Topic overview

stat.OT

271 works784 researchers

Open map Browse papers

Map preview

Start with the graph, then narrow the list

271works

784researchers

Next steps

Use the topic as a working map

Open the full map for clusters, then return here to scan ranked papers and people.

Inspect nearby papers, researchers, institutions and communities without opening a separate graph page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

preprint2016arXiv

A Graph Downsampling Technique Based On Graph Fourier Transform

In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled signal. Moreover, if the signal is not bandlimited, we provide a quality measure for comparing different downsampling schemes. Using this quality measure, we propose a greedy downsampling algorithm. Most of the prevailing approaches consider undirected graphs, and exploit the topological properties of the graph in order to downsample the grid, while the proposed method exploits spectral properties of graph signals, and is applicable to directed graphs, undirected graphs, and graphs with negative edge-weights. We provide several experiments demonstrating our downsampling scheme, and compare our quality measure with measures like normalized cuts.

preprint2016arXiv

The BIN_COUNTS Constraint: Filtering and Applications

We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of the Balanced Academic Curriculum Problem and of the Balanced Nursing Workload Problem. For both these problems we carry out numerical studies involving our reformulations. Finally, we present a further application of the $χ^2$ test constraint in the context of confidence interval analysis.

preprint2016arXiv

BayesVarSel: Bayesian Testing, Variable Selection and model averaging in Linear Models using R

This paper introduces the R package BayesVarSel which implements objective Bayesian methodology for hypothesis testing and variable selection in linear models. The package computes posterior probabilities of the competing hypotheses/models and provides a suite of tools, specifically proposed in the literature, to properly summarize the results. Additionally, \ourpack\ is armed with functions to compute several types of model averaging estimations and predictions with weights given by the posterior probabilities. BayesVarSel contains exact algorithms to perform fast computations in problems of small to moderate size and heuristic sampling methods to solve large problems. The software is intended to appeal to a broad spectrum of users, so the interface has been carefully designed to be highly intuititive and is inspired by the well-known lm function. The issue of prior inputs is carefully addressed. In the default usage (fully automatic for the user)BayesVarSel implements the criteria-based priors proposed by Bayarri et al (2012), but the advanced user has the possibility of using several other popular priors in the literature. The package is available through the Comprehensive R Arc

preprint2016arXiv

J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test

This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to assign prior mass to a general law - is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923). However, our historical investigation also suggests that in 1932 J. B. S. Haldane made an important contribution to the development of the Bayes factor by proposing the use of a mixture prior comprising a point mass and a continuous probability density. Jeffreys was aware of Haldane's work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have played a much bigger role in the statistical development of the Bayes factor than has hitherto been assumed.

preprint2016arXiv

Demmartingales and the functionnal Hill process for small parameters

Association of random variables and Demimartingales are recent fields for handling asymptotic behaviors of sums of dependent random variables. We apply their techniques to establish the asymptotic law of a demimartingale We next apply the results to find the asymptotic behavior the functional Hill process for small parameters within the Extreme Value Theory (EVT) field. Such a result would have been very hard to find whithout demimartingales techniques.

preprint2014arXiv

The Final Solutions of Monty Hall Problem and Three Prisoners Problem

Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory, or quantum language), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy).And we believe that this quantum language is the most powerful language to describe science. The purpose of this paper is to describe the Monty-Hall problem and the three prisoners problem in quantum language. We of course believe that our proposal is the final solutions of the two problems. Thus in this paper, we can answer the question: "Why have philosophers continued to stick to these problems?" And the readers will find that these problems are never elementary, and they can not be solved without the deep understanding of "probability" and "dualism". KEY WORDS: Philosophy of probability, Fisher Maximum Likelihood Method, Bayes' Method,The Principle of Equal (a priori) Probabilities

preprint2016arXiv

Stop the tests: Opinion bias and statistical tests

When statisticians quarrel about hypothesis testing, the debate usually focus on which method is the correct one. The fundamental question of whether we should test hypothesis at all tends to be forgotten. This lack of debate has its roots on our desire to have ideas we believe and defend. But cognitive experiments have been showing that, when we do choose ideas, we become prey to a large number of biases. Several of our biases can be grouped together in a single description, an opinion bias. This opinion bias is nothing more than our desire to believe in something and to defend it. Also, despite our feelings, believing has no solid logical or philosophical grounds. In this paper, I will show that if we combine the fact that even logic can never prove an idea right or wrong and the problems our brains cause when we pick ideas, hypothesis testing and its terminology are a recipe for disaster. Testing should have no place when we are thinking about hypothesis.

