The effect of missing data on robust Bayesian spectral analysis

Christmas, Jacqueline

doi:10.1109/mlsp.2013.6661980

Cited by 6 publications

(9 citation statements)

References 14 publications

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“…The selection of a subset of frequencies and the choice of priors cause more of the observed signal to be absorbed into the noise distribution. For an analysis of the effects of missing data on this model, see [37].…”

Section: Discussionmentioning

confidence: 99%

Bayesian Spectral Analysis With Student-t Noise

2014

IEEE Trans. Signal Process.

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Abstract-We introduce a Bayesian spectral analysis model for one-dimensional signals where the observation noise is assumed to be Student-t distributed, for robustness to outliers, and we estimate the posterior distributions of the Student-t hyperparameters, as well as the amplitudes and phases of the component sinusoids. The integrals required for exact Bayesian inference are intractable, so we use variational approximation. We show that the approximate phase posteriors are Generalised von Mises distributions of order 2 and that their spread increases as the signal to noise ratio decreases. The model is demonstrated against synthetic data, and real GPS and Wolf's sunspot data.

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Section: Discussionmentioning

confidence: 99%

Bayesian Spectral Analysis With Student-t Noise

2014

IEEE Trans. Signal Process.

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“…Third, there should ideally be no missing data points (Cowpertwait & Metcalfe, 2009), although Broersen (2006) and Christmas (2013) discuss potential ways around this common problem. Our suggestion is that researchers interpolate the time series (e.g., with polynomial splines; Won Suk et al, 2019) and subsequently re-sample it at regular intervals.…”

Section: Limitations and Considerationsmentioning

confidence: 99%

Spectral and Cross-Spectral Analysis - a Tutorial for Psychologists and Social Scientists

Vowels¹,

Vowels²,

Wood³

2020

Preprint

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Social scientists have become increasingly interested in using intensive longitudinal methods to study social phenomena that change over time. Many of these phenomena are expected to exhibit cycling fluctuations (e.g., sleep, mood, sexual desire). However, researchers typically employ analytical methods which are unable to model such patterns. We present spectral and cross-spectral analysis as means to address this limitation. Spectral analysis provides a means to interrogate time series from a different, frequency domain perspective, and to understand how the time series may be decomposed into their constituent periodic components. Cross-spectral extends this to dyadic data and allows for synchrony and time offsets to be identified. The techniques are commonly used in the physical and engineering sciences, and we discuss how to apply these popular analytical techniques to the social sciences while also demonstrating how to undertake estimations of significance and effect size. In this tutorial we begin by introducing spectral and cross-spectral analysis, before demonstrating its application to simulated univariate and bivariate individual- and group-level data. We employ cross-power spectral density techniques to understand synchrony between the individual time series in a dyadic time series, and circular statistics and polar plots to understand phase offsets between constituent periodic components. Finally, we present a means to undertake non-parameteric boostrapping in order to estimate the significance, and derive a proxy for effect size. A Jupyter Notebook (Python 3.6) is provided as supplementary material to aid researchers who intend to apply these techniques.

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“…In this paper the time intervals between observations are assumed to be equal, but this does not need to be the case [24].…”

Section: The Modelmentioning

confidence: 99%

“…The n term not only accounts for the white noise, but when the model is trained on only a subset of the Fourier frequencies it also absorbs the effects of the missing frequencies [24].…”

Section: The Modelmentioning

confidence: 99%

“…define the frequencies, ω, and prior hyperparameters initialise the values of each variable while not converged do update the signal posteriors using (21)(22)(23)(24)(25)(26)(27) for each observation set, s do update the posteriors for B We have chosen to initialise the variables randomly to demonstrate that the model converges to a good solution. We could converge more quickly if we chose to initialise the amplitudes and phases from the results of a Fast Fourier Transform (FFT).…”

Section: Summary Of Algorithmmentioning

confidence: 99%

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Predicting sea waves in the presence of pink noise

Christmas

2016

2016 IEEE Congress on Evolutionary Computation (CEC)

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Abstract-It has been shown that the power output of some wave energy converters can be greatly increased if they respond to very short-term predictions of the shapes of the waves. Observations of sea waves are traditionally made using buoys carrying GPS and accelerometers. The recent development of low-cost MEMS devices has led to cheaper devices, but also to a renewed interest in the effects of pink (1/f ) noise and signal processing methods for mitigating its effects. Bandpass filtering reduces the effects of this noise, but its remaining influence disrupts, in particular, the phase of the signal, which has significant consequences for prediction. We introduce a Bayesian model that promotes the smooth theoretical spectral shapes of the signal and the pink noise and estimates the true signal from one or more sets of observations recorded in parallel. The signal we are aiming to discover is the profile of sea waves at a fixed location; the spectral shape is determined by the PiersonMoskowitz model. We demonstrate the model on synthetic data and give some preliminary results for the prediction of real sea waves.

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The effect of missing data on robust Bayesian spectral analysis

Cited by 6 publications

References 14 publications

Bayesian Spectral Analysis With Student-t Noise

Bayesian Spectral Analysis With Student-t Noise

Spectral and Cross-Spectral Analysis - a Tutorial for Psychologists and Social Scientists

Predicting sea waves in the presence of pink noise

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