A Bayesian Approach to Calibration Intervals and Properly Calibrated Tolerance Intervals

Hamada, Michael S.; Pohl, Andrew J.; Spiegelman, Cliff; Wendelberger, Joanne

doi:10.1080/00224065.2003.11980207

Cited by 7 publications

(3 citation statements)

References 9 publications

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“…A number of approximating methods (including bootstrapping [33][34][35][36], asymptotics [31,37,38], or Bayesian methods [15,39]) are available to estimate the prediction interval. Any of these methods can be effective, especially when large amounts of calibration data are available.…”

Section: Nonlinear Calibrationmentioning

confidence: 99%

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Bayesian Methods for Ion Selective Electrodes

et al. 2012

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With the increasing use of ion-selective electrodes in environmental and health applications, it is important to know the precision of estimated concentrations. A Bayesian model for non-linear calibration is introduced which provides estimates of measurement precision by incorporating uncertainty in calibration parameters and inherent random noise in emf response. The analysis of lead in 17 soil samples demonstrates that large gains in precision are possible when calibrations are extended to include multiple electrodes and standard addition data. The results highlight the need for improved calibration and routine use of standard addition as ion selective electrodes become increasingly popular for demanding, real world applications.

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Section: Nonlinear Calibrationmentioning

confidence: 99%

“…Bayesian methods of statistical calibration are well-established [15] and are becoming increasing popular in analysis of chemical data [16,17] including ISEs [18]. In many cases, the Bayesian method is still used in a standard optimization setting, where only point estimates and the calibration parameters, e.g.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Methods for Ion Selective Electrodes

et al. 2012

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“…An alternative to the frequentist approach described above is to use a Bayesian approach as presented in . In addition to the data from the calibration experiment, we treat x ∗ as unknown parameters for the new measurement y ∗ and obtain the posterior on all the model parameters including x ∗ .…”

Section: Analysis Methodsmentioning

confidence: 99%

Statistical analysis for nuclear forensics experiments

Anderson‐Cook

Burr

Hamada

et al. 2015

Statistical Analysis

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As with any type of forensics, nuclear forensics seeks to infer historical information using models and data. This article connects nuclear forensics and calibration. We present statistical analyses of a calibration experiment that connect several responses to the associated set of input values and then 'make a measurement' using the calibration model. Previous and upcoming real experiments involving production of PuO 2 powder motivate this article. Both frequentist and Bayesian approaches are considered, and we report findings from a simulation study that compares different analysis methods for different underlying responses between inputs and responses, different numbers of responses, different amounts of natural variability, and replicated or non-replicated calibration experiments and new measurements. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

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Incorporating variability in honey bee waggle dance decoding improves the mapping of communicated resource locations

Schürch¹,

Couvillon²,

Burns³

et al. 2013

J Comp Physiol A

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Honey bees communicate to nestmates locations of resources, including food, water, tree resin and nest sites, by making waggle dances. Dances are composed of repeated waggle runs, which encode the distance and direction vector from the hive or swarm to the resource. Distance is encoded in the duration of the waggle run, and direction is encoded in the angle of the dancer's body relative to vertical. Glass-walled observation hives enable researchers to observe or video, and decode waggle runs. However, variation in these signals makes it impossible to determine exact locations advertised. We present a Bayesian duration to distance calibration curve using Markov Chain Monte Carlo simulations that allows us to quantify how accurately distance to a food resource can be predicted from waggle run durations within a single dance. An angular calibration shows that angular precision does not change over distance, resulting in spatial scatter proportional to distance. We demonstrate how to combine distance and direction to produce a spatial probability distribution of the resource location advertised by the dance. Finally, we show how to map honey bee foraging and discuss how our approach can be integrated with Geographic Information Systems to better understand honey bee foraging ecology.

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A Bayesian Approach to Calibration Intervals and Properly Calibrated Tolerance Intervals

Cited by 7 publications

References 9 publications

Bayesian Methods for Ion Selective Electrodes

Bayesian Methods for Ion Selective Electrodes

Statistical analysis for nuclear forensics experiments

Incorporating variability in honey bee waggle dance decoding improves the mapping of communicated resource locations

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