Global efforts to mitigate climate change are guided by projections of future temperatures. But the eventual equilibrium global mean temperature associated with a given stabilization level of atmospheric greenhouse gas concentrations remains uncertain, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions. Here we use ensemble simulations of simple climate-carbon-cycle models constrained by observations and projections from more comprehensive models to simulate the temperature response to a broad range of carbon dioxide emission pathways. We find that the peak warming caused by a given cumulative carbon dioxide emission is better constrained than the warming response to a stabilization scenario. Furthermore, the relationship between cumulative emissions and peak warming is remarkably insensitive to the emission pathway (timing of emissions or peak emission rate). Hence policy targets based on limiting cumulative emissions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rate or concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67 trillion tonnes of CO(2)), about half of which has already been emitted since industrialization began, results in a most likely peak carbon-dioxide-induced warming of 2 degrees C above pre-industrial temperatures, with a 5-95% confidence interval of 1.3-3.9 degrees C.

/pdf/warming-caused-by-cumulative-carbon-emissions-towards-the-1izc23tsof.pdf

Warming caused by cumulative carbon emissions towards the trillionth tonne

Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron's spiking probability to three typical covariates: the neuron's own spiking history, concurrent ensemble activity, and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron's spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and non-GLM likelihood functions using simulated data and multivariate single-unit activity data simultaneously recorded from the motor cortex of a monkey performing a visuomotor pursuit-tracking task. The point process framework provides a flexible, computationally efficient approach for maximum likelihood estimation, goodness-of-fit assessment, residual analysis, model selection, and neural decoding. The framework thus allows for the formulation and analysis of point process models of neural spiking activity that readily capture the simultaneous effects of multiple covariates and enables the assessment of their relative importance.

/pdf/a-point-process-framework-for-relating-neural-spiking-1m68sz6j3v.pdf

A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects.

In this paper, multivariate regression is adopted to improve spectral quality, without diminishing spatial quality, in image fusion methods based on the well-established component substitution (CS) approach. A general scheme that is capable of modeling any CS image fusion method is presented and discussed. According to this scheme, a generalized intensity component is defined as the weighted average of the multispectral (MS) bands. The weights are obtained as regression coefficients between the MS bands and the spatially degraded panchromatic (Pan) image, with the aim of capturing the spectral responses of the sensors. Once it has been integrated into the Gram-Schmidt spectral-sharpening method, which is implemented in environment for visualizing images (ENVI) program, and into the generalized intensity-hue-saturation fusion method, the proposed preprocessing module allows the production of fused images of the same spatial sharpness but of increased spectral quality with respect to the standard implementations. In addition, quantitative scores carried out on spatially degraded data clearly confirm the superiority of the enhanced methods over their baselines.

Improving Component Substitution Pansharpening Through Multivariate Regression of MS $+$ Pan Data

Improvement of health care requires making changes in processes of care and service delivery. Although process performance is measured to determine if these changes are having the desired beneficial effects, this analysis is complicated by the existence of natural variation—that is, repeated measurements naturally yield different values and, even if nothing was done, a subsequent measurement might seem to indicate a better or worse performance. Traditional statistical analysis methods account for natural variation but require aggregation of measurements over time, which can delay decision making. Statistical process control (SPC) is a branch of statistics that combines rigorous time series analysis methods with graphical presentation of data, often yielding insights into the data more quickly and in a way more understandable to lay decision makers. SPC and its primary tool—the control chart—provide researchers and practitioners with a method of better understanding and communicating data from healthcare improvement efforts. This paper provides an overview of SPC and several practical examples of the healthcare applications of control charts.

https://qualitysafety.bmj.com/content/qhc/12/6/458.full.pdf

Statistical process control as a tool for research and healthcare improvement

The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.

NPCR and UACI Randomness Tests for Image Encryption

Introduction to Statistical Quality Control (2nd ed.)

Introduction to Probability and Statistics for Engineers and Scientists

As the title indicates, this book discusses using the likelihood function for both modeling and inference. It is written as a textbook with a fair number of examples. The author conveniently provides code using the statistical package R for all relevant examples on his web site. He assumes a list of prerequisites that would typically be covered in the  rst year of a master’s degree in statistics (or possibly in a solid undergraduate program in statistics). A good background in probability and theory of statistics, familiarity with applied statistics (such as tests of hypotheses, con dence intervals, least squares and p values), and calculus are prerequisites for using this book. The author presents interesting philosophical discussions in Chapters 1 and 7. In Chapter 1 he explains the differences between a Bayesian versus frequentist approach to statistical inference. He states that the likelihood approach is a compromise between these two approaches and that it could be called a Fisherian approach. He argues that the likelihood approach is non-Bayesian yet has Bayesians aspects and that it has frequentist features but also some nonfrequentist aspects. He references Fisher throughout the book. In Chapter 7 the author discusses the controversial informal likelihood principle, “two datasets (regardless of experimental source) with the same likelihood should lead to the same conclusions.” It is hard to be convinced that how data were collected does not affect conclusions. Chapters 2 and 3 provide de nitions and properties for likelihood functions. Some advanced technical topics are addressed in Chapters 8, 9, and 12, including score function, Fisher information, minimum variance unbiased estimation, consistency of maximum likelihood estimators, goodness-of- t tests, and the EM algorithm. Six chapters deal with modeling. Chapter 4 presents the basic models, binomial and Poisson, with some applications. Chapter 6 focuses on regression models, including normal linear, logistic, Poisson, nonnormal, and exponential family, and deals with the related issues of deviance, iteratively weighted least squares, and the Box–Cox transformations. Chapter 11 covers models with complex data structure, including models for time series data, models for survival data, and some specialized Poisson models. Chapter 14 examines quasi-likelihood models, Chapter 17 covers random and mixed effects models, and Chapter 18 introduces the concept of nonparametric smoothing. The remaining chapters put more emphasis on inference. Chapter 5 deals with frequentist properties including bias of point estimates, p values, con dence intervals, con dence intervals via bootstrapping, and exact inference for binomial and Poisson models. Chapter 10 handles nuisance parameters using marginal and conditional likelihood, modi ed pro le likelihood, and estimated likelihood methods. Chapter 13 covers the robustness of a speci ed likelihood. Chapter 15 introduces empirical likelihood concepts, and Chapter 16 addresses random parameters. This book works  ne as a textbook, providing a nice introduction to a variety of topics. For engineers, this book can also serve as a good initial exposure to possibly new concepts without overwhelming them with details. But when applying a speci c topic covered in this book to real problems, a more specialized book with greater depth and/or more practical examples may be desired.

In All Likelihood: Statistical Modeling and Inference Using Likelihood

(2002). Introduction to Statistics and Data Analysis. Technometrics: Vol. 44, No. 1, pp. 90-90.

Introduction to Statistics and Data Analysis

(2007). Introduction to Engineering Statistics and Six Sigma. Technometrics: Vol. 49, No. 2, pp. 229-229.

Roger M. Sauter

Papers

Introduction to Statistical Quality Control (2nd ed.)

Introduction to Probability and Statistics for Engineers and Scientists

In All Likelihood: Statistical Modeling and Inference Using Likelihood

Introduction to Statistics and Data Analysis

Introduction to Engineering Statistics and Six Sigma