Accuracy and precision

Summary

Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other. In other words, precision is a description of random errors, a measure of statistical variability. Accuracy has two definitions:

More commonly, it is a description of only systematic errors, a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this trueness.

Alternatively, ISO defines accuracy as describing a combination of both types of observational error (random and systematic), so high accuracy requires both high precision and high trueness.

In the first, more common definition of "accuracy" above, the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or neither. In simpler t

Official source

https://en.wikipedia.org/wiki/Accuracy_and_precision

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An accuracy study of resistive methods for elliptic PDEs

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We numerically study the resistive method for the numerical approximation of elliptic PDEs. In particular we focus on the resistive method for weakly setting solution values in specific subdomains or interfaces in the domain.

2016

Exploring stabilisation techniques for the reduced basis approximation of avection-diffusion PDEs

Christèle Marie Zbinden

In this thesis, we explore possible stabilisation methods for the reduce basis approximation of advection-diffusion problems, for which the advection term is dominating. The options we consider are mainly inspired by the Variational Multiscale method (VMS), which decomposes the solution of a variational problem into its coarse scale component, from a coarse scale space, and a fine scale component, from a fine scale space. Our stabilisation proposals are divided into three classes. The first one groups methods that rely on a stabilisation parameter. The second class uses VMS at the algebraic level to attempt stabilisation. Finally the third class is also inspired by VMS at the algebraic level, but with the additional constraint that the fine scale space is orthogonal to the coarse scale space. Numericals tests reported in this thesis show that the methods of the first class is not viable options as the best stabilisation parameter among those tested is the stabilisation parameter that is used at the high fidelity level. Although the stabilisation methods of the second class give accurate results when applied to stable problems, they were also dismissed by the numerical tests, as they did not improve the accuracy of the already stabilised problem. The third class also performs well when applied to stable problems. It has been shown in [7] one of those methods can improve accuracy. However in the current implementation, this result was not achieved here.

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Hardware accelerators based on two-terminal non-volatile memories (NVMs) can potentially provide competitive speed and accuracy for the training of fully connected deep neural networks (FC-DNNs), with respect to GPUs and other digital accelerators. We recently proposed [S. Ambrogio et al., Nature, 2018] novel neuromorphic crossbar arrays, consisting of a pair of phase-change memory (PCM) devices combined with a pair of 3-Transistor 1-Capacitor (3T1C) circuit elements, so that each weight was implemented using multiple conductances of varying significance, and then showed that this weight element can train FC-DNNs to software-equivalent accuracies. Unfortunately, however, real arrays of emerging NVMs such as PCM typically include some failed devices (e.g.,

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