Linked Questions

1 vote
0 answers
34 views

Probabilistic predictions from a frequentist point of view [duplicate]

I'm trying to understand how a frequentist would approach statements like "having observed X, the probability of Y happening is Z". For concreteness, let's say we conducted $n_1$ identical, ...
Andrea Allais's user avatar
1 vote
0 answers
26 views

Prediction Intervals and Tolerance Intervals [duplicate]

I have a question regarding interpretation of prediction intervals and confidence intervals. The definitions I've seen is: (1) A prediction interval for a single future observation is an interval ...
Paul's user avatar
  • 149
24 votes
1 answer
10k views

Linear regression prediction interval

If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between ...
bmx's user avatar
  • 241
5 votes
2 answers
5k views

One Sigma error and 68% tolerance interval

I have first a clarifying question, and second, a question asking about how to do something, depending on the answer to the first question. Suppose you have a set of data of some PDF which is non-...
zephyr's user avatar
  • 153
13 votes
2 answers
2k views

Can we make probabilistic statements with prediction intervals?

I've read through the many excellent discussions on the site regarding interpretation of confidence intervals and prediction intervals, but one concept is still a bit puzzling: Consider the OLS ...
kevinykuo's user avatar
  • 641
11 votes
1 answer
280 views

What is the name of the percentage that defines a prediction interval?

For example, say I'm creating a forecast for weather patterns and I am looking for a 95% prediction interval (essentially an upper and lower bound for that forecast); what is the name of that 95% ...
Trevor Lowe's user avatar
2 votes
2 answers
2k views

Confidence interval vs. prediction interval misunderstanding

Problem I have a time series data set with about 50 observations. I'd like to compute an interval that may contain the next/future value in the time series (the 51st data point). I tried using a 90% ...
jerbear's user avatar
  • 21
0 votes
1 answer
2k views

How to create forecast data prediction interval bands

I have seasonal data from which I create forecasts. The steps I perform are: deseasonalizing the data, finding the linear regression for the deseasonalized points, predicting a few points from the ...
Adrian's user avatar
  • 205
3 votes
1 answer
917 views

How many samples needed to determine value 4 sigma away from mean?

I have a source that generates computer files varying between 20,000 and 40,000 bytes in length. I think (strongly assume so) that they vary in length according to a Normal distribution. They average ...
Paul Uszak's user avatar
2 votes
1 answer
275 views

Confidence in a range estimate, and +- 2sigma rule of thumb

It's common to see people report variability in their realized sample through the $\bar{x} \pm 2s$ range, where $\bar{x}$ is the realized mean and $s$ the realized standard deviation estimate in their ...
FZS's user avatar
  • 405
1 vote
1 answer
155 views

95% limits of a normally distributed parameter

How do I find the 95% limits of the population distribution of a normally distributed parameter? I've taken the mean and SD from 10 different readings of the parameter. Will the 95% limits be mean +/-...
boredgames's user avatar
0 votes
0 answers
52 views

Probability distribution of new data given old data

Say we observe data $D$, which comes from a probability distribution $P[D|\theta]$, where $\theta$ are the unknown model parameters. Given this information, what is the probability distribution of the ...
Aleksejs Fomins's user avatar