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At least 487 records · Page 27Linked to original sources
arXiv2019

Hybrid Resource Scheduling for Aggregation in Massive Machine-type Communication Networks

Data aggregation is a promising approach to enable massive machine-type communication (mMTC). Here, we first characterize the aggregation phase where a massive number of machine-type devices transmits to their respective aggregator. By using non-orthogonal multiple access (NOMA), we present a hybrid access scheme where several machine-type devices (MTDs) share the same orthogonal channel. Then, we assess the relaying phase where the aggregatted data is forwarded to the base station. The system performance is investigated in terms of average number of MTDs that are simultaneously served under imperfect successive interference cancellation (SIC) at the aggregator for two scheduling schemes, namely random resource scheduling (RRS) and channel-dependent resource scheduling (CRS), which is then used to assess the performance of data forwarding phase.

cs.NI↗
arXiv2019

Detecting and classifying moments in basketball matches using sensor tracked data

Data analytics in sports is crucial to evaluate the performance of single players and the whole team. The literature proposes a number of tools for both offence and defence scenarios. Data coming from tracking location of players, in this respect, may be used to enrich the amount of useful information. In basketball, however, actions are interleaved with inactive periods. This paper describes a methodological approach to automatically identify active periods during a game and to classify them as offensive or defensive. The method is based on the application of thresholds to players kinematic parameters, whose values undergo a tuning strategy similar to Receiver Operating Characteristic curves, using a ground truth extracted from the video of the games.

stat.AP↗
arXiv2019

On the Convergence Rate of the Quasi- to Stationary Distribution for the Shiryaev-Roberts Diffusion

For the classical Shiryaev--Roberts martingale diffusion considered on the interval $[0,A]$, where $A>0$ is a given absorbing boundary, it is shown that the rate of convergence of the diffusion's quasi-stationary cumulative distribution function (cdf), $Q_{A}(x)$, to its stationary cdf, $H(x)$, as $A\to+\infty$, is no worse than $O(\log(A)/A)$, uniformly in $x\ge0$. The result is established explicitly, by constructing new tight lower- and upper-bounds for $Q_{A}(x)$ using certain latest monotonicity properties of the modified Bessel $K$ function involved in the exact closed-form formula for $Q_{A}(x)$ recently obtained by Polunchenko (2017).

stat.CO↗
arXiv2020

On Finite Exchangeability and Conditional Independence

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent or completely dependent. We also provide a sufficient condition for an exchangeable vector so that its elements are marginally independent. We then generalize these results and conditions for exchangeable random networks. In this case, it is demonstrated that the situation is more complex. We show that the independence structure of exchangeable random networks lies in one of six regimes that are two-fold dual to one another, represented by undirected and bidirected independence graphs in graphical model sense with graphs that are complement of each other. In addition, under certain additional assumptions, we provide necessary and sufficient conditions for the exchangeable network distributions to be faithful to each of these graphs.

math.ST↗
arXiv2019

Model based Level Shift Detection in Autocorrelated Data Streams using a moving window

Standard Control Chart techniques to detect level shift in data streams assume independence between observations. As data today is collected with high frequency, this assumption is seldom valid. To overcome this, we propose to adapt the off-line test procedure for detection of outliers based on one-step prediction errors proposed by Tsay (1988) into an on-line framework by considering a moving window. Further, we present two algorithms, that in combination, estimate an appropriate test value for our control chart. We test our method on AR(1) processes exposed to level shifts of different sizes and compare it to CUSUM applied to one-step prediction errors. We find that, even though both methods perform comparable when tuned correctly, our method has higher probability of identifying the correct change point of the process. Furthermore, for more complicated processes our method is easier to tune, as the range of window size to be tested is independent of the process.

