The distribution of composite measurements: How to be certain of the uncertainties in what we measure

Silverman, Mark P.; Strange, Wayne; Lipscombe, Trevor Davis

doi:10.1119/1.1738426

Cited by 29 publications

(18 citation statements)

References 9 publications

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“…Signal-to-noise ratios were computed as the ratio of P300 amplitude and corresponding SEM. Since ratios cannot be assumed to be normally distributed [37], we applied non-parametric statistical methods. For most analyses, we focused on the Pz and Cz channels.…”

Section: Eeg Recording and Analysismentioning

confidence: 99%

Signal and noise in P300 recordings to visual stimuli

Heinrich¹,

Bach²

2008

Doc Ophthalmol

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The P300 of the event-related potential is typically obtained for infrequent target stimuli that are embedded in a sequence of frequent irrelevant stimuli. The P300 has been suggested as a marker of high-level cognitive processing and might be useful in ophthalmology to confirm the diagnosis of a functional disorder. However, typical P300 measurements require relatively lengthy recording sessions. It would therefore be desirable to minimize the required time and to maximize the signal-to-noise ratio by finding the optimal balance between parameters such as stimulus probability and the number of target trials or the recording time. This is different from previous studies, which assessed the amplitude only. We recorded event-related potentials to visual stimuli using standard oddball paradigms with various target frequencies ranging from 2:1 (target majority) to 1:16 (massive non-target majority). We compared the signal-to-noise ratios for a fixed number of target trials as well as for a fixed total recording time and assessed effects of the immediate stimulus history. As expected, P300 amplitudes depend strongly on target infrequency. This did not reach saturation within the range tested. For a given number of target trials, the signal-to-noise ratio also increases with target infrequency. For a given recording duration, the signal-to-noise ratio is optimal around 1:8. In the 1:4 condition, the signal-to-noise ratio can be improved by excluding trials that were preceded by a target trial.

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Section: Eeg Recording and Analysismentioning

confidence: 99%

Signal and noise in P300 recordings to visual stimuli

Heinrich¹,

Bach²

2008

Doc Ophthalmol

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“…The topic of uncertainty propagation may be considered elementary by many practicing scientists, but in this manuscript we will argue that some of the fundamental aspects of this method are not well appreciated in the mass spectrometry community. The mathematical aspects of uncertainty propagation of ratio variables are often overlooked in many disciplines [3][4][5]. This manuscript addresses the shortcomings of traditional uncertainty propagation formulas for ratios of correlated analytical signals such as isotopic intensities in mass spectrometry.…”

Section: Introductionmentioning

confidence: 99%

Signal correlation in isotope ratio measurements with mass spectrometry: Effects on uncertainty propagation

Meija¹,

Mester²

2007

Spectrochimica Acta Part B: Atomic Spectroscopy

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“…The subscript j in relations (26) and (27) denotes that each random sample, whether Gaussian or Bernoulli, is independent of all the others.…”

Section: Mean-square Displacementmentioning

confidence: 99%

“…where the Bernoulli variate t ε is defined in relation (27). Note that an occurrence of 0 t ε = terminates the entire process by setting ( )…”

Section: Langevin Equation: Update Algorithm and Computer Simulationmentioning

confidence: 99%

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Silverman¹

2017

JMP

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Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

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The distribution of composite measurements: How to be certain of the uncertainties in what we measure

Cited by 29 publications

References 9 publications

Signal and noise in P300 recordings to visual stimuli

Signal and noise in P300 recordings to visual stimuli

Signal correlation in isotope ratio measurements with mass spectrometry: Effects on uncertainty propagation

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

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