Least squares when both variables have uncertainties

Orear, J.

doi:10.1119/1.12972

Cited by 139 publications

(68 citation statements)

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“…Iterative approaches are therefore required. Several equation forms have been proposed and discussed (Barker and Diana, 1974;Borcherds and Sheth, 1995;Brauers and Finlayson-Pitts, 1997;Bruzzone and Moreno, 1998;Chong, 1991Chong, , 1994Christian and Tucker, 1984;Christian et al, 1986;Gonzalez et al, 1992;Irwin and Quickenden, 1983;Jones, 1979;Kalantar, 1990Kalantar, , 1991Krane and Schecter, 1982;Leduc, 1987;Lybanon, 1984ab, 1985Macdonald and Thompson, 1992;MacTaggart and Farwell, 1992;Markovsky and Van Huffel, 2007;Moreno, 1996;Neri et al, 1990Neri et al, , 1991Orear, 1982;Pasachoff, 1980;Pearson, 1901;Press et al, 1992a,b;Reed, 1990;Riu and Rius, 1995;Squire et al, 1990;Williamson, 1968;York, 1966York, , 1969York et al, 2004). This list is large to provide a comprehensive reference for the reader.…”

Section: Methods When Both X and Y Have Errorsmentioning

confidence: 99%

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008

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Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheetbased template is made available that employs one method for bivariate fitting.

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Section: Methods When Both X and Y Have Errorsmentioning

confidence: 99%

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008

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“…In the case of model fits, an effective variance technique (Orear, 1982) was used, which gives the parameter estimates and their standard errors based on the uncertainties of all input parameters. The reduced chi-squared statistic ( red 2 , the sum of squared errors, weighted by the variance of the observations and divided by the number of degrees of freedom) is given for model fits as a measure of the goodness of fit accounting for the uncertainties in the observations.…”

Section: Uncertainties and Statistical Criteriamentioning

confidence: 99%

The experimental determination of REE partition coefficients in the water-calcite system

2017

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“…For linear fits the procedure suggested by Orear (1982) was used. Other fits were performed with the built-in procedure of IgorPro based on minimization of 2 .…”

Section: Methodsmentioning

confidence: 99%

Separation of Presynaptic and Postsynaptic Contributions to Depression by Covariance Analysis of Successive EPSCs at the Calyx of Held Synapse

2002

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Synaptic short-term plasticity is considered to result from multiple cellular mechanisms, which may include presynaptic and postsynaptic contributions. We have recently developed a nonstationary EPSC fluctuation analysis (Scheuss and Neher, 2001) to estimate synaptic parameters and their transient changes during short-term synaptic plasticity. Extending the classical variance-mean approach, a short train of stimuli is applied repetitively, and the resulting EPSCs are analyzed for means, variances, and covariances. This provides estimates of the quantal size and quantal content for each EPSC in the train, and furthermore, an estimate of the number of release sites. The latter is less sensitive to heterogeneity in the release probability than that of the variance-mean approach. Here, we applied this analysis to the calyx of Held synapse in brainstem slices of young rats (postnatal day 8-10). We found significant negative covariance in the amplitude of successive EPSCs in a train. The analysis showed that the 10-fold depression in the EPSC amplitude during 100 Hz trains at elevated extracellular Ca 2ϩ concentration resulted from a 2.5-fold reduction in quantal size caused by postsynaptic AMPA receptor desensitization and saturation, and a fourfold reduction in quantal content, which was partially relieved by application of cyclothiazide. The number of release sites estimated by covariance analysis was Ϸ2000 and significantly larger than estimates from variancemean parabolas.Key words: synaptic transmission; short-term plasticity; quantal analysis; covariance analysis; release site; release probability; quantal size Short-term synaptic plasticity is considered as an important element of information processing in neuronal circuits (Abbott et al., 1997;Tsodyks and Markram, 1997). Multiple cellular mechanisms have to be considered to contribute to synaptic short-term plasticity. Because these act most likely simultaneously and in parallel (Zucker, 1989;Fisher et al., 1997), their individual contributions cannot readily be studied in separation. Especially at synapses with large quantal contents, presynaptic and postsynaptic contributions to short-term plasticity are difficult to separate. Ideally, one would like to obtain independent measures of the number of released quanta (quantal content) and of the average quantal size to indicate presynaptic and postsynaptic efficacy of synaptic transmission, respectively. These parameters can, in principle, be provided by fluctuation or quantal analysis of EPSC amplitudes. However, variance-mean analysis according to a binomial model of synaptic transmission (for review, see Clements and Silver, 2000) has so far mainly been applied to steadystate sequences recorded under a variety of conditions (Silver et al., 1998;Reid and Clements, 1999;Oleskevich et al. 2000). Sequences of double pulses (Oleskevich et al., 2000) and repetitive trains of stimuli (Clamann et al., 1989;Meyer et al., 2001) have also been used, but no analysis dedicated to short-term plasticity in such nonstationa...

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Least squares when both variables have uncertainties

Cited by 139 publications

References 0 publications

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

The experimental determination of REE partition coefficients in the water-calcite system

Separation of Presynaptic and Postsynaptic Contributions to Depression by Covariance Analysis of Successive EPSCs at the Calyx of Held Synapse

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