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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.

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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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### 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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### Using an RMSE with derived confidence interval, to generate a prediction interval for an estimate

Previous questions have asked about creating prediction intervals for estimates derived from random forests or boosted regression trees, in a similar way to is easily achieved with linear regression ...
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### Detecting outliers using 95% PI around a natural spline fit

Please see the picture below: I wanted to mark the points that are not consistent with their adjacent points as outlier. What I did was to fit a natural spline fit to 1000 observations (the purple ...
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### Is it possible to get a prediction interval for logistic regression via a latent variable?

carbocation asked how to compute prediction intervals for logistic regression. The answer was that prediction intervals don't make sense for logistic regression because the response variable only ...
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### prediction interval of a new prediction out of a weighted linear regression model

This question is based on the example 11.1 out of the book Applied linear statistical models of Kutner, Nachtsheim, Neter and Li. You can find the data here. First they calculate a simple linear ...
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### Prediction intervals for HTS forecasting

So I have a lot of time series with a hierarchical structure, and need to produce forecast for each base series and its aggregates by the hierarchical structure. I have decided to produce forecast ...
225 views

### What is the mathematics behind the GAM prediction intervals?

From the R gam function available in the gam and mgcv package there is the option to obtain ...
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### Derivation of prediction intervals for a normally distributed population with unknown population standard deviation

I have via the ISO standard 16269 found the solution to a problem that I've been working on. Based on a couple of independent samples from a normally distributed population, I would like to determine ...
630 views

### Is this interpretation of prediction intervals correct?

I have a regression model relating to a ''normal'' population. If a new observation which corresponds to point $x$ is outside the prediction interval at $x$, do I have a reason to suspect the new ...
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### How to test whether 2 prediction intervals are statistically different?

I've been struggling with this for a while now, hopefully someone will know how to help me :) Here it is : 1) I'm using a linear mixed effects model on longitudinal data (biological values of many ...
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### Prediction Interval for Mean of Predictions

This question is about creating a prediction interval for the mean of predictions from a regressor. Let's say I have arbitrary regression function (not necessarily parametric, could be random forest, ...
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### Prediction interval for function of binary outcomes in GLM

I have a large data set with binary outcomes $\vec{y} = (y_1,\dots,y_n)$ with $y_i\in\{0,1\}$ and covariates $\mathbf{X} = (\vec{x}_1, \dots ,\vec{x}_n)^\top$. One of the goals of the model I am ...
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### Prediction intervals for generalized least squares model with heteroscedastic errors

I wanted to model some data with heteroscedastic errors using a gls model of the form ...
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### Is chaining neural networks in this way a good way to estimate a prediction interval?

Suppose you want to predict the outcome of some real valued function $f$. The details of the function are unknowable and it also has a stochastic component. You identify some variables $\theta$ which ...
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### Bootstrapped prediction intervals: Quantile, median, SE...?

I am trying to construct prediction intervals for a non linear model via Boostrap. What I do is to apply the usual bootstrap procedure, here you have pseudo-code for 1000 iterations: ...
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207 views

### Prediction Intervals for Incremental OLS regression

I am implementing incremental OLS regression algorithm where the data points arrive one at a time. As the regression parameters are determined by the formula, $(X'X)^{-1} X'y$ and the Sherman-Morrison ...
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### Prediction Intervals for Robust Regression: Formulation and are they larger than for OLS?

I have created regression models using robust regression - in particular, LTS and MM-estimators (using the R package robustbase). I am now looking to creation prediction intervals. The standard ...
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### How do I compute a prediction interval from generalized estimating equation output?

Suppose I have repeated observations on individuals, which I've analyzed using a generalized estimating equation (GEE). What is the procedure for computing the prediction interval for future ...
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### prediction interval for heteroscedastic data

Here are some data: ...
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### Confidence interval for (unobserved) sample mean

Suppose I take two samples, $a$ and $b$, from a population (or super population) but that I only observe $b$. However, I want to construct a confidence interval for $\bar{a}$, the average of the ...
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### Ways to estimate error in a machine learning algorithm's predictions by outputting a probability distribution

I want to make it so that my machine-learning algorithm, when given an input, outputs the parameters of a Gaussian distribution, with the goal of getting an expected error on the prediction. The ...
50 views

### (G)LM prediction interval with heteroscedasticity

I am trying to get prediction intervals from some non-linear data which also exhibits heteroscedasticity. ...
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### Predicting the variance of a future sample

Suppose that I have the dataset for wealth distribution for 50 different countries. Each country's data consists of the wealth figures for 100 random individuals in that country. Some countries have ...
59 views

### How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y). I would like to test whether individuals belonging to another population (...
869 views

### Posterior predictive distributions and predictive intervals

I'm confused about the role of posterior predictive distributions in Bayesian inference and predictive inference. As I understand it, the frequentist approach would typically involve fitting the MLE, ...
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### Is a comparison between Bayesian and frequentist prediction intervals sensible?

I am aware that frequentist confidence intervals and Bayesian credible intervals have quite different interpretations, and are not comparable. I'm wondering if the same is true for prediction ...
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### infinitesimal jackknife confidence intervals for bagged learners are NOT prediction intervals, right?

Wager, Hastie, and Efron present a method for computing confidence intervals for RF predictions. Confidence intervals have to do with the variability of the expectation, not the expectation of the ...
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### Using clusters to estimate model variance

I am working with a blackbox prediction model which takes known inputs and outputs a single mean response. I know this model's residuals to be heteroskedastic, but also can assume the error term of ...
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### How to get prediction interval given non normal data?

I'll start by saying that I have very little background in statistics and that my question title above is probably worded incorrectly. If I need to change the title to more accurately reflect my ...
879 views

### Precision of Prediction Intervals for Multiple Linear Regression

As discussed in 33433, the prediction interval for single linear regression is most precise at the mean of the $x$ values. Does this also hold true for multiple linear regression, that is: the ...
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### How to calculate prediction intervals based on Chebyshev inequality?

I have recently read the article by Gardner (1988) who proposes Chebyshev inequality-based prediction intervals for forecast: suppose we have a model selected on the usual basis of one-step-ahead ...
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### Prediction intervals for forecasts using spectral analysis

I have circadian data which typically have a period of around 24 hours so using spectral analysis seems appropriate. I've used spectrum resampling which is quite robust to changes in period which ...
52 views

### Testing and validating a limit for experimental data

I have found some similar questions to the one I pose here, but the answers are either over my head, or seem to be slightly off point to what I am trying to accomplish. If it's a true repeat, I ...
74 views

### Regression: Should I use the prediction interval obtained given n=9 and an outlier (Cook's D= 0.558) present?

The data I'm working with has 9 observations. I'm using only one predictor variable. Using SAS, I fit the model and checked the residuals. The typical model assumptions appear to be met, but there ...
306 views

### Prediction interval in principal component regression

I would like to obtain a prediction interval from a model returned by the R package pls. The predict method does not seem to be able to return this value. I wonder ...
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I understand how the adaboost algorithm works to produce a prediction of a class, however one thing I haven't seen is how to get a measure of accuracy for that prediction. For example, if I fit a ...
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