Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

How Porosity and Permeability Vary Spatially With Grain Size, Sorting, Cement Volume, and Mineral Dissolution In Fluvial Triassic Sandstones: The Value of Geostatistics and Local Regression

Although it is well known that sandstone porosity and permeability are controlled by a range of parameters such as grain size and sorting, amount, type, and location of diagenetic cements, extent and type of compaction, and the generation of intergranular and intragranular secondary porosity, it is less constrained how these controlling parameters link up in rock volumes (within and between beds) and how they spatially interact to determine porosity and permeability. To address these unknowns, this study examined Triassic fluvial sandstone outcrops from the UK using field logging, probe permeametry of 200 points, and sampling at 100 points on a gridded rock surface. These field observations were supplemented by laser particle-size analysis, thin-section point-count analysis of primary and diagenetic mineralogy, quantitiative XRD mineral analysis, and SEM/EDAX analysis of all 100 samples. These data were analyzed using global regression, variography, kriging, conditional simulation, and geographically weighted regression to examine the spatial relationships between porosity and permeability and their potential controls. The results of bivariate analysis (global regression) of the entire outcrop dataset indicate only a weak correlation between both permeability porosity and their diagenetic and depositional controls and provide very limited information on the role of primary textural structures such as grain size and sorting. Subdividing the dataset further by bedding unit revealed details of more local controls on porosity and permeability. An alternative geostatistical approach combined with a local modelling technique (geographically weighted regression; GWR) subsequently was used to examine the spatial variability of porosity and permeability and their controls. The use of GWR does not require prior knowledge of divisions between bedding units, but the results from GWR broadly concur with results of regression analysis by bedding unit and provide much greater clarity of how porosity and permeability and their controls vary laterally and vertically. The close relationship between depositional lithofacies in each bed, diagenesis, and permeability, porosity demonstrates that each influences the other, and in turn how understanding of reservoir properties is enhanced by integration of paleoenvironmental reconstruction, stratigraphy, mineralogy, and geostatistics.

Increasing the accuracy of Nitrogen Dioxide (NO2) pollution mapping using geographically weighted regression (GWR) and geostatistics.

Nitrogen Dioxide (NO2) is known to act as an environmental trigger for many respiratory illnesses. As a pollutant it is difficult to map accurately, as concentrations can vary greatly over small distances. In this study three geostatistical techniques were compared, producing maps of NO2 concentrations in the United Kingdom (UK). The primary data source for each technique was NO2 point data, generated from background automatic monitoring and background diffusion tubes, which are analysed by different laboratories on behalf of local councils and authorities in the UK. The techniques used were simple kriging (SK), ordinary kriging (OK) and simple kriging with a locally varying mean (SKlm). SK and OK make use of the primary variable only. SKlm differs in that it utilises additional data to inform prediction, and hence potentially reduces uncertainty. The secondary data source was Oxides of Nitrogen (NOx) derived from dispersion modelling outputs, at 1km x 1km resolution for the UK. These data were used to define the locally varying mean in SKlm, using two regression approaches: (i) global regression (GR) and (ii) geographically weighted regression (GWR). Based upon summary statistics and cross-validation prediction errors, SKlm using GWR derived local means produced the most accurate predictions. Therefore, using GWR to inform SKlm was beneficial in this study.

Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

A Common KIF6 Polymorphism Increases Vulnerability to Low-Density Lipoprotein Cholesterol: Two Meta-Analyses and a Meta-Regression Analysis

Background: We sought to determine if a common polymorphism can influence vulnerability to LDL cholesterol, and thereby influence the clinical benefit derived from therapies that reduce LDL cholesterol.

Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Development and application of a multiple linear regression model to consider the impact of weekly waste container capacity on the yield from kerbside recycling programmes

The paper describes the development and application of a multiple linear regression model to identify how the key elements of waste and recycling infrastructure, namely container capacity and frequency of collection affect the yield from municipal kerbside recycling programmes. The overall aim of the research was to gain an understanding of the factors affecting the yield from municipal kerbside recycling programmes in Scotland. The study isolates the principal kerbside collection service offered by 32 councils across Scotland, eliminating those recycling programmes associated with flatted properties or multi occupancies. The results of a regression analysis model has identified three principal factors which explain 80% of the variability in the average yield of the principal dry recyclate services: weekly residual waste capacity, number of materials collected and the weekly recycling capacity. The use of the model has been evaluated and recommendations made on ongoing methodological development and the use of the results in informing the design of kerbside recycling programmes. The authors hope that the research can provide insights for the ongoing development of methods to optimise the design and operation of kerbside recycling programmes.

