Narrow Results

The Bloomberg Carbon Clock is a web-based and real-time estimate of the global average atmospheric CO₂ level. The work was conceived to help non-scientists understand the seasonal nature of atmospheric composition, and offers a click-through explanation of the CO₂ data’s meaning, history, and implications. The Carbon Clock was designed to satisfy both scientific rigor and aesthetic appeal.

Econometrics has become an integral part of training in modern economics and business. Together with microeconomics and macroeconomics, econometrics has been taught as one of the three core courses in most undergraduate and graduate economic programs in the world. This chapter discusses the philosophy and methodology of econometrics in economic research, the roles and limitations of econometrics, and the differences between econometrics and mathematical economics as well as mathematical statistics. A variety of illustrative econometric examples are given, which cover various fields of economics and finance.

Metrologists are increasingly being faced with challenges in statistical data analysis and modeling, data reduction, and uncertainty evaluation, that require an ever more demanding and comprehensive analytical and computational toolkit as well as a strategy for communication of more complex results. For example, conventional assumptions of Gaussian (or normal) measurement errors may not apply, which then necessitates alternative procedures for uncertainty evaluation.

This contribution, aimed at metrologists whose specialized knowledge is in a particular area of science, and whose prior study of topics in probability or statistics will have been merely introductory, provides illustrative examples and suggestions for self-study. These examples aim to empower metrologists to attain a working level of concepts, statistical methods, and computational techniques from these particular areas, to become self-sufficient in the statistical analysis and modeling of their measurement data, and to feel comfortable evaluating, propagating, and communicating the associated measurement uncertainty.

The contribution also addresses modern computational requirements in measurement science. Since it is becoming clear to many metrologists that tools like Microsoft Excel, Libreoffice Calc, or Apple’s Numbers often are in-sufficiently flexible to address emerging needs, or simply fail to provide required specialized tools, this contribution includes accompanying R code with detailed explanations that will guide scientists through the use of a new computing tool.

One of the main goals of modern cosmology is to probe inflationary theories by looking on the imprint of primordial gravitational waves in the cosmic microwave background (CMB) polarization field. Future CMB experiments face the great challenge to search for this primordial B-mode signal. However, the CMB sky is also filled with secondary B-modes, including CMB lensing and astrophysical foregrounds. Extracting the CMB B-mode polarization from astrophysical contaminations is a primordial task towards detection of the primordial signal. We use the analytical method of blind separation (ABS) proposed by Zhang, P., et al. (2019) to reconstruct the CMB B-mode power spectrum in the presence of foregrounds and white noise considering a full sky analysis for r = 0.

Null hypothesis significance testing (NHST) has been a fixture of psychological research for decades. Despite much debate about the appropriateness, suitability, and philosophy of NHST, the field still has yet to move away from the practice. One factor in the unwillingness or inability to move away from NHST is the lack of alternative practices available. In the current chapter, we suggest several possibilities for analyzing and reporting results without reliance on NHST.

Shortly after his escape, in 1968, from the DDR to the Western world, Harald Fritzsch made a fast career in physics while investigating the strong force in elementary particles. Inspired by Gell-Mann, Yang and Mills and many others, he contributed to the rise of the Standard Model, and in particular the developments of theories for the color confinement mechanism.

This chapter covers the statistical techniques using linear regression for quantitative outcomes, logistic regression for qualitative outcomes and Cox regression for time-to-event outcomes. Examples of result interpretation and presentation by means of tables for univariate and multivariate analyses were shown.

The following sections are included:

• THE ROLE OF STATISTICS IN BUSINESS AND ECONOMICS
  • TV Show Ratings
  • ABC GPA
  • One, Two, Three, “Fore!”
  • Health Benefits of Oat Bran
  • Fertilizer Choice and Plant Growth Rate

• DESCRIPTIVE VERSUS INFERENTIAL STATISTICS
  • Baseball Players’ Batting Averages
  • Monthly Unemployment Rates
  • Comparison of Male and Female Earnings
  • Returns on Stocks and Bonds
  • Pitfalls of Comparing the Earnings of Males and Females
  • Sampling Survey of Residents’ Voting Decision
  • Unemployment Rate
  • Quality Control Via Sampling Data
  • A Record Drop in Stock Prices

• DEDUCTIVE VERSUS INDUCTIVE ANALYSIS IN STATISTICS

• Summary

• Questions and Problems

In this paper, we summarize some of the main observational challenges for the standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and describe how results recently presented in the parallel session “Large-scale Structure and Statistics” (DE3) at the “Fourteenth Marcel Grossman Meeting on General Relativity” are related to these challenges.

For about a decade, the baryon acoustic oscillation (BAO) peak at about 105h⁻¹ Mpc has provided a standard ruler test of the ΛCDM cosmological model, a member of the Friedmann–Lemaître–Robertson–Walker (FLRW) family of cosmological models— according to which comoving space is rigid. However, general relativity does not require comoving space to be rigid. During the virialisation epoch, when the most massive structures form by gravitational collapse, it should be expected that comoving space evolves inhomogeneous curvature as structure grows. The BAO peak standard ruler should also follow this inhomogeneous evolution if the comoving rigidity assumption is false. This “standard” ruler has now been detected to be flexible, as expected under general relativity.

