Advocating a statistical definition for the BRDF

The definition of BRDF as a ratio of radiance to irradiance assumes that the geometrical optics framework applies, implicitly meaning that spatial coherence and diffraction of light have no significant effect in the reflection process. However, recent applications of BRDF push at increasing the angular resolution and thus at reducing the solid angles for illumination and collection. Therefore speckle, an optical effect inherent to the stochastic nature of scattering objects, becomes apparent. We suggest that BRDF should be redefined as the statistical average over that effect.

Improvement of the method for comparing subsidence of structures using the Fischer’s F-test and the Foster-Stuart test

To improve the quality of construction and increase the durability of engineering structures under construction, complex geodetic works should be performed, including geodetic observations of deformations of structures. These observations are carried out during the construction of buildings and structures and their operation, mainly before the period of deformation stabilization. In this regard, a reliable statistical definition of deformations close to the limit is necessary, based on the data of geodetic observations. The research helps to improve the definition of deformations of structures using the Fischer’s F-test and the Foster-Stuart test, based on analysis of the measurements of horizontal and vertical monitoring of industrial structures. According to the results, the magnitude of the subsidence plays a more significant role from than its absolute value, thus the value of the deformation intensity is of primary importance in justifying observation periodicity.

A Simple Approach to Assess if a Financial “Bubble” is Present: The Case of Bitcoin

This article’s goal is to evaluate if the recent price behavior of Bitcoin can be characterized as a financial market “bubble”. To deal with this assessment, we adopt a statistical definition of a “bubble” derived from the efficient market hypothesis and we propose a simple method to test this proposition, based on the time-series model known as random walk. We analyze the data available for Bitcoin prices, together with an asset selected as benchmark, and perform statistical tests derived from simple regression equations. The main conclusion is that there is consistent evidence that that Bitcoin follows the pattern of a financial “bubble” – at least, such pattern is more evident in the case of Bitcoin than in the stock index used as benchmark.

Mobbing as a problem in management ethics

A positive company image and its good reputation are usually results of ethical and honest behaviour towards employees and may improve competitiveness, increase profits, customer satisfaction, and create new job jobs. However, it often occurs in dynamically developing firms where ethical norms are not kept and this process can be seen in the lack of equal chances to get a job – people without connections remain without work. According to research, mobbing is a very serious problem. Psychological terror or mobbing in work life involves hostile and unethical communication that is conducted in a systematic manner by one or more individuals, mainly toward one individual, who, due to mobbing, is pushed into a helpless and defenceless position and held there by means of continuing mobbing activities. These actions occur on a very frequent basis (statistical definition: at least once a week) and over a long period (statistical definition: at least six months’ duration). Because of the high frequency and long duration of hostile behaviour, this maltreatment results in considerable mental, psychosomatic, and social misery.

On the meaning of independence in climate science

The concept of independence has been frequently mentioned in climate science research, but has rarely been defined and discussed in a theoretically robust and quantifiable manner. In this paper we argue that any discussion must start from a clear and unambiguous definition of what independence means and how it can be determined. We introduce an approach based on the statistical definition of independence, and illustrate with simple examples how it can be applied to practical questions. Firstly, we apply these ideas to climate models, which are frequently argued to not be independent of each other, raising questions as to the robustness of results from multi-model ensembles. We explore the dependence between models in a multi-model ensemble, and suggest a possible way forward for future weighting strategies. Secondly, we discuss the issue of independence in relation to the synthesis of multiple observationally based constraints on the climate system, using equilibrium climate sensitivity as an example. We show that the same statistical theory applies to this problem, and illustrate this with a test case, indicating how researchers may estimate dependence between multiple constraints.

On the meaning of independence in climate science

The concept of independence has been frequently raised in climate science, but has rarely been defined and discussed in a theoretically robust and quantifiable manner. Improved understanding of this topic is critical to better understanding of climate change. In this paper, we introduce a unifying approach based on the statistical definition of independence, and illustrate with simple examples how it can be applied to practical questions.

A statistical definition for reproducibility and replicability

Everyone agrees that reproducibility and replicability are fundamental characteristics of scientific studies. These topics are attracting increasing attention, scrutiny, and debate both in the popular press and the scientific literature. But there are no formal statistical definitions for these concepts, which leads to confusion since the same words are used for different concepts by different people in different fields. We provide formal and informal definitions of scientific studies, reproducibility, and replicability that can be used to clarify discussions around these concepts in the scientific and popular press.