Some results on Gaussian mixtures

Felgueiras, Miguel; Santos, Rui; Martins, João Paulo

doi:10.1063/1.4897790

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…Let v denote the random variable corresponding to this Gaussian mixture (this is called the “vote-share per county” in Fig 1 ). This Gaussian mixture is a unimodal distribution with mode at μ , skewness value β 1 = 0, kutosis value , and variance Using the Pearson system, the Gaussian scale mixture can be shown to be approximately a t -distribution [ 82 ]. More specifically, Let and c 2 = ( β 2 − 3)/(5 β 2 − 9) be the Pearson coefficients corresponding to the Gaussian mixture, and let , and m = (1 − c 2 )/ c 2 .…”

Section: The Modelmentioning

confidence: 99%

“…More specifically, Let and c 2 = ( β 2 − 3)/(5 β 2 − 9) be the Pearson coefficients corresponding to the Gaussian mixture, and let , and m = (1 − c 2 )/ c 2 . Then, the scaled and shifted random variable α ( v − μ ) is approximately distributed as a Student's t -distribution with m degrees of freedom [ 82 ]. Notice that the parameters μ , α , and m of this Student's t -distribution can be completely specified once the external parameters N 0 , N 0 are estimated (as was shown above), and the number of counties in the state n , and total number of votes N i in each county are given (these data are publicly available in many countries).…”

Section: The Modelmentioning

confidence: 99%

See 1 more Smart Citation

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Braha

Aguiar

2017

PLoS ONE

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Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science—elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.

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Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Braha

Aguiar

2017

PLoS ONE

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“…Using the Pearson system, the Gaussian scale mixture can be shown to be approximately a t-distribution [82]. More specifically, Let c 0 ¼ 2s 2 v b 2 =ð5b 2 À 9Þ and c 2 = (β 2 − 3)/(5β 2 − 9) be the Pearson coefficients corresponding to the Gaussian mixture, and let a ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ð1 À c 2 Þ=c 0 p , and m = (1 − c 2 )/c 2 .…”

Section: Derivation Of the Stationary Vote-share Distribution Across Countiesmentioning

confidence: 99%

“…More specifically, Let c 0 ¼ 2s 2 v b 2 =ð5b 2 À 9Þ and c 2 = (β 2 − 3)/(5β 2 − 9) be the Pearson coefficients corresponding to the Gaussian mixture, and let a ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ð1 À c 2 Þ=c 0 p , and m = (1 − c 2 )/c 2 . Then, the scaled and shifted random variable α (v − μ) is approximately distributed as a Student's t-distribution with m degrees of freedom [82]. Notice that the parameters μ, α, and m of this Student's t-distribution can be completely specified once the external parameters N 0 , N 0 are estimated (as was shown above), and the number of counties in the state n, and total number of votes N i in each county are given (these data are publicly available in many countries).…”

Section: Derivation Of the Stationary Vote-share Distribution Across Countiesmentioning

confidence: 99%

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Braha

Aguiar

2018

Preprint

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Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science--elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.

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“…In our symposium (by presenter order), Miguel Felgueiras [2] investigate Gaussian mixtures with independent components and introduce a shifted and scaled t-Student distribution as an approximation for the distribution of Gaussian mixtures. Filipe J. Marques [6] study the distribution of the linear combination ofindependent Gamma random variables.…”

Section: Faculdade De Ciências E Tecnologia and Cma -Universidade Nova mentioning

confidence: 99%

Preface of the "Symposium on computational statistical methods"

Caeiro¹

2014

AIP Conference Proceedings

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In the last decades, computers power has increased exponentially and that power hasallowed the arisen of new and more complex computational statistical models and methods.In this symposium, we bring together researchers working or applying computational statistical. All the submitted papers in the symposium have been peer reviewed and selected on the basis of the originality, signi cance and clarity.In our symposium (by presenter order), Miguel Felgueiras [2] investigate Gaussian mixtures with independent components and introduce a shifted and scaled t-Student distribution as an approximation for the distribution of Gaussian mixtures. Filipe J. Marques [6] study the distribution of the linear combination ofindependent Gamma random variables. Ayana Mateus [8] presents an R package implementation of several nonparametric randomness tests. Fernanda Figueiredo [3] makes a comparison of sampling plans by variables using the bootstrap and Monte Carlo simulations. Luís M. Grilo [4]apply the bootstrap methodology to construct control charts, before and after a Box-Cox transformation, and compare their robustness and performance.João P. Martins [7] analyze the performance of a maximum likelihood computational algorithm for the prevalence rate estimation. Dora Prata Gomes [9] explores the statistical software R for modeling spatial extreme precipitation data. Finally, Frederico Caeiro [1]employ the Monte Carlo methodology to compare the finite sample behavior of two reduced bias estimators of the extreme value index.

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Some results on Gaussian mixtures

Cited by 5 publications

References 6 publications

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Voting contagion: Modeling and analysis of a century of U.S. presidential elections

Preface of the "Symposium on computational statistical methods"

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