Distributions.jl: Definition and Modeling of Probability Distributions in the JuliaStats Ecosystem

Besançon, Mathieu; Papamarkou, Theodore; Anthoff, David; Arslan, Alex; Byrne, Simon; Lin, Dahua; Pearson, John

doi:10.48550/arxiv.1907.08611

Cited by 7 publications

(10 citation statements)

References 14 publications

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“…We simulated all sets of differential equations using the 5th order adaptive time-stepping method based on the Runge-Kutta method with appropriated coefficient choices defined by Tsitouras [47] and implementated in Julia programming language [48,49] available in the packet DifferentialEquations.jl [50]. A sufficient large number of integration steps are discarded (a transient trajectory) before trajectories of 1000 time-points are recorded to be analyzed.…”

Section: Datamentioning

confidence: 99%

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A direct method to detect deterministic and stochastic properties of data

et al. 2022

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A fundamental question of data analysis is how to distinguish noise corrupted deterministic chaotic data from time-correlated stochastic fluctuations. For short data, even the distinction of chaotic signals from uncorrelated stochastic data may be a hard task, since trajectory properties may not be properly reflected by the data. Despite its importance, direct tests of chaos vs. stochasticity in finite time series including the most typical case of largely noise corrupted time series still lack of a definitive quantification. Here we present a novel approach based on recurrence analysis, a nonlinear level approach to deal with data. Namely, we use the probability of occurrence of recurrence microstates or ordinal permutation patterns, to overcome limitations in the quantification of deterministic and stochastic data. The main idea of the approach is the identification of how recurrence microstates and permutation patterns are affected by time reversibility of data, and how its behavior can be used to distinguish stochastic and deterministic data. We demonstrate its efficiency for a bunch of paradigmatic systems under strong noise influence, as well as for real-world data, covering electronic circuit, sound vocalization and human speeches, neuronal activity, heart beat data, and geomagnetic indexes. Interestingly, we identify this way squid neuronal activity as from deterministic, human speech data as from non-stationary deterministic, but heart rate data from stochastic origin. Our results support the conclusion that the method distinguishes deterministic from stochastic fluctuations in simulated and empirical data even under strong noise corruption, finding applications involving various areas of science and technology. In particular, for deterministic signals, the quantification of chaotic behavior may be of fundamental importance because it is believed that chaotic properties of some systems play important functional roles, opening doors to a better understanding and/or control of the physical mechanisms behind the generation of the signals.

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Section: Datamentioning

confidence: 99%

“…Gaussian noise distribution generated using the Julia programming language package Distributions.jl [49].…”

Section: Uniform Gaussian Noisementioning

confidence: 99%

A direct method to detect deterministic and stochastic properties of data

et al. 2022

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“…Suppose this is not the case, and define θ ∈ R n1×n2 by θi,j = θi,j − log k, e θk, so that i,j e θi,j = 1. Then we have All simulations are run with Julia 1.4.1 [5], where, besides the standard library, we use the libraries Cubature (version 1.5.1), Distributions [4,30] (version 0.23.2), StatsBase (version 0.33.0), PyPlot (version 2.9.0), and GLM [3] (version 1.3.9). Algorithm 2 is stopped at a relative distance in the Frobenius norm between two consecutive iterates of less than 10 −6 or 400,000 iterations, whichever comes first.…”

Section: B2 Mle For Mtp 2 Distributions On a Gridmentioning

confidence: 99%

Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions

Hütter¹,

Cheng²,

Rigollet³

et al. 2020

Preprint

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We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear frequently in statistics and probability. In particular, for distributions with β-Hölder smooth densities where β ∈ (0, 2), we observe polynomially faster minimax rates of estimation when, additionally, the total positivity condition is imposed. Moreover, we demonstrate fast algorithms to compute the proposed estimators and corroborate the theoretical rates of estimation by simulation studies.

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“…The purpose of this review is to complement Warne et al (2019) and Schnoerr et al (2017) by providing an accessible, didactic guide to pseudo-marginal methods (Andrieu et al, 2010;Andrieu and Roberts, 2009;Doucet et al, 2015) for the inference of kinetic rate parameters of biochemical reaction network models using the chemical Langevin description. For all of our examples, we provide accessible implementations using the open source, high performance Julia programming language (Besançon et al, 2019;Bezanson et al, 2017) 1 .…”

Section: Introductionmentioning

confidence: 99%

A practical guide to pseudo-marginal methods for computational inference in systems biology

Warne

Baker

Simpson

2020

Journal of Theoretical Biology

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For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing (https://github.com/davidwarne/Warne2019 GuideToPseudoMarginal).

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Distributions.jl: Definition and Modeling of Probability Distributions in the JuliaStats Ecosystem

Cited by 7 publications

References 14 publications

A direct method to detect deterministic and stochastic properties of data

A direct method to detect deterministic and stochastic properties of data

Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions

A practical guide to pseudo-marginal methods for computational inference in systems biology

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