Hasil untuk "stat.OT"

Tiffany A. Timbers, Mine Çetinkaya-Rundel

Teaching data science presents unique challenges and opportunities that cannot be fully addressed by simply borrowing pedagogical strategies from its parent disciplines of statistics and computer science. Here, we present ten simple rules for teaching data science, developed and refined by leading educators in the community and successfully applied in our own data science classrooms.

Hanti Lin

While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial standards for evaluating non-deductive inferences have been assumed separately in those areas, but can actually be justified by a unifying principle.

Hanti Lin

There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a form of internalist reliabilism -- internalist in the conventional sense, yet reliabilist in certain unconventional and intriguing ways. Crucially, in developing the thesis that reliabilism does not imply externalism, my aim is not to stretch the meaning of `reliabilism' merely to sever the implication. Instead, it is to gain a deeper understanding of frequentist statistics, which stands as one of the most sustained attempts by scientists to develop an epistemology for their own use.

Richard S. J. Tol

New Matlab functions for network centrality are introduced. Instead of the mean distance, the generalized mean distance is used. If closer relationships are prioritized, this closeness measure is also defined for unconnected graphs. Instead of distance to all nodes, distance to selected nodes is considered. Besides the vertical in- and out-closeness measures, horizontal cross-closeness is proposed.

Djemel Ziou

In this paper, we establish the links between the Lehmer and Hölder mean families and maximum weighted likelihood estimator. Considering the regular one-parameter exponential family of probability density functions, we show that the maximum weighted likelihood of the parameter is a generalized weighted mean family from which Lehmer and Hölder mean families are derived. Some of the outcomes obtained provide a probabilistic interpretation of these mean families and could therefore broaden their uses in various applications.

Russell J. Bowater

A principle is modified that underlies the theory of organic fiducial inference as this theory was presented in an earlier paper. This modification, which is arguably a natural one to make, allows Bayesian inference to sometimes have a minor role within the theory in question and, as a consequence, allows more information from the data to be incorporated into the way a full conditional fiducial density is defined in certain cases. The new version of the principle concerned is applied to examples that were analysed previously using the older version of this principle.

David Kane

Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their computing skills (in the context of data analysis), the greater their likely success. Introductory courses should feature almost no mathematical/statistical formulas beyond simple algebra.

Hamed Masnadi-Shirazi, Alireza Masnadi-Shirazi, Mohammad-Amir Dastgheib

We present a step by step mathematical derivation of the Kalman filter using two different approaches. First, we consider the orthogonal projection method by means of vector-space optimization. Second, we derive the Kalman filter using Bayesian optimal filtering. We provide detailed proofs for both methods and each equation is expanded in detail.

Samuel Henry

The debate surrounding the hot hand in the NBA has been ongoing for many years. However, many of the previous works on this theme has focused on only the very next sequential shot attempt, often on very select players. This work looks in more detail the effect of a made or missed shot on the next series of shots over a two-year span, with time between shots shown to be a critical factor in the analysis. Also, multi-year streakiness is analyzed, and all indications are that players cannot really sustain their good (or bad) fortune from year to year.

Yunfan Wang, Vic Patrangenaru

In this paper after a brief revision of VW-means, which are extrinsic means on real and complex projective spaces, relative to the Veronese-Whitney embeddings, we give two examples of sample VW means computations on planar Kendall shape spaces. Here we derive large sample and pivotal nonparametric bootstrap confidence regions for VW-antimeans, using VW-anti-covariance matrices, and their sample counterparts

Yiping Cheng

In statistics education, the concept of population is widely felt hard to grasp, as a result of vague explanations in textbooks. Some textbook authors therefore chose not to mention it. This paper offers a new explanation by proposing a new theoretical framework of population and sampling, which aims to achieve high mathematical sensibleness. In the explanation, the term population is given clear definition, and the relationship between simple random sampling and iid random variables are examined mathematically.

Richard Pettigrew

In this paper, we explore how we should aggregate the degrees of belief of of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of way of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, or fix first and then aggregate? Or should we try to do both at once? And when do these different procedures agree with one another? In this paper, we focus particularly on the final question.

Hien D. Nguyen, Geoffrey J. McLachlan

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location- scale distributions are reviewed.

M. Ángeles Gallego, M. Victoria Ibáñez, Amelia Simó

In this paper, we propose a generalization to germ-grain models of the inhomogeneous K-function of Point Processes. We apply them to a sample of images of peripheral blood smears obtained from patients with Sickle Cell Disease, in order to decide whether the sample belongs to the thin, thick or morphological region.

Joris M. Mooij, Dominik Janzing, Bernhard Schölkopf

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

Christian P. Robert

This note is an extended read of my read of Laplace's book Theorie Analytique des Probabilites, when considered from a Bayesian viewpoint but without historical nor comparative pretentions. A deeper analysis is provided in Dale (1999).

Caren Marzban, Ulvi Yurtsever

A methodology is proposed for inferring the topology underlying point cloud data. The approach employs basic elements of Morse Theory, and is capable of producing not only a point estimate of various topological quantities (e.g., genus), but it can also assess their sampling uncertainty in a probabilistic fashion. Several examples of point cloud data in three dimensions are utilized to demonstrate how the method yields interval estimates for the topology of the data as a 2-dimensional surface embedded in R^3.

Robert E. Kass

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mischaracterize the process of statistical inference and I propose an alternative "big picture" depiction.

Murphy Choy

Investment approaches in financial instruments have been varied and often produce unpredictable results. Many investors in the earlier days of investment banking suffered catastrophical losses due to poor strategy and lack of understanding of the financial market. With the development of investment banking, many innovative investment strategies have been proposed to make portfolio returns higher than the overall market. One of the most famous theories of portfolio creation and management is the modern portfolio theory proposed by Harry Markowitz. In this paper, we shall apply the theory in creating a portfolio of stocks as well as managing it.

James M. Flegal, Galin L. Jones

This file is the Sweave documentation for the examples provided in Flegal, J. M. and Jones, G. L. (2010), "Implementing Markov chain Monte Carlo: Estimating with confidence", in Handbook of Markov Chain Monte Carlo, edited by Brooks, S., Gelman, A., Jones, G., and Meng, X. published by Chapman & Hall/CRC Press.