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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31 views

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 ...
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Prediction intervals from Linear regression and Arima for DYNAMIC forecasting

I am comparing prediction intervals from linear regression and ARIMA for a simple AR(1) model: p = lag(p) The models were built on monthly data from 2003-2013 years. Predictions were made for 2014 ...
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Calculate prediction interval with stats::predict

I'm forecasting for the first time, so please for some patience. I want to calculate lower bound of 95% interval on my point forecast. I have the following model for estimation and forecasting a ...
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Сonfidence interval mean response and prediction interval for Instrumental Variables regression

I evaluated the regression model using the 2SLS method which is presented in the ivreg R package. Using predict can get fitted ...
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41 views

Utility of the whole distribution (other than the mean) in Bayesian posterior predictive

In prediction task, when using Bayesian fashion of predictors, I think in most the cases, people just use posterior mean for each individual estimate. I wonder if there's any utility of the higher ...
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Using AIC weights to determine prediction intervals for a single model structure

I am working with fitting regression models to data, and producing prediction intervals would be useful. Unfortunately, the data often has few data points, and is reported as mean rather than ...
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Quantile regression vs probability density estimation

If you want to predict a range for a regression problem using a deep network, you can do quantile regression and go with (for example) 5% and 95% quantiles. The other option is predicting a ...
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Bootstrap and prediction interval (Kumar & Srivastava 2012)

I am reading the paper Kumar & Srivastava (2012) and I am trying to understand it. However, I have some difficulties to understand some elements in the paper. First of all, let me present you some ...
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How to Derive Prediction Intervals for Orthogonal Distance Regression using `scipy.odr`?

Questions How can I derive prediction intervals for predictions based on new observations from the output of scipy.odr? Is it also possible (or necessary) to take ...
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Marginal mean after OLS, where X is a combination of seen and unseen observations

Looking for advice on a package in R or Python and an approach to help me construct a confidence interval for a marginal mean (or maybe we'll call it a prediction). Say I run OLS regression with $y$ ...
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Prediction Intervals (Conformal Predictions) for Regression Problems

So I've been looking into the idea of looking into conformal predictions, or to obtain prediction intervals instead of just single point predictions. Basically my take is that I would have my deep ...
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How do I calculate confidence level or interval?

I have this data for exam grades in English Literature: 2019: the numbers achieving (A*, A, B, C, D, E) are (1, 5, 4, 7, 2, 0, 0) 2018: the numbers achieving (A*, A, B, C, D, E) are (2, 4, 3, 7, 0, 1, ...
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Significance of datapoint outside prediction band

With linear regression I am plotting 25 bodies of text with their vocabulary count (independent variable X) and occurrence of a particular word (for example: "this"). I have a linear ...
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Why do different divisions of the same text corpus result in different regressions?

Background I am comparing a small text of 169 words to a bigger text consisting of 19.000 words. I am trying to plot a linear regression of different texts that can result from the different ways of ...
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How to calculate the prediction interval for regression through the origin?

I know the predicative interval for a single value of Y for a given Value of X_0 is: However, what would this formula be if the regression was forced through the origin?
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variance of theoretical mean of y at given value of x in regression [duplicate]

Could someone tell me where I might find information on deriving the standard error used in confidence and prediction intervals of y at a given value of x on a regression line. I can't find anything ...
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Prediction intervals for a single random variable

Prediction intervals seem to be talked about most in the context of regression, but I want to reduce it to one random variable to understand the reasoning. Assume you are sampling from a normal ...
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Why are the ends of the prediction interval wider in the regression? [duplicate]

Usually, the prediction interval has this shape in the image. I don't know why the end of the interval is wider than the center.
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77 views

Neural Network Assumptions in a Time series

I was wondering whether an artificial neural network regression, like ARIMA, requires statistically insignificant residual autocorrelation -- and, if so, why? I presume that, if I am using the ANN ...
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Project time series from previous time series examples and characteristics

Say I want to open a shop but first I want to project the likely sales in the first 5 years to see if it is a viable option. I have data pertaining to 100s of other start ups, including their success ...
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How do I compute the prediction interval by hand for a multiplicative time series decomposition model?

