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Questions tagged [prediction-interval]

A prediction interval (also forecast interval) is an interval that covers the future (or otherwise unknown, but *observable*) value of a random variable with some prespecified probability.

A prediction interval is an interval that covers the future (or otherwise unknown) value of a random variable with some prespecified probability.

Prediction intervals are conceptually related to confidence intervals, but they are not the same. A prediction interval pertains to a realization (which has not yet been observed, but will be observed in the future), whereas a confidence interval pertains to a parameter (which is in principle not observable, e.g., the population mean). See Rob Hyndman's blog post "The difference between prediction intervals and confidence intervals" for more illustration.

In a time series context, prediction intervals are also known as forecast intervals.

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Difference between confidence intervals and prediction intervals

For a prediction interval in linear regression you still use $\hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x$ to generate the interval. You also use this to generate a confidence interval of $E[Y|x_0]$. What's the difference between the two?
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What is the difference between estimation and prediction?

For example, I have historical loss data and I am calculating extreme quantiles (Value-at-Risk or Probable Maximum Loss). The results obtained is for estimating the loss or predicting them? Where can one draw the line? I am confused.
melon
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Prediction interval for lmer() mixed effects model in R

I want to get a prediction interval around a prediction from a lmer() model. I have found some discussion about this: http://rstudio-pubs-static.s3.amazonaws.com/24365_2803ab8299934e888a60e7b16113f619.html http://glmm.wikidot.com/faq but they seem…
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Bootstrap prediction interval

Is there any bootstrap technique available to compute prediction intervals for point predictions obtained e.g. from linear regression or other regression method (k-nearest neighbour, regression trees etc.)? Somehow I feel that the sometimes proposed…
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How to calculate the prediction interval for an OLS multiple regression?

What is the algebraic notation to calculate the prediction interval for multiple regression? It sounds silly, but I am having trouble finding a clear algebraic notation of this.
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How to determine the confidence of a neural network prediction?

To illustrate my question, suppose that I have a training set where the input has a degree of noise but the output does not, for example; # Training data [1.02, 1.95, 2.01, 3.06] : [1.0] [2.03, 4.11, 5.92, 8.00] : [2.0] [10.01, 11.02, 11.96, 12.04]…
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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 observations and predictions $e_i=real(x_i)-(mx_i+b)$,…
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What non-Bayesian methods are there for predictive inference?

In Bayesian inference a predictive distribution for future data is derived by integrating out unknown parameters; integrating over the posterior distribution of those parameters gives a posterior predictive distribution—a distribution for future…
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How to compute prediction bands for non-linear regression?

The help page for Prism gives the following explanation for how it computes the prediction bands for non-linear regression. Please excuse the long quote, but I am not following the second paragraph (that explains how $G|x$ is defined and $dY/dP$ is…
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Prediction interval based on cross-validation (CV)

In the text books and youtube lectures I learned a lot about iterative models such as boosting, but I never saw anything about deriving a prediction interval. Cross validation is used for the following: Model selection: Try different models and…
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Obtaining a formula for prediction limits in a linear model (i.e.: prediction intervals)

Let's take the following example: set.seed(342) x1 <- runif(100) x2 <- runif(100) y <- x1+x2 + 2*x1*x2 + rnorm(100) fit <- lm(y~x1*x2) This creates a model of y based on x1 and x2, using a OLS regression. If we wish to predict y for a given x_vec…
Tal Galili
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Computing prediction intervals for logistic regression

I would like to understand how to generate prediction intervals for logistic regression estimates. I was advised to follow the procedures in Collett's Modelling Binary Data, 2nd Ed p.98-99. After implementing this procedure and comparing it to R's…
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How to: Prediction intervals for linear regression via bootstrapping

I am having trouble to understand how to use bootstrapping to calculate prediction intervals for a linear regression model. Can somebody outline a step-by-step procedure? I searched via google but nothing really makes sense to me. I do understand…
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How to calculate prediction intervals for LOESS?

I have some data that I fitted using a LOESS model in R, giving me this: The data has one predictor and one response, and it is heteroscedastic. I also added confidence intervals. The problem is that the intervals are confidence intervals for the…
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Prediction and Tolerance Intervals

I have a couple of questions for prediction and tolerance intervals. Let's agree on the definition of the tolerance intervals first: We are given a confidence level, say 90%, the percentage of the population to capture, say 99%, and a sample size,…
Ioannis Souldatos
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