stat.ME↗
arXiv2019

Truth, Proof, and Reproducibility: There's no counter-attack for the codeless

Current concerns about reproducibility in many research communities can be traced back to a high value placed on empirical reproducibility of the physical details of scientific experiments and observations. For example, the detailed descriptions by 17th century scientist Robert Boyle of his vacuum pump experiments are often held to be the ideal of reproducibility as a cornerstone of scientific practice. Victoria Stodden has claimed that the computer is an analog for Boyle's pump -- another kind of scientific instrument that needs detailed descriptions of how it generates results. In the place of Boyle's hand-written notes, we now expect code in open source programming languages to be available to enable others to reproduce and extend computational experiments. In this paper we show that there is another genealogy for reproducibility, starting at least from Euclid, in the production of proofs in mathematics. Proofs have a distinctive quality of being necessarily reproducible, and are the cornerstone of mathematical science. However, the task of the modern mathematical scientist has drifted from that of blackboard rhetorician, where the craft of proof reigned, to a scientific workflow that now more closely resembles that of an experimental scientist. So, what is proof in modern mathematics? And, if proof is unattainable in other fields, what is due scientific diligence in a computational experimental environment? How do we measure truth in the context of uncertainty? Adopting a manner of Lakatosian conversant conjecture between two mathematicians, we examine how proof informs our practice of computational statistical inquiry. We propose that a reorientation of mathematical science is necessary so that its reproducibility can be readily assessed.

math.HO↗
arXiv2020

Leveraging Auxiliary Information on Marginal Distributions in Nonignorable Models for Item and Unit Nonresponse

Often, government agencies and survey organizations know the population counts or percentages for some of the variables in a survey. These may be available from auxiliary sources, for example, administrative databases or other high quality surveys. We present and illustrate a model-based framework for leveraging such auxiliary marginal information when handling unit and item nonresponse. We show how one can use the margins to specify different missingness mechanisms for each type of nonresponse. We use the framework to impute missing values in voter turnout in a subset of data from the U.S.\ Current Population Survey (CPS). In doing so, we examine the sensitivity of results to different assumptions about the unit and item nonresponse.

stat.ME↗
arXiv2022

Rediscovering a little known fact about the t-test and the F-test: Algebraic, Geometric, Distributional and Graphical Considerations

We discuss the role that the null hypothesis should play in the construction of a test statistic used to make a decision about that hypothesis. To construct the test statistic for a point null hypothesis about a binomial proportion, a common recommendation is to act as if the null hypothesis is true. We argue that, on the surface, the one-sample t-test of a point null hypothesis about a Gaussian population mean does not appear to follow the recommendation. We show how simple algebraic manipulations of the usual t-statistic lead to an equivalent test procedure consistent with the recommendation. We provide geometric intuition regarding this equivalence and we consider extensions to testing nested hypotheses in Gaussian linear models. We discuss an application to graphical residual diagnostics where the form of the test statistic makes a practical difference. By examining the formulation of the test statistic from multiple perspectives in this familiar example, we provide simple, concrete illustrations of some important issues that can guide the formulation of effective solutions to more complex statistical problems.

stat.OT↗
arXiv2019

Continuously Updated Data Analysis Systems

When doing data science, it's important to know what you're building. This paper describes an idealized final product of a data science project, called a Continuously Updated Data-Analysis System (CUDAS). The CUDAS concept synthesizes ideas from a range of successful data science projects, such as Nate Silver's FiveThirtyEight. A CUDAS can be built for any context, such as the state of the economy, the state of the climate, and so on. To demonstrate, we build two CUDAS systems. The first provides continuously-updated ratings for soccer players, based on the newly developed Augmented Adjusted Plus-Minus statistic. The second creates a large dataset of synthetic ecosystems, which is used for agent-based modeling of infectious diseases.

stat.OT↗
arXiv2019

Karl Pearson and the Logic of Science: Renouncing Causal Understanding (the Bride) and Inverted Spinozism

Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics -- the prevalent inductive logic of contemporary science. However, before working in statistics, K.Pearson had other interests in life, namely, in this order, philosophy, physics, and biological heredity. Key concepts of his philosophical and epistemological system of anti-Spinozism (a form of transcendental idealism) are carried over to his subsequent works on the logic of scientific discovery. This article's main goal is to analyze K.Pearson early philosophical and theological ideas and to investigate how the same ideas came to influence contemporary science, either directly or indirectly -- by the use of variant theories, methods and dialects of statistics, corresponding to variant statistical inference procedures and their specific belief calculi.

