Confusion with Uncertainties

In summary, the speaker is seeking to determine the uncertainty in their fitted model to their data. They are confused about how the variance can give them this uncertainty and are asking for help in interpreting this. They mention the standard error of the mean and the square root of the variance, but are still struggling to understand how these can help determine uncertainty. The speaker also mentions confidence intervals and their relation to determining uncertainty. They mention that textbooks or the web can provide more information on how to calculate confidence intervals and note that the half-width of a CI can be an intuitive way to gauge uncertainty.
  • #1
Hey :-)
I want to establish the uncertainty in my fitted model to my data
I can evaluate the variance for the predicted model, but I'm getting very confused as to how the variance can then give me the uncertainty in my model :S
I know that the standard error of the mean may be taken as the standard deviation divided by the root of the number of measurements, and that the square root of the variance gives the standard deviation- but I am really struggling to see how from these I could interpretate an uncertainty. I am very baffled at the moment- so any help would be massively appreciated :-)
Cheers
 
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  • #2
Radiohannah said:
Hey :-)
I want to establish the uncertainty in my fitted model to my data
I can evaluate the variance for the predicted model, but I'm getting very confused as to how the variance can then give me the uncertainty in my model :S
I know that the standard error of the mean may be taken as the standard deviation divided by the root of the number of measurements, and that the square root of the variance gives the standard deviation- but I am really struggling to see how from these I could interpretate an uncertainty. I am very baffled at the moment- so any help would be massively appreciated :-)
Cheers

Are you familiar with confidence intervals?
 
  • #3
Is that similar to determining a 'confidence'... being some percentage calculated from a given number of degrees of freedom? I do think so. :-)

So, I might be wrong, but if the variance is a measure of the spread of the data (from my best fit model??) , I can determine some confidence limits? Does that come from a value for chi^2?
 
  • #4
Radiohannah said:
Is that similar to determining a 'confidence'... being some percentage calculated from a given number of degrees of freedom? I do think so. :-)

So, I might be wrong, but if the variance is a measure of the spread of the data (from my best fit model??) , I can determine some confidence limits? Does that come from a value for chi^2?

Confidence intervals (CIs) generally assume an underlying normal distribution and are calculated based on the Gaussian model using the standard error of the sample(s) (which is an estimate of the standard deviation of the population). I won't tell you exactly how to calculate them. This is easily found in textbooks or on the web.

Note that the half-width of a CI relative to a point estimate is often (but not always) an intuitive way to gauge uncertainty. For example, suppose your point estimate is 2 and your 95% CI is 1.8 to 2.2. This means (informally) that you have a 10% uncertainty regarding the value of the point estimate with 95% confidence.

EDIT: More formally, this means that the estimated parameter is contained in the interval with p=0.95 based on a Gaussian model.
 
Last edited:
  • #6
You're welcome.
 

1. What does the term "uncertainty" mean in a scientific context?

In science, uncertainty refers to the lack of exact knowledge about a measurement or result due to limitations in the measurement process or inherent variability in the system being studied. It is an essential part of scientific investigations and is often quantified using statistical methods.

2. How do scientists deal with uncertainties in their research?

There are several ways that scientists handle uncertainties in their research. One common approach is to use multiple measurements or experiments and calculate the average or mean value. Another method is to use error bars to visually represent the range of possible values for a given measurement. Additionally, scientists may use statistical analysis to quantify and account for uncertainties in their data.

3. Is uncertainty the same as error in scientific measurements?

No, uncertainty and error are not the same in scientific measurements. Error refers to the difference between the measured value and the true value, while uncertainty is the lack of exact knowledge about a measurement. Uncertainty can include both random and systematic errors, but it is not the same as error.

4. Can uncertainties ever be completely eliminated in scientific research?

No, it is not possible to completely eliminate uncertainties in scientific research. There will always be limitations in the measurement process and inherent variability in the systems being studied. However, scientists can minimize uncertainties by using precise and accurate measurement techniques and by conducting multiple experiments.

5. How do uncertainties impact the reliability of scientific results?

Uncertainties can have a significant impact on the reliability of scientific results. Large uncertainties can make it difficult to draw meaningful conclusions from the data and can decrease the confidence in the results. Scientists must carefully consider and report uncertainties in their research to ensure the reliability and accuracy of their findings.

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