12 questions linked to/from Prediction and Tolerance Intervals
1 vote
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, ...
1 vote
23 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 ...
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9k 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 ...
• 241
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### 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 ...
• 621
4k 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-...
• 143
246 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% ...
• 111
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% ...
• 21
1k 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 ...
• 195
753 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 ...
• 534
140 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 ...
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1 vote
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 ...