# 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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### How can I best get a prediction interval for future group or nested group means with LMM (lme4)?

I am building a linear mixed model of an experimental data set. The data can be grouped into individual experiments, and further each experiment consists of clusters within which a sample is observed ...
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### How to represent the interval or uncertainty on regression predictions in an 'experimental vs predicted' plot?

Using an example similar to the one from R predict, simulate some independent variable ($x$) data, map them to an observed ...
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### Get a range of values (val_1 to val_2) instead of one value in linear regression

So, the idea is that I use linear regression and I get an equation y = a * x + b. So when I give a value x I get a predicted ...
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### Prediction interval for sum of weighted bernoulli random variables with estimated probability p

Suppose $X_1,...,X_n$ are independent bernoulli random variables with success parameter $p$, i.e. the common pmf is $f(x)=p^x (1-p) ^{1-x}$ for $x=1$ or $x=0$. I am interested in finding a prediction ...
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### Why is my statistical prediction interval not as I'd expect? (statsmodels, python)

I am using the statsmodels python package to perform multivariate linear regression. I want to produce 80% prediction interval bands as part of my result. The statsmodels package can produce ...
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### Unexplainable cyclical patterns on prediction intervals for time-series forecasting using Extreme Gradient Boosting regressor

I am following the documentation of skforecast to make time-series forecasting using the Extreme Gradient Boosting regressor (i.e., ...
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### What is the Formula for Prediction Interval in Multivariate Case? [duplicate]

I am using linear model to do prediction, and I would like to calculate my prediction's prediction interval, which, when there is only one predictor, is However, my model has three predictors. What ...
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### What is the Matrix form of the prediction interval for Weighted Least Squares Regression

For ordinary least squares, I know the confidence interval is $\hat{Y} ± t\cdot\sqrt{\hat{\sigma}^2 * x_{new}(X^{\top}X)^{-1}x_{new}^{\top}}$ and $X$ is the design matrix, n is the number of ...
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### Using Confidence Intervals for finding confidence of forecasting model

My question is quite a general one. Can I use the width of the confidence interval (let's say a 95% confidence interval) to find out how confident my model is while doing time series forecasting? I am ...
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### How much can I forecast in the future?

Given some time series data and a forecasting model (maybe conventional models like ARIMA, Prophet, etc, or deep-learning-based models like NBEATS, Transformers, etc), I want to find out how much in ...
35 views

### Is it possible to calculate prediction interval without info on the predictor x?

I can see from here that prediction interval for a new response Y (setting is simple linear regression) is However I've read here that Apparently, no calculation related to x is needed according to ...
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### Prediction Intervals for a Two-Part Model?

I have fit a two-part model, where the first part is using a logistic regression to model the probability of seeing Y, and the second part is using a Gamma GLM regression with a log link to model the ...
135 views

### One tailed prediction intervals for Multiple Linear regression

After having fit a multiple regression model to my data, I am using it for predicting my dependent variable. I understand how one can predict and compute (using R) two tailed prediction intervals at a ...
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### Substraction of predicted values: taking in to account prediction intervals

I'm trying to make a prediction of the number of annual flu hospitalizations. In order to do so I'm trying to subtract the predicted number of hospitalizations when there is no flu from the predicted ...
84 views

### estimation of a yearly prediction interval for monthly data

I have a monthly time series and my objective is to provide my client with the next 12 point forecasts along with a yearly forecast. To obtain the yearly forecast, I simply summed up the 12 points ...
1 vote
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### Bootstrapping (aleatoric and epistemic) risk score uncertainty

I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk $$r_i = f(x_i; \epsilon_i), \quad 0 \leq r_i \leq 1,$$ where $x_i$ is some ...
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### Using remaining useful life predictions to assess model fit with right censored data

I am modelling time to failure of some units. All units are made my the same manufacturer and there are no recorded covariates to distinguish between the units. This means that the central, $95\%$ say,...
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### Prediction interval generalized estimating equations

Because I have time dependent covariates and the full covariate conditional mean assumption (Pepe and Anderson, 1994) does not hold, I have fitted a continuous longitudinal response with generalized ...
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### Missing Prediction Intervals by R package autoTS

I'm using autoTS R package to fit automatic time series estimation and prediction to a very very large number of time series. One of the outputs of the prediction function (my.predictions()) is a 95% ...
85 views

### Risk score uncertainty quantification

I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk $$r_i = f(x_i, \varepsilon)$$ where $x_i$ is some available information about the ...
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### Bootstrapping with quantiles of data instead of SD*z?

I have recently been bootstrapping the confidence intervals of a neural network model estimated to data. I execute the following psudo-code, which seems similar to previous bootstraps I have done: ...
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### Intuition for confidence intervals vs prediction intervals for linear regression

I am having a bit of trouble understanding the difference between a confidence and prediction interval in the context of linear regression, and in what scenario we would use either of them. I've posed ...
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### Is there a way to calculate prediction intervals for decision tree or extra trees regression models?

I only see examples of prediction intervals for random forest and linear regressions but do not see much about ensemble models. I'm not sure if my understanding about prediction intervals is correct. ...
1 vote
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### Distribution-free prediction intervals in linear regression

I've found some literature on the subject, but it is rather difficult to read. I am wondering if the following simplified method makes sense. My question is what part is correct in this methodology, ...
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### How can we call difference between observed values and prediction interval?