preprint2016arXiv

On $p$-values

Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context $p$-values are one measure of approximation, a small $p$-value indicating a poor approximation. Approximation regions are defined and distinguished from confidence regions.

preprint2012arXiv

Probability Distribution of the Quality Factor of a Mode-Stirred Reverberation Chamber

We derive a probability distribution, confidence intervals and statistics of the quality (Q) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of the idealized random cavity field with assumed perfect stir efficiency. It is shown that Q exhibits a Fisher-Snedecor F-distribution whose degrees of freedom are governed by the number of simultaneously excited cavity modes per stir state. The most probable value of Q is between a fraction 2/9 and 1 of its mean value, and between a fraction 4/9 and 1 of its asymptotic (composite Q) value. The arithmetic mean value is found to always exceed the values of all other theoretical metrics for centrality of Q. For a rectangular cavity, we retrieve the known asymptotic Q in the limit of highly overmoded regime.

preprint2016arXiv

Apocalypse Now? Reviving the Doomsday Argument

Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe containing a greater number of observers. Here we present a Bayesian reformulation of the Doomsday Argument which is immune to this effect. By marginalising over the spatial configuration of observers, we find that any preference for a larger total number of observers has no impact on the inferred local number. Our results remain unchanged when we adopt either the Self-Indexing Assumption (SIA) or the Self-Sampling Assumption (SSA). Furthermore the median value of our posterior distribution is found to be in agreement with the frequentist forecast. Humanity's prognosis for the coming century is well approximated by a global catastrophic risk of 0.2% per year.

preprint2016arXiv

Solution for the Indefinite Integral of the Standard Normal Probability Density Function

Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this anti-derivative in infinite elementary terms that, when being differentiated, directly yields the standard normal density function. We derive this function using infinite partial integration and review its relation to the cumulative distribution function for the standard normal distribution and the error function.

preprint2016arXiv

Progress on a Conjecture Regarding the Triangular Distribution

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval can be performed via an order statistics-based method. It had been conjectured that such a method can be conducted using only a constant number of likelihood function evaluations, on average, as the sample size becomes large. We prove two theorems that validate this conjecture. Graphical and numerical results are presented to supplement our proofs.

preprint2016arXiv

A Scalable Framework for NBA Player and Team Comparisons Using Player Tracking Data

The release of NBA player tracking data greatly enhances the granularity and dimensionality of basketball statistics used to evaluate and compare player performance. However, the high dimensionality of this new data source can be troublesome as it demands more computational resources and reduces the ability to easily interpret findings. Therefore, we must find a way to reduce the dimensionality of the data while retaining the ability to differentiate and compare player performance. In this paper, Principal Component Analysis (PCA) is used to identify four principal components that account for 68% of the variation in player tracking data from the 2013-2014 regular season and intuitive interpretations of these new dimensions are developed by examining the statistics that influence them the most. In this new high variance, low dimensional space, you can easily compare statistical profiles across any or all of the principal component dimensions to evaluate characteristics that make certain players and teams similar or unique. A simple measure of similarity between two player or team statistical profiles based on the four principal component scores is also constructed. The Statistical D

preprint2016arXiv

Understanding Convolutional Neural Networks

Convoulutional Neural Networks (CNNs) exhibit extraordinary performance on a variety of machine learning tasks. However, their mathematical properties and behavior are quite poorly understood. There is some work, in the form of a framework, for analyzing the operations that they perform. The goal of this project is to present key results from this theory, and provide intuition for why CNNs work.

preprint2016arXiv

Designing Modular Software: A Case Study in Introductory Statistics

Modular programming is a development paradigm that emphasizes self-contained, flexible, and independent pieces of functionality. This practice allows new features to be seamlessly added when desired, and unwanted features to be removed, thus simplifying the user-facing view of the software. The recent rise of web-based software applications has presented new challenges for designing an extensible, modular software system. In this paper, we outline a framework for designing such a system, with a focus on reproducibility of the results. We present as a case study a Shiny-based web application called intRo, that allows the user to perform basic data analyses and statistical routines. Finally, we highlight some challenges we encountered, and how to address them, when combining modular programming concepts with reactive programming as used by Shiny.

preprint2016arXiv

A Devastating Example for the Halfer Rule

How should we update de dicto beliefs in the face of de se evidence? The Sleeping Beauty problem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other examples. A full generalization is not always given; one notable exception is the Halfer Rule, under which the agent updates her uncentered beliefs based on only the uncentered part of her evidence. In this brief article, I provide a simple example for which the Halfer Rule prescribes credences that, I argue, cannot be reasonably held by anyone. In particular, these credences constitute an egregious violation of the Reflection Principle. I then discuss the consequences for halfing in general.

