# 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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### 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 ...
87 views

### 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'...
1 vote
373 views

### 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. ...
406 views

### 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. ...
64 views

### 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 ...
1 vote
40 views

### 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&...
1 vote
138 views

### 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 ...
2k views

### 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 ...
411 views

### 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 ...
124 views

### 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 $Y$ ...
197 views

### 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 Learning in a Random World. An assumption of conformal ...
1 vote
1k views

### 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 ...
1 vote
191 views

### 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 ...
105 views

### 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 ...
1 vote
23 views

### 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 ...
77 views

### 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 ...
48 views

### 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 ...
1 vote
111 views

### 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 ...
145 views

### Given a regression model, is there a way to evaluate confidence of a prediction?

What are methods for evaluating the predictive probability or something equivalent in a regression problem? In classification problems a predictive probability will be outputted given an input. For ...
2k views

### 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 ...
1 vote
107 views

### 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 ...
1 vote
190 views

### 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 ...
83 views

### 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 ...
134 views

### 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 ...
1 vote
689 views