stat.OT↗
arXiv2019

Stochastic differential theory of cricket

A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical meaning associated with them. This is in contrast with the traditional system of rating/ranking teams based on combination of different statical cumulants. Further more, using this formalism, a new method to calculate the winning probability as a progression of number of balls is given.

physics.soc-ph↗
arXiv2023

Distributed Hypothesis Testing over a Noisy Channel: Error-exponents Trade-off

A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to $n$ independent and identically distributed samples, denoted by $\mathbf{U}$ and $\mathbf{V}$, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of $(\mathbf{U},\mathbf{V})$ based on $\mathbf{V}$ and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off.

stat.OT↗
arXiv2019

A statistical framework for measuring the temporal stability of human mobility patterns

Despite the growing popularity of human mobility studies that collect GPS location data, the problem of determining the minimum required length of GPS monitoring has not been addressed in the current statistical literature. In this paper we tackle this problem by laying out a theoretical framework for assessing the temporal stability of human mobility based on GPS location data. We define several measures of the temporal dynamics of human spatiotemporal trajectories based on the average velocity process, and on activity distributions in a spatial observation window. We demonstrate the use of our methods with data that comprise the GPS locations of 185 individuals over the course of 18 months. Our empirical results suggest that GPS monitoring should be performed over periods of time that are significantly longer than what has been previously suggested. Furthermore, we argue that GPS study designs should take into account demographic groups. KEYWORDS: Density estimation; global positioning systems (GPS); human mobility; spatiotemporal trajectories; temporal dynamics

stat.OT↗
arXiv2019

The Poisson binomial distribution -- Old & New

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the use of the Poisson binomial machinery. Some open questions of approximating rational fractions of the Poisson binomial are presented.

math.PR↗
arXiv2021

Investigating Sprawl using AIC and Recursive Partitioning Trees: A Machine Learning Approach to Assessing the Association between Poverty and Commute Time

Sprawl, according to Glaeser and Kahn, is the 21st century phenomenon that some people are not dependent on city-living due to automobiles and therefore can live outside public transportation spheres and cities. This is usually seen as pleasant and accompanied by improved qualities of life, but as they addressed, the problem remains that sprawl causes loss of jobs for those who cannot afford luxurious alternatives but only inferior substitutes (Glaeser and Kahn 2004). Therefore, through our question, we hope to suggest that sprawl has occurred in the U.S. and poverty is one of the consequences.

stat.AP↗
arXiv2019

Statistical Robust Chinese Remainder Theorem for Multiple Numbers

Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our knowledge, it is the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation. To address the problem, two novel approaches are established. One is to directly calculate a conditional maximum a posteriori probability (MAP) estimation of the residue clustering, and the other is based on a generalized wrapped Gaussian mixture model to iteratively search for MAP of both estimands and clustering. Residue error correcting codes are introduced to improve the robustness further. Experimental results show that the statistical schemes achieve much stronger robustness compared to state-of-the-art deterministic schemes, especially in heavy-noise scenarios.

stat.OT↗
arXiv2019

Reduced-bias estimation of spatial econometric models with incompletely geocoded data

The application of state-of-the-art spatial econometric models requires that the information about the spatial coordinates of statistical units is completely accurate, which is usually the case in the context of areal data. With micro-geographic point-level data, however, such information is inevitably affected by locational errors, that can be generated intentionally by the data producer for privacy protection or can be due to inaccuracy of the geocoding procedures. This unfortunate circumstance can potentially limit the use of the spatial econometric modelling framework for the analysis of micro data. Indeed, some recent contributions (see e.g. Arbia, Espa and Giuliani 2016) have shown that the presence of locational errors may have a non-negligible impact on the results. In particular, wrong spatial coordinates can lead to downward bias and increased variance in the estimation of model parameters. This contribution aims at developing a strategy to reduce the bias and produce more reliable inference for spatial econometrics models with location errors. The validity of the proposed approach is assessed by means of a Monte Carlo simulation study under different real-case scenarios. The study results show that the method is promising and can make the spatial econometric modelling of micro-geographic data possible.

stat.ME↗