high amount of citric acid (15.3 g/l). The log decrease in pomegranate and strawberry juices was extremely high (∼8 logs). The mathematical model was able to predict adequately the cell survival in orange, grapefruit, blackcurrant, and pineapple juices. However, the model failed to predict the cell survival in pomegranate and strawberry, most likely due to the very high levels of phenolic compounds in these two juices.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Ozone database in support of CMIP5 simulations: results and corresponding radiative forcing

A continuous tropospheric and stratospheric vertically resolved ozone time series, from 1850 to 2099, has been generated to be used as forcing in global climate models that do not include interactive chemistry. A multiple linear regression analysis of SAGE I+II satellite observations and polar ozonesonde measurements is used for the stratospheric zonal mean dataset during the well-observed period from 1979 to 2009. In addition to terms describing the mean annual cycle, the regression includes terms representing equivalent effective stratospheric chlorine (EESC) and the 11-yr solar cycle variability. The EESC regression fit coefficients, together with pre-1979 EESC values, are used to extrapolate the stratospheric ozone time series backward to 1850. While a similar procedure could be used to extrapolate into the future, coupled chemistry climate model (CCM) simulations indicate that future stratospheric ozone abundances are likely to be significantly affected by climate change, and capturing such effects through a regression model approach is not feasible. Therefore, the stratospheric ozone dataset is extended into the future (merged in 2009) with multimodel mean projections from 13 CCMs that performed a simulation until 2099 under the SRES (Special Report on Emission Scenarios) A1B greenhouse gas scenario and the A1 adjusted halogen scenario in the second round of the Chemistry-Climate Model Validation (CCMVal-2) Activity. The stratospheric zonal mean ozone time series is merged with a three-dimensional tropospheric data set extracted from simulations of the past by two CCMs (CAM3.5 and GISSPUCCINI)and of the future by one CCM (CAM3.5). The future tropospheric ozone time series continues the historical CAM3.5 simulation until 2099 following the four different Representative Concentration Pathways (RCPs). Generally good agreement is found between the historical segment of the ozone database and satellite observations, although it should be noted that total column ozone is overestimated in the southern polar latitudes during spring and tropospheric column ozone is slightly underestimated. Vertical profiles of tropospheric ozone are broadly consistent with ozonesondes and in-situ measurements, with some deviations in regions of biomass burning. The tropospheric ozone radiative forcing (RF) from the 1850s to the 2000s is 0.23Wm−2, lower than previous results. The lower value is mainly due to (i) a smaller increase in biomass burning emissions; (ii) a larger influence of stratospheric ozone depletion on upper tropospheric ozone at high southern latitudes; and possibly (iii) a larger influence of clouds (which act to reduce the net forcing) compared to previous radiative forcing calculations. Over the same period, decreases in stratospheric ozone, mainly at high latitudes, produce a RF of −0.08Wm−2, which is more negative than the central Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) value of −0.05Wm−2, but which is within the stated range of −0.15 to +0.05Wm−2. The more negative value is explained by the fact that the regression model simulates significant ozone depletion prior to 1979, in line with the increase in EESC and as confirmed by CCMs, while the AR4 assumed no change in stratospheric RF prior to 1979. A negative RF of similar magnitude persists into the future, although its location shifts from high latitudes to the tropics. This shift is due to increases in polar stratospheric ozone, but decreases in tropical lower stratospheric ozone, related to a strengthening of the Brewer-Dobson circulation, particularly through the latter half of the 21st century. Differences in trends in tropospheric ozone among the four RCPs are mainly driven by different methane concentrations, resulting in a range of tropospheric ozone RFs between 0.4 and 0.1Wm−2 by 2100. The ozone dataset described here has been released for the Coupled Model Intercomparison Project (CMIP5) model simulations in netCDF Climate and Forecast (CF) Metadata Convention at the PCMDI website (http://cmip-pcmdi.llnl.gov/).

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Equator-to-pole temperature differences and the extra-tropical storm track responses of the CMIP5 climate models

This paper aims to understand the physical processes causing the large spread in the storm track projections of the CMIP5 climate models. In particular, the relationship between the climate change responses of the storm tracks, as measured by the 2–6 day mean sea level pressure variance, and the equator-to-pole temperature differences at upper- and lower-tropospheric levels is investigated. In the southern hemisphere the responses of the upper- and lower-tropospheric temperature differences are correlated across the models and as a result they share similar associations with the storm track responses. There are large regions in which the storm track responses are correlated with the temperature difference responses, and a simple linear regression model based on the temperature differences at either level captures the spatial pattern of the mean storm track response as well explaining between 30 and 60 % of the inter-model variance of the storm track responses. In the northern hemisphere the responses of the two temperature differences are not significantly correlated and their associations with the storm track responses are more complicated. In summer, the responses of the lower-tropospheric temperature differences dominate the inter-model spread of the storm track responses. In winter, the responses of the upper- and lower-temperature differences both play a role. The results suggest that there is potential to reduce the spread in storm track responses by constraining the relative magnitudes of the warming in the tropical and polar regions.