The backreaction of inhomogeneities describes the effect of inhomogeneous structure on average properties of the Universe. We investigate this approach by testing the consistency of cosmological N-body simulations as non-linear structure evolves. Using the Delaunay Tessellation Field Estimator (DTFE), we calculate the kinematical backreaction Q from simulations on different scales in order to measure how much N-body simulations should be corrected for this effect. This is the first step towards creating fully relativistic and inhomogeneous N-body simulations. In this paper we compare the interpolation techniques available in DTFE and illustrate the statistical dependence of Q as a function of length scale.

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and EB, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-) dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.

In the previous chapters, we have discussed probability theory. In this chapter, we will introduce some basic concepts in statistics. The basic idea of statistical inference is to assume that the observed data is generated from some unknown probability distribution, which is often assumed to have a known functional form up to some unknown parameters. The purpose of statistical inference is to develop theory and methods to make inference on the unknown parameters based on observed data.

When we do usual Computation in Science, especially in Metrology, we assume that we do Mathematics. This is only partly true in spite of the fact that database handling and data processing are most important indeed. The field of Measurement plus Observation is much more entangled with Mathematics. The following survey “Metrology and Mathematics” will focus on selected ideas, concepts, rules, models, and structures, each of which is of a basic mathematical nature. When doing this, it is not surprising at all that most theoretical and applicational requirements in the field can be reduced to just a few basic logical and mathematical structures. This is also true for complex processes in fields like humanity and society. Signal and System Theory (SST) supports this claim. However, such an endeavour asks for an orderly and consistent definition of quantities and processes and of their mathematical models, called signals and systems. These models represent all kinds of issues, items, and phenomena in the real world. The term model indicates the superordinate means of mathematical description, observation, and representation in Science and Technology. The question arises, what the role of Logic and Mathematics looks like in detail. The term structure will be consistently pivotal. And, as is generally known, structures are best visualised by graphical means, here called Signal Relation Graphs (SRG).

Quantum counterparts of certain classical systems exhibit chaotic spectral statistics of their energy levels; eigenvalues of infinite random matrices model irregular spectra. Eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices admit a gamma distribution approximation, as do the hermitian unitary (GUE) and quaternionic symplectic (GSE) cases. Then chaotic and non-chaotic cases fit in the information geometric framework of the manifold of gamma distributions, which has been the subject of recent work on neighbourhoods of randomness for general stochastic systems.

In dermatology, the optical coherence tomography (OCT) is used to visualize the skin over few millimeters depth. These images are affected by speckle, which can alter their interpretation, but which also carries information that characterizes locally the visualized tissue. In this paper, we propose to differentiate the skin layers by modeling locally the speckle in OCT images. The performances of four probability density functions (Rayleigh, Lognormal, Nakagami and Generalized Gamma) to model the distribution of speckle in each skin layer are analyzed. From this study, we propose to classify the pixels of OCT images using the estimated parameters of the most appropriate distribution. Quantitative results with 30 images are compared to the manual delineations of five experts. The results confirm the potential of the method to generate useful data for robust segmentation.

A new data-driven method for morphodynamic seabed modelling and prediction that is able to account for morphological relationships across space is presented. The new method uses a two-dimensional spatial statistical model that first derives surfaces that are representative of the spatial morphological properties in both the cross-shore and alongshore directions simultaneously. It evaluates the spatial changes that occur between successive surfaces across the time series to derive a spatial-temporal function of the behaviour evolution. The resulting function is then extrapolated to obtain a prediction. The model is initially applied to idealised morphological scenarios with known morphological and evolution properties to assess its validity for morphological applications. The outcome from the idealised cases indicates that the model is relevant to such applications as it was able to identify morphological properties and evolution behaviour. It was also able to predict future states of the idealised morphology within a margin that is less than the natural variability of the feature.

The workshop focused on approaches to deduce changes in biological activity in cellular pathways and networks that drive phenotype from high-throughput data. Work in cancer has demonstrated conclusively that cancer etiology is driven not by single gene mutation or expression change, but by coordinated changes in multiple signaling pathways. These pathway changes involve different genes in different individuals, leading to the failure of gene-focused analysis to identify the full range of mutations or expression changes driving cancer development. There is also evidence that metabolic pathways rather than individual genes play the critical role in a number of metabolic diseases. Tools to look at pathways and networks are needed to improve our understanding of disease and to improve our ability to target therapeutics at appropriate points in these pathways.

We examine the evolution of the spatial counts-in-cells distribution of galaxies and show that the form of the galaxy distribution function does not change significantly as galaxies merge and evolve. In particular, bound merging pairs follow a similar distribution to that of individual galaxies. From the adiabatic expansion of the universe we show how clustering, expansion and galaxy mergers affect the clustering parameter b. We also predict the evolution of b with respect to redshift.

In the light of the ever changing and developing technology in the libraries, library managers across the sector and all over the world need to utilize all possible means of ensuring that the quality of services remains optimal. This paper shows some of the uses of different evaluation tools in an academic library. The paper will describe the practical use of surveys, larger and smaller, questionnaires, focus groups and stake holder meetings, all of which will yield different kinds of data. As part of quality management, the practical uses of this data will be explored.