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 the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Tests of sunspot number sequences: 3. Effects of regression procedures on the calibration of historic sunspot data

We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups RB above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of RB are then re-scaled to the full observed RGO group number RA using a variety of regression techniques. It is found that a very high correlation between RA and RB (rAB > 0.98) does not prevent large errors in the intercalibration (for example sunspot maximum values can be over 30 % too large even for such levels of rAB). In generating the backbone sunspot number (RBB), Svalgaard and Schatten (2015, this issue) force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (“Q  Q”) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However, other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.

Validation of improved TAMANN neural network for operational satellite-derived rainfall estimation in Africa

Real-time rainfall monitoring in Africa is of great practical importance for operational applications in hydrology and agriculture. Satellite data have been used in this context for many years because of the lack of surface observations. This paper describes an improved artificial neural network algorithm for operational applications. The algorithm combines numerical weather model information with the satellite data. Using this algorithm, daily rainfall estimates were derived for 4 yr of the Ethiopian and Zambian main rainy seasons and were compared with two other algorithms-a multiple linear regression making use of the same information as that of the neural network and a satellite-only method. All algorithms were validated against rain gauge data. Overall, the neural network performs best, but the extent to which it does so depends on the calibration/validation protocol. The advantages of the neural network are most evident when calibration data are numerous and close in space and time to the validation data. This result emphasizes the importance of a real-time calibration system.

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Estimation of the stoichiometry of volatile fatty acid production in the rumen of lactating cows

The purpose of this study was to improve the prediction of the quantity and type of Volatile Fatty Acids (VFA) produced from fermented substrate in the rumen of lactating cows. A model was formulated that describes the conversion of substrate (soluble carbohydrates, starch, hemi-cellulose, cellulose, and protein) into VFA (acetate, propionate, butyrate, and other VFA). Inputs to the model were observed rates of true rumen digestion of substrates, whereas outputs were observed molar proportions of VFA in rumen fluid. A literature survey generated data of 182 diets (96 roughage and 86 concentrate diets). Coefficient values that define the conversion of a specific substrate into VFA were estimated meta-analytically by regression of the model against observed VFA molar proportions using non-linear regression techniques. Coefficient estimates significantly differed for acetate and propionate production in particular, between different types of substrate and between roughage and concentrate diets. Deviations of fitted from observed VFA molar proportions could be attributed to random error for 100%. In addition to regression against observed data, simulation studies were performed to investigate the potential of the estimation method. Fitted coefficient estimates from simulated data sets appeared accurate, as well as fitted rates of VFA production, although the model accounted for only a small fraction (maximally 45%) of the variation in VFA molar proportions. The simulation results showed that the latter result was merely a consequence of the statistical analysis chosen and should not be interpreted as an indication of inaccuracy of coefficient estimates. Deviations between fitted and observed values corresponded to those obtained in simulations. (c) 2005 Elsevier Ltd. All rights reserved.

Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Linear predicted hexagonal search algorithm with moments

A novel Linear Hashtable Method Predicted Hexagonal Search (LHMPHS) method for block based motion compensation is proposed. Fast block matching algorithms use the origin as the initial search center, which often does not track motion very well. To improve the accuracy of the fast BMA's, we employ a predicted starting search point, which reflects the motion trend of the current block. The predicted search centre is found closer to the global minimum. Thus the center-biased BMA's can be used to find the motion vector more efficiently. The performance of the algorithm is evaluated by using standard video sequences, considers the three important metrics: The results show that the proposed algorithm enhances the accuracy of current hexagonal algorithms and is better than Full Search, Logarithmic Search etc.

Quantitative precipitation estimation over ocean using Bayesian approach from microwave observations during the typhoon season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

FunFOLDQA: a quality assessment tool for protein-ligand binding site residue predictions

The estimation of prediction quality is important because without quality measures, it is difficult to determine the usefulness of a prediction. Currently, methods for ligand binding site residue predictions are assessed in the function prediction category of the biennial Critical Assessment of Techniques for Protein Structure Prediction (CASP) experiment, utilizing the Matthews Correlation Coefficient (MCC) and Binding-site Distance Test (BDT) metrics. However, the assessment of ligand binding site predictions using such metrics requires the availability of solved structures with bound ligands. Thus, we have developed a ligand binding site quality assessment tool, FunFOLDQA, which utilizes protein feature analysis to predict ligand binding site quality prior to the experimental solution of the protein structures and their ligand interactions. The FunFOLDQA feature scores were combined using: simple linear combinations, multiple linear regression and a neural network. The neural network produced significantly better results for correlations to both the MCC and BDT scores, according to Kendall’s τ, Spearman’s ρ and Pearson’s r correlation coefficients, when tested on both the CASP8 and CASP9 datasets. The neural network also produced the largest Area Under the Curve score (AUC) when Receiver Operator Characteristic (ROC) analysis was undertaken for the CASP8 dataset. Furthermore, the FunFOLDQA algorithm incorporating the neural network, is shown to add value to FunFOLD, when both methods are employed in combination. This results in a statistically significant improvement over all of the best server methods, the FunFOLD method (6.43%), and one of the top manual groups (FN293) tested on the CASP8 dataset. The FunFOLDQA method was also found to be competitive with the top server methods when tested on the CASP9 dataset. To the best of our knowledge, FunFOLDQA is the first attempt to develop a method that can be used to assess ligand binding site prediction quality, in the absence of experimental data.