Related papers: Notes on statistical separation of classes of even…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…
The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
Lecture notes on elements of nonequilibrium statistical mechanics: (1) a characterization of the nonequilibrium condition, largely by contrast to equilibrium; (2) a retelling of some of the great performances of the more distant past,…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
Two different conceptions of emergence are reconciled as two instances of the phenomenon of detection. In the process of comparing these two conceptions, we find that the notions of complexity and detection allow us to form a unified…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of…
The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…
We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.
Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.