As in the topic title. Is it correct to call difference between observed values and prediction intervals a "difference prediction interval"? Or should I go for "O-E prediction interval&...
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### Parametric bootstrap *prediction* interval with heteroskedasticity and sandwich parameter covariance matrix

The sandwich estimator for OLS regressions where heteroskedasticity is suspected is $$var(\hat\beta) = (X'X)^{-1}X'ee'X(X'X)^{-1}$$ If I want confidence intervals on predictions, I can just take ...
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### Prediction interval: but instead, the probability that the next datum is above a fixed threshold?

I've been struggling with this problem, and I think I must be missing some important conceptual step. Imagine we observe $\theta_1 \sim N(\mu, \sigma^2)$, with unknown $\mu$ and known $\sigma^2$ (for ...
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### Wide prediction intervals for short time series: how to fix that?

I have very small time series data(24 points) for sales for different-different regions. I need to build Range Forecast (Confidence/Credible Intervals) for sales around it for every region. I tried FB'...
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### Confidence interval for the predicted values from normal distribution

Let's say I have some n samples of real values $y_{i}$ and predicted values $\hat{y_{i}}$. The predicted values were calculated from gradient boosting. The things I know from this gradient boosting ...
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### Aggregation of Interval Predictions

Given a montly time series, my objective is to provide my client with the next 12 point forecasts along with a yearly forecast. To obtain the yearly forecast, I simply sum up the 12 points forecasts. ...
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### Prediction interval when forecasting a function

I want to forecast a function of x, say with domain the integers from 1 to 100. My data comprises other such functions, observed at times up until now. The functions are given parametrically, so I ...
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### Predicting a in mixed effects logistic regression

I know there are several posts about intervals for lmer models (Prediction interval for lmer() mixed effects model in R) and glmer models (Confidence intervals in probabilities for mixed effects ...
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### Real future value out of 95% predict interval for ARIMA forecast

When the predicted future value actually materializes, does it matter if it is outside the predict interval? The value of prediction intervals is that they express the uncertainty in the forecasts. ...
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### Getting the confidence interval or some sort of range for predictions from optimizations

I am trying to calculate range for my model predictions after performing optimization and getting values of the optimized parameters. I am aware that we can get a standard error of the optimized ...
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### Estimate quantile coverage

I have implemented, say, a (Bayesian) quantile regression model and I want to assess it by comparing the predicted conditional quantile interval between $Q_1$ and $Q_3$ with the true one (in a ...
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### Is there a single regression quality metric for the median and the 95% percentile?

I want to evaluate the quality of prediction of two values the median and 95% percentile of a distribution. Is there a standard way to do this? I have thought about using "Mean Mean Average Error&...
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### Gaussian Process vs Linear regression: Prediction error

I'm trying to learn GP and every manual says that GP can deliver predictions with uncertainty. Now, as I have learned some linear regression, I don't understand why is that a big deal. The simplest ...
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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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### Prediction and confidence intervals - large number of predictions

I'm using a regression model to predict one quantity, $y$, given another, $x$. I'm trying to estimate the error in future predictions of $y$, but I'm wondering in which scenarios I can fairly use the ...
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### Is it better to use the prediction interval or the RMSE?

I use a measurement technique $X$ to assess if a good is within production specifications during its manufacturing. $X$ is slow but precise. I wish to find out if I can use a measurement technique $Y$ ...
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### Looking for a intuitive explanation behind standard error formulas in linear regression

Suppose, we perform a linear regression for target variable Y with two features X1 and X2 (referred to as X below), I see that various standard errors are calculated as  Mean\ residual\ error = MSE =...
1 vote
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### A question about the exchangeability assumption in conformal predictions

Conformal predictions allow one to add prediction intervals to arbitrary machine learning regression models. For more information see Algorithmic Predictions in a Random World. An assumption of ...
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### Confidence intervals for next frame video prediction

I'm using a ConvLSTM network for next frame video prediction. The output is a deterministic prediction of an image in the future. My question is: can a ConvLSTM model give me an interval of prediction ...
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### How to Combine ARMA + GARCH For Estimates + CI in Python

I know I'm trekking down a well beaten path with this type of question, but I find myself trying to clarify how to combine several snippets on the internet and coming up empty handed. There is one ...
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### Forecast with inputs that are previous forecasts

I have an hourly time series and I have built a linear regression model that has different inputs: Previous value of the time series. Value in the last period of the time series, it is a weekly ...
1 vote
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### Should boostrapped prediction intervals be normally distributed?

I am trying to implement boostrap prediction interval example of FPP3 book in python for learning purposes (https://otexts.com/fpp3/prediction-intervals.html). Prediction interval is estimated by ...
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### How to compute a prediction interval on rescaled power transformed data?

Given a training dataset $\mathcal{D} = \{ (x_i, y_i) \in \mathbb{R}_+^2 | 1 \leq i \leq n\}$ one can fit a linear regression $y_i = a \cdot x_i + b + \varepsilon_i = \hat{y}_i + \varepsilon_i$. That ...
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### 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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### Translating polyval from matlab to python

I need to translate a script from matlab to python. I run into an issue with the polyfit/polyval functions. Matlab polyval returns a "delta" value which is a standard error dependend on the ...
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