Role of vascular endothelial growth factor and placental growth factors during retinal vascular development and hyaloid regression

PURPOSE. Vascular endothelial growth factor (VEGF)-A and placental growth factor (PIGF) are members of a large group of homologous peptides identified as the VEGF family. Although VEGF-A is known to act as a potent angiogenic peptide in the retina, the vasoactive function of PIGF in this tissue is less well defined. This study has sought to elucidate the expression patterns and modulatory role of these growth factors during retinal vascular development and hyaloid regression in the neonatal mouse. METHODS. C57BL6J mice were killed at postnatal days (P)1, P3, P5, P7, P9, and P11. The eyes were enucleated and processed for in situ hybridization and immunocytochemistry and the retinas extracted for total protein or RNA. Separate groups of neonatal mice were also injected intraperitoneally daily from P2 through P9 with either VEGF-neutralizing antibody, PIGF-neutralizing antibody, isotype immunoglobulin (Ig)-G, or phosphate-buffered saline (PBS). The mice were then perfused with fluorescein isothiocyanate (FITC)-dextran, and the eyes were subsequently embedded in paraffin wax or flat mounted. RESULTS. Quantitative (real-time) reverse transcription-polymerase chain reaction (RT-PCR) demonstrated similar expression patterns of VEGF-A and PIGF mRNA during neonatal retinal development, although the fluctuation between time periods was greater overall for VEGF-A. The localization of VEGF-A and PIGF in the retina, as revealed by in situ hybridization and immunohistochemistry, was also similar. Neutralization of VEGF-A caused a significant reduction in the hyaloid and retinal vasculature, whereas PIGF antibody treatment caused a marked persistence of the hyaloid without significantly affecting retinal vascular development. CONCLUSIONS. Although having similar expression patterns in the retina, these growth factors appear to have distinct modulatory influences during normal retinal vascular development and hyaloid regression.

Determinants of WTP for Prosecco wine: A latent class regression with attitudinal responses

Purpose – Under investigation is Prosecco wine, a sparkling white wine from North-East Italy.
Information collection on consumer perceptions is particularly relevant when developing market
strategies for wine, especially so when local production and certification of origin play an important
role in the wine market of a given district, as in the case at hand. Investigating and characterizing the
structure of preference heterogeneity become crucial steps in every successful marketing strategy. The
purpose of this paper is to investigate the sources of systematic differences in consumer preferences.
Design/methodology/approach – The paper explores the effect of inclusion of answers to
attitudinal questions in a latent class regression model of stated willingness to pay (WTP) for this
specialty wine. These additional variables were included in the membership equations to investigate
whether they could be of help in the identification of latent classes. The individual specific WTPs from
the sampled respondents were then derived from the best fitting model and examined for consistency.
Findings – The use of answers to attitudinal question in the latent class regression model is found to
improve model fit, thereby helping in the identification of latent classes. The best performing model
obtained makes use of both attitudinal scores and socio-economic covariates identifying five latent
classes. A reasonable pattern of differences in WTP for Prosecco between CDO and TGI types were
derived from this model.
Originality/value – The approach appears informative and promising: attitudes emerge as
important ancillary indicators of taste differences for specialty wines. This might be of interest per se
and of practical use in market segmentation. If future research shows that these variables can be of use
in other contexts, it is quite possible that more attitudinal questions will be routinely incorporated in
structural latent class hedonic models.

Analysis of IL6 Signal Transduction Model using Reduced Rank Regression

This work presents the application of reduced rank regression to the field of systems biology. A computational approach is used to investigate the mechanisms of the janus-associated kinases/signal transducers and transcription factors (JAK/STAT) and mitogen activated protein kinases (MAPK) signal transduction pathways in hepatic cells stimulated by interleukin-6. The results obtained identify the contribution of individual reactions to the dynamics of the model. These findings are compared to previously available results from sensitivity analysis of the model which focused on the parameters involved and their effect. This application of reduced rank regression allows for an understanding of the individual reaction terms involved in the modelled signal transduction pathways and has the benefit of being computationally inexpensive. The obtained results complement existing findings and also confirm the importance of several protein complexes in the MAPK pathway which hints at benefits that can be achieved by further refining the model.