Bivariate data

Abstract: Over the last few decades, many researchers have produced landslide susceptibility maps using different techniques including the probability method (frequency ratio), the analytical hierarchy process (AHP), bivariate, multivariate, logistics regression, fuzzy logic and artificial neural network In addition, a number of parameters such as lithology, slope, aspect, land cover, elevation, distance to stream, drainage density, distance to lineament, seismicity, and distance to road are recommended to analyze the mechanism of landslides. The data quality is a very important issue in landslide studies, and more accurate results will be achieved if the data is adequate, appropriate and drawn from a wide range of parameters. The aim of this study was to evaluate the susceptibility of the occurrence of landslides in Trabzon province, situated in north east Turkey. This was achieved using the following five methods the frequency ratio model, AHP, the statistical index (Wi), weighting factor (Wf) methods, and the logistics regression model, incorporating a Geographical Information System (GIS) and remote sensing techniques. In Trabzon province there has been an increasing occurrence of landslides triggered by rainfall. These landslides have resulted in death, significant injury, damage to property and local infrastructure and threat of further landslides continues. In order to reduce the effects of this phenomenon, it is necessary to scientifically assess the area susceptible to landslide. To achieve this, landslide susceptible areas were mapped the landslide occurrence parameters were analyzed using five different methods. The results of the five analyses were confirmed using the landslide activity map containing 50 active landslide zones. Then the methods giving more accurate results were determined. The validation process showed that the Wf method is better in prediction than the frequency ratio model, AHP, the statistical index (Wi), and logistics regression model.

Abstract: Background data furnishing a two-sample Mendelian randomization (MR) study are often visualized with the aid of a scatter plot, in which single-nucleotide polymorphism (SNP)-outcome associations are plotted against the SNP-exposure associations to provide an immediate picture of the causal-effect estimate for each individual variant. It is also convenient to overlay the standard inverse-variance weighted (IVW) estimate of causal effect as a fitted slope, to see whether an individual SNP provides evidence that supports, or conflicts with, the overall consensus. Unfortunately, the traditional scatter plot is not the most appropriate means to achieve this aim whenever SNP-outcome associations are estimated with varying degrees of precision and this is reflected in the analysis. Methods We propose instead to use a small modification of the scatter plot-the Galbraith Radial plot-for the presentation of data and results from an MR study, which enjoys many advantages over the original method. On a practical level, it removes the need to recode the genetic data and enables a more straightforward detection of outliers and influential data points. Its use extends beyond the purely aesthetic, however, to suggest a more general modelling framework to operate within when conducting an MR study, including a new form of MR-Egger regression. Results We illustrate the methods using data from a two-sample MR study to probe the causal effect of systolic blood pressure on coronary heart disease risk, allowing for the possible effects of pleiotropy. The Radial plot is shown to aid the detection of a single outlying variant that is responsible for large differences between IVW and MR-Egger regression estimates. Several additional plots are also proposed for informative data visualization. Conclusions The Radial plot should be considered in place of the scatter plot for visualizing, analysing and interpreting data from a two-sample summary data MR study. Software is provided to help facilitate its use.

Abstract: Traditionally, geostatistical models are conditioned only on univariate and bivariate statistics such as the sample histogram and covariance or indicator covariances. Higher order sample statistics such as three, four, multi-point covariances, as obtained, for example, from a training image, would improve considerably stochastic images if they could be reproduced.