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A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy.

ABSTRACT: Double Electron-Electron Resonance (DEER) spectroscopy is a solid-state pulse Electron Paramagnetic Resonance (EPR) experiment that measures distances between unpaired electrons, most commonly between protein-bound spin labels separated by 1.5-8nm. From the experimental data, a distance distribution P(r) is extracted using Tikhonov regularization. The disadvantage of this method is that it does not directly provide error bars for the resulting P(r), rendering correct interpretation difficult. Here we introduce a Bayesian statistical approach that quantifies uncertainty in P(r) arising from noise and numerical regularization. This method provides credible intervals (error bars) of P(r) at each r. This allows practitioners to answer whether or not small features are significant, whether or not apparent shoulders are significant, and whether or not two distance distributions are significantly different from each other. In addition, the method quantifies uncertainty in the regularization parameter.

SUBMITTER: Edwards TH

PROVIDER: S-EPMC4996738 | biostudies-literature | 2016 Sep

REPOSITORIES: biostudies-literature

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A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy.

Edwards Thomas H TH Stoll Stefan S

Journal of magnetic resonance (San Diego, Calif. : 1997) 20160702

Double Electron-Electron Resonance (DEER) spectroscopy is a solid-state pulse Electron Paramagnetic Resonance (EPR) experiment that measures distances between unpaired electrons, most commonly between protein-bound spin labels separated by 1.5-8nm. From the experimental data, a distance distribution P(r) is extracted using Tikhonov regularization. The disadvantage of this method is that it does not directly provide error bars for the resulting P(r), rendering correct interpretation difficult. He ...[more]

PMID: 27414762

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Project description:Acceptance of novelty depends on the receiver's emotional state. This paper proposes a novel mathematical model for predicting emotions elicited by the novelty of an event under different conditions. It models two emotion dimensions, arousal and valence, and considers different uncertainty levels. A state transition from before experiencing an event to afterwards is assumed, and a Bayesian model estimates a posterior distribution as being proportional to the product of a prior distribution and a likelihood function. Our model uses Kullback-Leibler divergence of the posterior from the prior, which we termed information gain, to represent arousal levels because it corresponds to surprise, a high-arousal emotion, upon experiencing a novel event. Based on Berlyne's hedonic function, we formalized valence as a summation of reward and aversion systems that are modeled as sigmoid functions of information gain. We derived information gain as a function of prediction errors (i.e., differences between the mean of the posterior and the peak likelihood), uncertainty (i.e., variance of the prior that is proportional to prior entropy), and noise (i.e., variance of the likelihood function). This functional model predicted an interaction effect of prediction errors and uncertainty on information gain, which we termed the arousal crossover effect. This effect means that the greater the uncertainty, the greater the information gain for a small prediction error. However, for large prediction errors, greater uncertainty means a smaller information gain. To verify this effect, we conducted an experiment with participants who watched short videos in which different percussion instruments were played. We varied uncertainty levels by using familiar and unfamiliar instruments, and we varied prediction error magnitudes by including congruent or incongruent percussive sounds in the videos. Event-related potential P300 amplitudes and subjective reports of surprise in response to the percussive sounds were used as measures of arousal levels, and the findings supported the hypothesized arousal crossover effect. The concordance between our model's predictions and our experimental results suggests that Bayesian information gain can be decomposed into uncertainty and prediction errors and is a valid measure of emotional arousal. Our model's predictions of arousal may help identify positively accepted novelty.

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Dataset Information

A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy.

Publications

A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy.

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