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The important of error estimation

The word uncertainty was the first time introduced by the Karl Pearson which is

statistician and geneticist. Uncertainty is a term used in subtly different ways in a number of

fields, including physics, philosophy, statistics, economics, finance, insurance, psychology,

sociology, engineering, and information science. It applies to predictions of future events, to

physical measurements already made, or to the unknown. In physical chemistry, uncertainty in

measurement always occurs in the experiment. Uncertainty is measurement is stated by giving a

range of values likely to enclose the true value. This may be denoted by error bars on a graph, or by the

following notations. the uncertainty of a measurement is found by repeating the measurement enough

times to get a good estimate of the standard deviation of the values. Then, any single value has an

uncertainty equal to the standard deviation. However, if the values are averaged, then the mean

measurement value has a much smaller uncertainty, equal to the standard error of the mean, which is

the standard deviation divided by the square root of the number of measurements.

y Uncertainty is the quantitative estimation of error present in data; all measurementscontain some uncertainty generated through systematic error and/or random error.

y Acknowledging the uncertainty of data is an important component of reporting theresults of scientific investigation.

y Uncertainty is commonly misunderstood to mean that scientists are not certain of theirresults, but the term specifies the degree to which scientists are confident in their data.

y Careful methodology can reduce uncertainty by correcting for systematic error andminimizing random error. However, uncertainty can never be reduced to zero.

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Recognizing and reducing error

Error propagation is not limited to mathematical modeling. It is always a concern in scientific

research, especially in studies that proceed stepwise in multiple increments because error in

one step can easily be compounded in the next step. As a result, scientists have developed a

number of techniques to help quantify error. The use of controls in scientific experiments (see

our Research Methods: Experimentation module) helps quantify statistical error within an

experiment and identify systematic error in order to either measure or eliminate it. In research

that involves human judgment, such as studies that try to quantify the perception of pain relief

following administration of a pain-relieving drug, scientists often work to minimize error by

using "blinds." In blind trials, the treatment (i.e. the drug) will be compared to a control (i.e.

another drug or a placebo); neither the patient nor the researcher will know if the patient is

receiving the treatment or the control. In this way, systematic error due to preconceptions

about the utility of a treatment is avoided.

Error reduction and measurement efforts in scientific research are sometimes referred to as

quality assurance and quality control. Quality assurance generally refers to the plans that a

researcher has for minimizing and measuring error in his or her research; quality control refers

to the actual procedures implemented in the research. The terms are most commonly used

interchangeably and in unison, as in "quality assurance/quality control" (QA

/QC

). QA

/QC

includes steps such as calibrating instruments or measurements against known standards,

reporting all instrument detection limits, implementing standardized procedures to minimize

human error, thoroughly documenting research methods, replicating measurements to

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determine precision, and a host of other techniques, often specific to the type of research

being conducted, and reported in the Materials and Methods section of a scientific paper (see

our Scientific Writing I: Understanding Scientific Journals and Articles module).

Reduction of statistical error is often as simple as repeating a research measurement or

observation many times to reduce the uncertainty in the range of values obtained. Systematic

error can be more difficult to pin down, creeping up in research due to instrumental bias,

human mistakes, poor research design, or incorrect assumptions about the behavior of

variables in a system. From this standpoint, identifying and quantifying the source of systematic

error in research can help scientists better understand the behavior of the system itself.

The important

Estimating error is an important task in rendering. For many predictive rendering

applications such as simulation of car headlights, l ighting design or architectural design it is

import to provide an estimate of the actual error to ensure condence and accuracy of the

results. Even for applications where accuracy is not critical, error estimation is still useful for

improving aspects of the rendering algorithm. Examples include terminating the rendering

Algorithm automatically, adaptive sampling where the parameters of the rendering algorithm

are adjusted dynamically to minimize the error, and interpolating sparsely sampled radiance

within a given error bound. We present a general error bound estimation framework for global

Illumination rendering using photon density e