preprint2016arXiv

Scale and curvature effects in principal geodesic analysis

There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the method of dimension reduction in linear spaces, to Riemannian manifolds. One such generalization is known as principal geodesic analysis (PGA). This paper, in a novel fashion, obtains Taylor expansions in scaling parameters introduced in the domain of objective functions in PGA. It is shown this technique not only leads to better closed-form approximations of PGA but also reveals the effects that scale, curvature and the distribution of data have on solutions to PGA and on their differences to first-order tangent space approximations. This approach should be able to be applied not only to PGA but also to other generalizations of PCA and more generally to other intrinsic statistics on Riemannian manifolds.

preprint2016arXiv

Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R

The condvis package is for interactive visualization of sections in data space, showing fitted models on the section, and observed data near the section. The primary goal is the interpretation of complex models, and showing how the observed data support the fitted model. There is a video accompaniment to this paper available at https://www.youtube.com/watch?v=rKFq7xwgdX0. This is a preprint version of an article to appear in the Journal of Statistical Software.

preprint2016arXiv

Spatial Temporal Exponential-Family Point Process Models for the Evolution of Social Systems

We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through individual transition distributions for each actor in the system at a given time. We prove that these distributions have an analytic closed form under certain conditions and use the result to develop likelihood-based inference. We provide a computational framework to enable both simulation and inference in practice. Finally, we demonstrate the value of these models by analyzing alcohol and drug use over time in the context of adolescent friendship networks.

preprint2015arXiv

Sensor Selection for Target Tracking in Wireless Sensor Networks with Uncertainty

In this paper, we propose a multiobjective optimization framework for the sensor selection problem in uncertain Wireless Sensor Networks (WSNs). The uncertainties of the WSNs result in a set of sensor observations with insufficient information about the target. We propose a novel mutual information upper bound (MIUB) based sensor selection scheme, which has low computational complexity, same as the Fisher information (FI) based sensor selection scheme, and gives estimation performance similar to the mutual information (MI) based sensor selection scheme. Without knowing the number of sensors to be selected a priori, the multiobjective optimization problem (MOP) gives a set of sensor selection strategies that reveal different trade-offs between two conflicting objectives: minimization of the number of selected sensors and minimization of the gap between the performance metric (MIUB and FI) when all the sensors transmit measurements and when only the selected sensors transmit their measurements based on the sensor selection strategy. Illustrative numerical results that provide valuable insights are presented.

preprint2016arXiv

Probabilistic Population Projections for Countries with Generalized HIV/AIDS Epidemics

The United Nations (UN) issued official probabilistic population projections for all countries to 2100 in July 2015. This was done by simulating future levels of total fertility and life expectancy from Bayesian hierarchical models, and combining the results using a standard cohort-component projection method. The 40 countries with generalized HIV/AIDS epidemics were treated differently from others, in that the projections used the highly multistate Spectrum/EPP model, a complex 15-compartment model that was designed for short-term projections of quantities relevant to policy for the epidemic. Here we propose a simpler approach that is more compatible with the existing UN probabilistic projection methodology for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression model on current life expectancy, HIV prevalence and ART coverage. These are then converted to age- and sex-specific mortality rates using a new family of model life tables designed for countries with HIV/AIDS epidemics that reproduces the characteristic hump in middle adult mortality. These are then input to the standard cohort-component method, as for other co

preprint2016arXiv

Marginalization and Conditioning for LWF Chain Graphs

In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.

preprint2016arXiv

Robust Hypothesis Testing with $α$-Divergence

A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $α-$divergence distances, is proposed. Sion's minimax theorem is adopted to characterize the saddle value condition. Least favorable distributions, the robust decision rule and the robust likelihood ratio test are derived. If the nominal probability distributions satisfy a symmetry condition, the design procedure is shown to be simplified considerably. The parameters controlling the degree of robustness are bounded from above and the bounds are shown to be resulting from a solution of a set of equations. The simulations performed evaluate and exemplify the theoretical derivations.

preprint2013arXiv

On moment indeterminacy of the Benini income distribution

The Benini distribution is a lognormal-like distribution generalizing the Pareto distribution. Like the Pareto and the lognormal distributions it was originally proposed for modeling economic size distributions, notably the size distribution of personal income. This paper explores a probabilistic property of the Benini distribution, showing that it is not determined by the sequence of its moments although all the moments are finite. It also provides explicit examples of distributions possessing the same set of moments. Related distributions are briefly explored.

157 works