IV.—On Least Squares and Linear Combination of Observations

Aitken, A. C.

doi:10.1017/s0370164600014346

Cited by 729 publications

(387 citation statements)

References 3 publications

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“…At each stage the removed subset is predicted using the model which has been fitted to the remaining data. When all subsets have been removed, n predictions ( y (1) , y (2) , ..., y (n) ) of the n observed data points (y (1) , y (2) , ..., y (n) ) will have been calculated. The cross-validation error is then calculated as…”

Section: Cross-validationmentioning

confidence: 99%

“…MLS is an embellishment of the weighted least-squares approach (WLS) [1]. WLS recognises that all {y (i) , x (i) } pairs may not by equally important in estimating the polynomial coefficients.…”

Section: Moving Least-squaresmentioning

confidence: 99%

“…Sóbester [70] uses the analogy of imitating the specific timbre of a musical instrument with a synthesizer, using a weighted combination of tones. Consider a function f observed without error, according to the sampling plan X = {x (1) , x (2) , . .…”

Section: Radial Basis Functionsmentioning

confidence: 99%

“…Our initial slack variable formulation (39) was a tradeoff between model complexity and the degree to which errors larger than ε are tolerated and is governed by the constant C. A small constant will lead to a flatter prediction (more emphasis on minimizing 1 2 |w| 2 ), usually with fewer SVs, while a larger constant will lead to a closer fitting of the data (more emphasis on…”

Section: Choosing C and εmentioning

confidence: 99%

“…We then exchange the first point x (1) e with each of the remaining points in X c \ X e and retain the exchange which gives the best Morris-Mitchell criterion. This process is repeated for each remaining point x…”

Section: Here We Use the Auto-regressive Model Of Kennedy And O'haganmentioning

confidence: 99%

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Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,815

954

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The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.

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Section: Cross-validationmentioning

confidence: 99%

Section: Moving Least-squaresmentioning

confidence: 99%

Section: Radial Basis Functionsmentioning

confidence: 99%

Section: Choosing C and εmentioning

confidence: 99%

Section: Here We Use the Auto-regressive Model Of Kennedy And O'haganmentioning

confidence: 99%

See 3 more Smart Citations

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,815

954

View full text Add to dashboard Cite

show abstract

Bivariate genetic analysis of fasting insulin and glucose levels

et al. 1999

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The main aim of this study was to estimate the relative influence of genes and environment on fasting insulin levels, which were considered a proxy of insulin resistance. Possible sex differences in genetic and environmental influences, and the origin of the covariance between fasting insulin and glucose were investigated. Subjects were 209 pairs of middle-aged twins, divided into 5 sex-by-zygosity groups. A general bivariate model and a reciprocal causation model including fasting insulin and glucose were used in the analyses. For both quantitative genetic models, a model specifying additive genetic and unique environmental factors, which were the same in males and females, showed the best fit to the data. Heritability estimates were modest and highly similar in both models: 20-25% of the variance in fasting insulin, and around 50% of the variance in fasting glucose levels could be attributed to genetic factors. The two models could not be discriminated on the basis of their fit to the data. A submodel of the general bivariate model suggested that the covariance between glucose and insulin has a unique environmental basis, whereas for the reciprocal causation model both causal paths were needed to explain the phenotypic correlation between insulin and glucose and estimates of the reciprocal paths were of opposite sign, an indication for the expected negative feedback loop. Genet. Epidemiol. 16:426-446, 1999.

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Tracking and Kalman Filtering Made Easy

Brookner¹

1998

317

211

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IV.—On Least Squares and Linear Combination of Observations

Cited by 729 publications

References 3 publications

Recent advances in surrogate-based optimization

Recent advances in surrogate-based optimization

Bivariate genetic analysis of fasting insulin and glucose levels

Tracking and Kalman Filtering Made Easy

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