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Related Concept Videos

The Power Superposition Principle01:19

The Power Superposition Principle

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Consider a circuit with two sinusoidal voltage sources. Each one influences the circuit independently, and the superposition principle helps us understand the combined effect by adding up the responses from each source.
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Maximum Power Transfer01:16

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Numerous practical applications within engineering disciplines, such as telecommunications, necessitate optimizing power delivery to a connected load. This pursuit, however, entails inherent internal losses, which can either equal or exceed the power supplied to the load. The Thevenin equivalent circuit is helpful in finding the maximum power a linear circuit can deliver to a load. It is assumed in this context that the load resistance can be adjusted.
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Power01:08

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The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between two points on its trajectory. While none of these quantities or relations involves time explicitly, we know that the time available to accomplish work is often just as important as the amount of work itself. For example, sprinters in a race may have achieved the same velocity at the finish, therefore,...
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Consider a linear AC Thevenin equivalent circuit connected to a load impedance.
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Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes...
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Instantaneous power is important in electrical circuits, mainly when dealing with sinusoidal input. Instantaneous power, denoted as p(t), results from the multiplication of the instantaneous voltage (v(t)) across an element and the instantaneous current (i(t)) flowing through it. This relationship adheres to the passive sign convention and represents a fundamental principle in electrical engineering.
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The power prior: theory and applications.

Joseph G Ibrahim1, Ming-Hui Chen2, Yeongjin Gwon2

  • 1Department of Biostatistics, University of North Carolina, Chapel Hill, 27599, NC, U.S.A.

Statistics in Medicine
|September 9, 2015
PubMed
Summary

The power prior, an informative Bayesian prior from historical data, offers advantages across diverse fields like clinical trials and economics. This review details its properties, applications, and benefits over other informative priors.

Keywords:
Bayesian designborrowingclinical trialsdiscountinghistorical datainformative prior

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Methodological Review

Background:

  • The power prior is an informative prior distribution derived from historical data.
  • It has broad applicability across numerous disciplines, including clinical trials, genetics, and economics.
  • Its utility spans both experimental design and data analysis contexts.

Purpose of the Study:

  • To provide a comprehensive review of the power prior and its applications.
  • To elucidate the theoretical properties, variations, and advantages of the power prior.
  • To showcase its use in various statistical models and areas.

Main Methods:

  • Systematic review of power prior literature.
  • Examination of theoretical properties and formulation variations.
  • Analysis of applications in generalized linear models, survival models, and random effects models.
  • Investigation of frequentist properties in posterior inference.
  • Conducting simulation studies and real data analyses.

Main Results:

  • The power prior is a versatile tool with established theoretical properties.
  • It demonstrates advantages over alternative informative priors in various statistical settings.
  • Empirical performance is examined through simulation studies and real-world data applications.
  • Its utility in Bayesian clinical trial design is illustrated.

Conclusions:

  • The power prior is a valuable and adaptable statistical methodology.
  • It offers significant benefits for incorporating historical data into statistical analyses.
  • The review highlights its extensive applications and potential for future research.