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 ...
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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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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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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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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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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 ...
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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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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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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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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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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 ...
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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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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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How to best represent uncertainty in a time series forecast model?
Now that I know why it is important to represent the uncertainty of a model, I would like to know how to best represent uncertainty in a time series forecasting model.
My previous question introduced ...
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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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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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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 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 ...
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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 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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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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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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