# 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.

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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 $E[Y|x_0]$....
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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 ...
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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/...
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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 ...
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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; ...
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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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### 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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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### Prediction interval for binomial random variable

What is the formula (approximate or exact) for a prediction interval for a Binomial random variable? Assume $Y \sim \mathsf{Binom}(n, p)$, and we observe $y$ (drawn from $Y$). The $n$ is known. Our ...
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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 ...
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### Calculate prediction interval for ridge regression?

Does anyone know how to compute the prediction interval for ridge regression? and what's its relation with prediction interval of OLS regression?
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### Shape of confidence and prediction intervals for nonlinear regression

Are the confidence and prediction bands around a non-linear regression supposed to be symmetrical around the regression line? Meaning they do not take on the hour-glass shape as in the case of the ...
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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 ...
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### How to find a GBM Prediction Interval

I am working with GBM models using the caret package and looking to find a method to solve the prediction intervals for my predicted data. I have searched extensively but only come up with a few ...
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### How to calculate the confidence interval for time-series prediction?

I have a time series (let's say $X_1$ to $X_n$), and I need to predict the next sample (let say $X_{n+1}, X_{n+2},\dots, X_{n+k}$) using model such as neural network, or multiple linear regression. At ...
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### Prediction interval = credible interval?

I am wondering if prediction interval and credible interval evaluate the same thing. For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate ...
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### Predicting Uncertainty in Random Forest Regression [duplicate]

Scenario: I'm trying to build a random forest regressor to accelerate probing a large phase space. I'm using python/scikit-learn to perform the regression, and I'm able to obtain a model that has a ...
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### Empirical Prediction interval for time series forecast based on quantile regression

As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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### Forecast accuracy metric that involves prediction intervals

I'm in the process of generating a time series forecast for a company's product revenue and am looking for some way to show accuracy over time - e.g. after say 6 months they want to see how the actual ...
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### How do I calculate prediction intervals for random forest predictions?

In regression problems random forests yield a prediction for each case by averaging the results of each single tree in the forest. I would like to draw a 95% prediction interval around each prediction....
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### Predictive maintenace model to identify indication of failure before it happens

Situation I'm working on a problem where I'm using sensor data to predict machine failure before the failure happens and I need some advice on which methods to explore. Specifically, I want to ...
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### Prediction intervals for kNN regression

I would like compute prediction intervals for predictions made by kNN regression. I can't find any explicit reference to confirm, so my question is - is this approach to computing prediction intervals ...
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### Calculating Prediction Interval

I have the following data located here. I am attempting to calculate the 95% confidence interval on the mean purity when the hydrocarbon percentage is 1.0. In R, I enter the following. ...
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### Random forests confidence intervals and prediction

This is a short simulation to check the coverage, when used as predictive intervals, of the random forest confidence intervals introduced in the paper: S. Wager, T. Hastie and B. Efron. Confidence ...
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### Calculating prediction intervals when using cross validation

Are standard deviation estimates calculated via: $s_N = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}.$ (http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation) for ...
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### Bootstrap Prediction Interval: which residuals to use and which method?

I ask this question referring to the post: Bootstrap prediction interval, where a step by step method for calculating the prediction interval for linear regression models is explained. In the ...
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### Gaussian process prediction interval

How can the prediction interval of a Gaussian process be evaluated? I don't know how to estimate this interval though I can find a 95 % confidence interval for the mean line.
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### Does it make sense to generate prediction intervals for the estimates of a logistic regression?

Say I have a binary outcome of 0 or 1 and suppose I were to use logistic regression model to estimate the probability a new sample will have an outcome of 1. I have read answers (for example here: ...
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### The "sum" of prediction intervals

Suppose I have a regression model which yields a couple of predicted values with their respective prediction intervals and the random quantity that I am interested in is the sum of (some subset) of ...
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### Derivation of confidence and prediction intervals of predictions for probit and logit (and GLMs in general)

The derivation of the prediction interval for the linear model is quite simple: Obtaining a formula for prediction limits in a linear model . How to derive the confidence and prediction intervals for ...
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### Forecasting Poisson, accuracy and prediction intervals

I'm trying to forecast Poisson data, divided in groups, of 1-26 months of data, depending on the group. Of the pooled data ...
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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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### Does a prediction interval have to contain the mean?

I am having a huge problem with a conceptual problem that I came up with. Say a company has a distribution that is highly skewed. Something similar to an exponential or lognormal only more extreme. ...
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### Does more variables mean tighter confidence intervals?

Assume that the true (but unknown) relationship in a population between $Y$ and $X1, X2, X3, X4$ is $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4.$$ Further assume that I have a ...
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### R: glm(...,family=poisson) plot confidence and prediction intervals [closed]

I could not find many information on how to plot a confidence interval and a prediction interval for a Poisson regression (for example with glm()). What are some ...
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### How does R calculate prediction intervals in the forecast package?

I have a large dataset with different factors that I want to forecast to the future. These forecasts I will then later on use as inputs for a Monte Carlo simulation. My idea would be to use arima ...
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