This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty of the "chaos" type occurs in many systems, is fundamental to understand these systems.
We give the first explicit formulas for the joint third and fourth central moments of the multinomial distribution, by differentiating the moment generating function. A general formula for the joint factorial moments was previously given in Mosimann (1962).
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of conditional independence, an extended version of Bayes' Theorem is then proposed with illustrations from both hypothetical and real-world examples of disease diagnosis.
Book review published as: Aronow, Peter M. and Fredrik Sävje (2020), "The Book of Why: The New Science of Cause and Effect." Journal of the American Statistical Association, 115: 482-485.
The complexity of a maximum likelihood estimation is measured by its maximum likelihood degree ($ML$ degree). In this paper we study the maximum likelihood problem associated to chemical networks composed by one single chemical reaction under the equilibrium assumption.
We propose a score function for Bayesian clustering. The function is parameter free and captures the interplay between the within cluster variance and the between cluster entropy of a clustering. It can be used to choose the number of clusters in well-established clustering methods such as hierarchical clustering or $K$-means algorithm.
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
This is part of a collection of discussion pieces on David Donoho's paper 50 Years of Data Science, appearing in Volume 26, Issue 4 of the Journal of Computational and Graphical Statistics (2017).
In this article, I summarise Peter Hall's contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him.
The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates the advantages of using the signature of a stream as the feature set for machine learning.
In this paper, we prove that the Renyi entropy of linearly normalized partial maxima of independent and identically distributed random variables is convergent to the corresponding limit Renyi entropy when the linearly normalized partial maxima converges to some nondegenerate random variable.
Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new Bayesian technique for analysing spatial point patterns. The technique is described in detail, and demonstrated on numerical examples.
This is a review of the book "Mixed Effects Models and Extensions in Ecology with R" by Zuur, Ieno, Walker, Saveliev and Smith (2009, Springer). I was asked to review this book for The American Statistician in 2010. After I wrote the review, the invitation was revoked. This is the review.
We should cease teaching frequentist statistics to undergraduates and switch to Bayes. Doing so will reduce the amount of confusion and over-certainty rife among users of statistics.
A long memory process has self-similarity or scale-invariant properties in low frequencies. We prove that the log of the scale-dependent wavelet variance for a long memory process is asymptotically proportional to scales by using the Taylor expansion of wavelet variances.