Estimation of the Hurst exponent from noisy data: a Bayesian approach

Makarava, N.; Holschneider, Matthias

doi:10.1140/epjb/e2012-30221-1

Cited by 8 publications

(7 citation statements)

References 51 publications

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“…The first phase is designed to check for possible multifractality in the process under examination. Whereas several Bayesian procedures have been proposed to characterize stochastic processes (Krog et al, 2018; Makarava et al, 2011; Makarava & Holschneider, 2012; Moscoso del Prado Martín, 2013; Sørbye & Rue, 2018; Thornton & Gilden, 2005), none of them tackles the issue of multifractality. Our test for multifractality focuses on the distribution of the increments of the series.…”

Section: Frequency-domain Analyses: Power Spectral Density Analysismentioning

confidence: 99%

A Bayesian classifier for fractal characterization of short behavioral series.

Solfo¹,

Leeuwen²

2023

Psychological Methods

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Serial tasks in behavioral research often lead to correlated responses, invalidating the application of generalized linear models and leaving the analysis of serial correlations as the only viable option. We present a Bayesian analysis method suitable for classifying even relatively short behavioral series according to their correlation structure. Our classifier consists of three phases. Phase 1 distinguishes between monoand possible multifractal series by modeling the distribution of the increments of the series. To the series labeled as monofractal in Phase 1, classification proceeds in Phase 2 with a Bayesian version of the evenly spaced averaged detrended fluctuation analysis (Bayesian esaDFA). Finally, Phase 3 refines the estimates from the Bayesian esaDFA. We tested our classifier with very short series (viz., 256 points), both simulated and empirical ones. For the simulated series, our classifier revealed to be maximally efficient in distinguishing between mono-and multifractality and highly efficient in assigning the monofractal class. For the empirical series, our classifier identified monofractal classes specific to experimental designs, tasks, and conditions. Monofractal classes are particularly relevant for skilled, repetitive behavior. Short behavioral series are crucial for avoiding potential confounders such as mind wandering or fatigue. Our classifier thus contributes to broadening the scope of time series analysis for behavioral series and to understanding the impact of fundamental behavioral constructs (e.g., learning, coordination, and attention) on serial performance.

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Section: Frequency-domain Analyses: Power Spectral Density Analysismentioning

confidence: 99%

A Bayesian classifier for fractal characterization of short behavioral series.

Solfo¹,

Leeuwen²

2023

Psychological Methods

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“…A computationally simple choice is to adopt flat, noninformative priors. In the case of fGn, the Hurst parameter H has typically been assigned a uniform prior, argued for in terms of having no knowledge about the parameter (Benhmehdi et al, ; Makarava et al, ; Makarava & Holschneider, ). Also, it is suggested to use the Jeffreys prior for the marginal standard deviation of the model, that is, π ( τ −1/2 )∼ τ 1/2 .…”

Section: Pc Priors For the Parameters Of Fgnmentioning

confidence: 99%

“…Alternative approaches include the use of wavelets (Abry & Veitch, 1998;McCoy & Walden, 1996) and maximum likelihood and Whittle estimation; see Beran et al (2013) for a comprehensive overview. Using a Bayesian framework, H has typically been assigned a uniform prior (Benhmehdi, Makarava, Menhamidouche, & Holschneider, 2011;Makarava, Benmehdi, & Holschneider, 2011;Makarava, & Holschneider, 2012). This is computationally simple, and due to lack of prior knowledge, a noninformative prior might seem like a good choice.…”

Section: Introductionmentioning

confidence: 99%

Fractional Gaussian noise: Prior specification and model comparison

Sørbye

Rue

2017

Environmetrics

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Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ of a first‐order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ. Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

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“…See [28] for general background on mixed effects models and [29,30] for details on the Bayesian estimation of H from the observation of Y. As in this reference, for the analysis of the experimental Dictyostelium discoideum cell track data, we took a scaling invariant Jeffreys-like prior for λ [31] with density π (λ) ∼ λ −1 , a flat, (or diffuse) prior for β with density π (β) 1, as well as a flat prior for H with density π (H ) = χ [0,1] [32].…”

Section: B Fractional Brownian Motionmentioning

confidence: 99%

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion

et al. 2014

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Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

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Estimation of the Hurst exponent from noisy data: a Bayesian approach

Cited by 8 publications

References 51 publications

A Bayesian classifier for fractal characterization of short behavioral series.

A Bayesian classifier for fractal characterization of short behavioral series.

Fractional Gaussian noise: Prior specification and model comparison

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion

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