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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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% ...
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Risk score uncertainty quantification

I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk $$ r_i = f(x_i) + \varepsilon_i$$ where $x_i$ is some available information about ...
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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. ...
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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 =...
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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 ...
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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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Upper Bound for Size of Prediction Interval

I was thinking of this problem, and I'm not sure if I'm right with this approach. X is a R.V. with unknown distribution, bounded to the interval [a,b], with a < b and both finite. If I take a very ...
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Uncertainity band in Neural networks

I am working on a problem where I have to give the uncertainty band of my predictions like the image attached. I have seen a StackExchange solution for this, but in the solution code, we are using ...
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How can I find the prediction interval for a no-intercept simple linear regression model?

I have a dataset in which the $x$ and $y$ values represent metrics roughly equivalent to monthly sales opportunities vs. completed deals. These appear to be linearly correlated. I'm performing a no-...
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Obtaining individual level classifications from predicted probabilities

I need to produce predictions for a binary state at the individual level. The response variable is imbalanced, about 99:1, with the positive class being the minority. Each row in my dataset represents ...
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Using historical proportions for prediction intervals estimated at a more aggregated level?

Currently, I am working on quite a general problem where I need to forecast some business-related value like target events (clicks, acquisitions, etc). Given the number of different breakdowns (by ...
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Agricultural product decision making under price volatility

I am recently doing agricultural price forecasting to make decision in which month the company should buy them (normally when the price is low). But, the company decided to not buy all of stock they ...
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Logistic regression: how to compute a prediction interval

Suppose I have a simple logistic regression model: $log(p/(1-p)) = \beta_0 + \beta_1x$ Then I know: $p/(1-p) = e^{\beta_0 + \beta_1x}$ and $p = e^{\beta_0 + \beta_1x}/(1 + e^{\beta_0 + \beta_1x})$ How ...
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Estimating Prediction Intervals for Class Probabilities in Random Forests

I have found multiple questions here (e.g. this) and great academic papers (e.g. this and this) about calculating prediction intervals for Random Forest and other techniques applied to regression ...
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Analytical Leave-one-out prediction variance for Kriging

I make extensive use of Kriging (Gaussian Process regression) methods in my work especially using the leave-one-out error calculation that you can get from the Gram matrix. Background: To compute the ...
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Prediction Intervals the Same in Multi-Step with R Forecast Package - Why?

Using the R forecast package for a multi-step time series forecasting exercise, I've noticed that sometimes I get the same prediction interval at each step (6 months, in my case) and sometimes, I get ...
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Point Estimates using forecast in R for Multi-Step TS Forecast -- Sometimes Same/Sometimes Not -- Why?

I am using the simple forecast(data, h = 6) function in R - as I work through Hyndman's 'Forecasting: Principles and Practice" textbook - which returns forecasts from the ETS algorithm. I'm not ...
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How to use a sample from the posterior predictive distribution

Suppose I have a sample drawn from a posterior predictive distribution of a previously trained Bayesian Network (or any other Bayesian model). I.e., I have a vector $\tilde{\textbf{y}}_n = [\tilde{{y}}...
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Prediction Intervals on Judgment Forecasts - Possible?

Are there any R packages available or general methodologies for calculating prediction intervals on multi-step judgmental forecasts? I've looked at Hyndman's text and the R forecast package - which ...
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Binomial distribution - estimating confidence interval without mean?

This question is probably easy but I couldn't find the answer, nor remember my lectures in statistic. I have an (infinite) bag of red (A) and blue (B) chips, i.e. $P(A) = p = 1 - P(B)$ I want to ...
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Calculate regression confidence and prediction intervals from the standard errors of the fitted parameters AND the correlation coefficient

In many fields of the natural sciences, it is common practice to report the results of regression analysis as y = a1 + a2 * x. Bad luck, no uncertainties are ...
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When training data is much less than the prediction perdio

Given training data on tweets and their retweets, how would you predict the number of retweets of a given tweet after 7 days after only observing 2 days worth of data? Its strikes me that this ...
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What interval should I use to describe the variation caused by the randomness in stratified random sampling?

I have a population with n individuals. I decide that stratified random sampling is appropriate and I randomly survey a single individual in each strata, ultimately surveying ...
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Simple constant-width prediction interval for a regression model

Consider the following approach to generating prediction intervals for a regression problem: Train a regression model on a training set. Let $f$ denote the fitted model, i.e. $f(x_i)$ is the model's ...
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Summation of median and quantiles of multiple forecasted variables

Assume that I have Y1_hat with its P10_1 and P90_1 and Y2_hat with its P10_2 and P90_2. Is it valid to sum Y1_hat and Y2_hat, sum P10_1 and P10_2, and sum P90_1 and P90_2? and would that present any ...
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