# Tagged Questions

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

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### what is the estimated variance of predictions from mixed model?

I have fitted the following lmer model (assume it is "correct") with lme4: Y ~ X1 + X2 + X3 + (1 | year) + (1 | site) + (1 | site:year) where X1-X3 are ...
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### Confidence and Prediction Intervals for Multiple Linear Regression Model

I am looking for a derivation of confidence and prediction intervals for a multiple linear regression model. I have seen that for a given vector of predictors $(x^*)$ and $X$ denoting the design ...
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### Obtaining uncertainties from an errors-in-variables machine learning algorithm

In my field, every value reported comes with a 1-sigma uncertainty value. I'm using random forest regressors to estimate a value. All of my inputs have 1-sigma uncertainty information with them. ...
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### Combining prediction intervals

I'm using ML regressors (neural networks and random forests) to predict some numbers. I can put in my inputs and get out a value and its prediction interval. The inputs to my regressors are noisy, ...
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### Prediction Intervals with Heteroscedasticity

I am using R to perform linear regression. I have seen ways to calculate prediction intervals, but these depend on homoscedastic data. Is there a way to calculate prediction intervals with ...
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### Prediction intervals for levels using a VAR model in second differences

Given a VAR model for the second differences of a vector time series, $\Delta^2 y$, how to obtain the one-step-ahead (and possibly $h$-step-ahead) prediction intervals for the series in levels, $y$? ...
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### how does predicted median go above 95% prediction interval when using GBM with quantile loss function

I was checking out how to create prediction intervals with Gradient boosted regression trees using Scikit-learn. If you set the alpha at .95 or .05, you can get the 95% prediction interval around the ...
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### How can I calculate the PI of (simple) exponential smoothing?

I would like to calculate the prediction intervals of exponential smoothing. In R there is a function (ses in a forecast package) which calculates the point forecast and also the prediction intervals. ...
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### R: Calculating prediction intervals (95%, seasonal naive and holt winters)

Could somebody explain to me the theory behind how R calculates the 95% prediction intervals for my 12 step ahead forecasts in (1) a seasonal naive model and (2) a Holt-Winters forecast. My code is ...