# 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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### 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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### Multivariate, multi-series time data more appropriate for regression or ARIMA/time-series?

I have the following case for which I am needing to forecast a value, say, 12 months out: Many individual entities each with their own time series. Each entity has the same data structure For each ...
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### How do you change log-linear transformed prediction interval values for a regression back to original scale in r?

I have a simple regression model where I needed to log-transform the dependent variable because the model residuals were non-normal. Now my model is ok in that respect. So, I ran the model. But, ...
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### Question about confidence intervals and prediction intervals

Considering following linear multiple regression model: \begin{equation} y=X\beta + e, \end{equation} where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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### Estimating intercept from interval for slope and prediction interval

Suppose we have collected some data and formed a simple linear regression model for $Y$ versus $X$ . Suppose further that $[a,b]$ is an $\alpha$ % confidence interval for the true slope $\beta_{1}$, ...
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### Can you use a given prediction interval to find the predicted value of Y on the estimated regression line?

Suppose you don't know the estimates of a linear regression model (b0, b1 are unknown) and you are given a 95% prediction interval at x = 6 to be [5,15]. Then, since prediction intervals are ...
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### Is the train/test split necessary for parametric models like logistic regression?

In order to have an estimate of the prediction error in a machine learning model, I am used to split my dataset into a training set and a test set. I will train my model on the training set and ...
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### How to "add" coherent distributions from reconciled distributional forecasts?

I am trying to understand how to "add" coherent distributions from reconciled probabilistic forecasts, assuming the base forecasts are normally distributed as discussed in https://otexts.com/...
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### Prediction and Confidence intervals and overall error probability estimation

I wanted to understand difference between Prediction and Confidence intervals and found an ...
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### Should forecasts be based on the forecast error of the previous, or do I add expected errors on top afterwards?

Consider a model that makes a forecast, given previous points. From the test set I know the forecast residual distribution for $h_1, h_2, ..., h_n$ Now, when I make a new forecast, I will incorporate ...
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### Should I use the prediction interval or inverse prediction interval to calculate the uncertainty of x when using reverse regression?

I'm calibrating a piece of lab instrumentation. I create solutions of known concentration (x) and measure my instrument response (y). On unknown samples, I measure the response and use the regression ...
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### Upper Limits in High-Energy Physics

I am not sure where to write my question. This is a Particle Physics question, but it has more to do with Statistics than with Physics, I think. Please tell me if this is not the right site. So: In ...
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### Comparing prediction intervals to find probability of outcome

I had a thought I was curious about. I was reading some of the other posts, but they didn't answer the question specifically. Say I have a regression y = X'B ~ N(mu,sigma2) From this regression, I ...
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### Linear regression prediction intervals not increasing when extrapolating beyond training set

If I'm using a model in a predictive capacity it would be useful to have a quick way of seeing whether I'm applying it outside of the data space it was trained in, and thus I should take care with the ...
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### Comparing non-parametric correlations

I have two correlation (Spearman's rho) matrices from a single sample (before/ after intervention) and I would like to compare them to see whether intervention changed each or some of these ...
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### novelty detection to prevent prediction outside training dataset

I have a training dataset composed of $d$ independent variables $\bf X$ and a dependent variable $\bf y$ for $n$ observations. I have trained a model with this $n$ observations. What I want to do now ...
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### How to calculate uncertainty for predictions coming from cascade of models?

I have developed a bunch of models to predict house prices. It is a 3 fold process: I fit a gbm (first_model) and get the first prediction (first_pred), there are some sub-models (simple lineer ...
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### Likelihood that a prediction falls above (below) 110% (90%) of the prediction

For my client I have to predict some products' prices with gbm (scikit). So in the production, I am to give prediction intervals. That is, I need to provide how likely a real price falls above 110% or ...
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### Prediction intervals for location scale model

Regarding the example below from Chapter 3 of A.C. Davison's Statistical Models, I'm wondering why $Q = (Y_+-\bar Y)/S$ depends only on $g$.
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### Why does prophet produce much tighter prediction intervals than ETS?

I'm currently working on a forecast problem, where narrow prediction intervals are preferred. When I look at the prediction intervals of ETS and prophet forecasts, I'm surprised that the prophet ...
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### How to calculate prediction interval in GLM (Gamma) / TweedieRegression in Python?

I have checked much source from webs about conducting the prediciton interval, especially in GLM function. One of the approaches is about Prediction Intervals for Machine Learning https://...
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### Prediction interval for linear regression with autoregressive error

Suppose that ${y_{t}}$ and ${x_{t}}$ are time series variables. A simple linear regression model with autoregressive errors of order ${p}$, say AR(P), can be written as \begin{equation} y_{t}= \...
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### Prediction of Variance vs Variance of Prediction

Is the prediction of the variance the same as the variance of the prediction? I know the concept of prediction intervals, used to specificy the variance of the prediction. I also know (G)ARCH models, ...
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### Generic Prediction Interval Methods

I'm trying to implement a generic method to calculate prediction intervals for univariate forecast methods. While the literature is quite clear on how such a prediction interval is define (e.g., here ...
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### How to intuitively understand the shapes of confidence and prediction intervals in simple linear regression [duplicate]

Assume the linear regression $Y=b_{0}+b_{1}X$ The $100(1-a)$% prediction interval for $x=x_{*}$ is given by whereas the The $100(1-a)$% confidence interval for $E(Y|X=x_{*})$ is given by What I don'...
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### How to interpret confidence interval and prediction interval in simple regression "in/with the context of sampling distribution"?

With the context of sampling distribution, in regression analysis, is the following an appropriate interpretation? Assumptions : X & Y have a linear relationship sample size is large enough for ...
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### Prediction of Mean and Variance with remlscore?

I would like to do a prediction of the mean and variance with confidence and prediction intervals using remlscore in statmod, i....
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### Is it possible to calculate the prediction intervals for top down, bottom up, and middle out reconciliation of hierarchical time series?

I have read in several places (heres one) that we can not calculate prediction intervals for the classical reconciliation approaches, top down, middle out, and bottom up, and hence optimal ...
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### Accounting for multiple layers of uncertainty in a model

Let's say I have data on 10 stores that sell widgets, each of which received num_orders number of orders in a certain timeframe, and sold a total of ...
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### What is the probablity the y value produced in a linear regression is correct?

Apologies in advance if I am using the wrong terminology. Is the y value produced by a linear regression model assumed to be the mean of a normal distribution? Meaning there is a 50% chance the actual ...
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### Prediction interval for regression with time series data

Suppose that ${y_{t}}$ and ${x_{t}}$ are time series variables. A simple linear regression model with autoregressive errors of order ${p}$, say AR(P), can be written as \begin{equation} y_{t}= \...
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### Calculating the quantile of random forest test cases

I want to calculate the quantile of the observed value of a test case with respect to the prediction interval generated from a random forest, so for each test case I want the proportion of the ...