Say, I use a simple multiplicative decomposition on a time series dataset as defined in Chapter 6.8 of FPP2: $y_t = \hat{S}_t \times \hat{A}_t$, where $\hat{A}_t = \hat{T}_t \times \hat{R}_t$, so ...
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Predicting Rare Events (Incidents) from Sequence Data: Using RNNs

I have a problem I am interested in, and I am thinking of it in the context a neural network sequence model (any appropriate variation of RNN) BUT please correct me if another model is more apt: Data:...
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add linear trend back into time series prediction (in R)

I have the following GARCH(1,1) model ...
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How is modeling the time series error/variance, e.g. ARCH or GARCH models, different from modeling time varying forecast intervals?

I'm having a hard time understanding the intuitive difference between modeling the volatility or variance of a time series as it is done in ARCH and GARCH models: $$Y_t = c+\epsilon_t+\phi_1Y_{t-1}+....
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Understanding plot for stats::predict

I created a time series for 15 years (in each year 123 days), and I created a forecast using stats::predict for the next 5 years. ...
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OLS Prediction Error of sum of m future observations

A paper I'm reading states the "The prediction error of a sum of m future observations (as is needed for determining energy savings) is given by Theil (1971)" Due to covid I don't have access to the ...
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Bootstrap method for the construction of PI

I did physical measurements with a machine. There I could set 3 independent input variables and got 10 dependent output variables (qoi) per measurement. I did 1000 measurements. Thereby the shape of ...
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how to get predicted intervals? code no giving me those values [closed]

I am doing a cross validation in a training data and I am getting my predicted values with my test data. I want to do a plot with predicted versus observed with the predicted intervals but my code is ...
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Business-driven regression metric interpretation

I'm working on a model for income prediction and use RMSE as a metric for it. The desired output is the true_income±delta i.e. ...
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Prediciton interval estimation for GBDT and sum of prediction

I want to create an estimate of the prediction interval for the sum of predictions n-steps ahead for a general estimator f(X) in the presences of auto-correlation in the residuals, and less training ...
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27 views

Does the length of a prediction interval decrease with sample size?

For a general prediction interval given by $x_{0}^T\hat{\beta} \pm t_{n-p,\alpha/2}\times s \sqrt{1+x_{0}^T(X^TX)^{-1}x_{0}} $, I have been taught that as n tends to infinity we can approximate this ...
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Estimation of out of sample confidence interval

Background: I have estimated the following logistic function y(t) = a/(1+bexp(ctime)), where a, b and c are the estimated coefficients, and time = 1,2,3,,,T. I want to project y into the future t = T+...
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Average Coverage Error (ACE)

This paper mentions ACE. It is defined as following ACE = PICP - PINC where PICP and PINC stand for Prediction Interval Coverage Probability and Prediction Interval Nominal Confidence, ...
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Calculating Prediction Intervals for multistep univariate time series forecasting using Bootstrapping

I understand the way to compute the prediction interval at 5% and 95% for one step forward forecast based on Bill's answer to the question at Bootstrap prediction interval. The idea being that based ...
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230 views

How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

The question is a bit similar to question 147242 . I'm dealing with a multiple linear regression model, say: $$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 $$ and I'm looking for an algebraic equation to ...
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Estimate an error bound for an estimate

I have two datasets regarding historical data (say, quarterly revenues for companies over time). The first is the actual results of this data and the other is available estimates for these results ...
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21 views

Good proportion of training data to get prediction interval using bootstrap

I am trying to get prediction intervals thanks to bootstrap: I train 1000 linear regressions with different subsets of my training data. Say I have 1,000,000 rows in my dataset, what would be a good ...
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Does it make sense to propensity scores for re weighting samples in prediction tasks?

When reading the literature on propensity scores, the focus is mainly on estimating treatment effects (be it ATE, ATT, or else). But that, in linear models terms, is equivalent to asking questions ...
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Is there a possibility to combine WLS with bootstrapping methodology for prediction purposes in R?

This is my first post, so here I go: I used R to create a bootstrap prediction interval for a one-predictor logarithmic regression model. Here are the steps for the creation of the bootstrap ...
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Buld prediction intervals for glmmTMB

I'm using glmmTMB to build a mixed effect logistic model from which I want to draw predictions. The predict() function applied to a glmmTMB model allows extracting the ML prediction and the relative ...
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307 views

Standard Error of prediction for Logistic Sigmoid function

Standard Error of prediction for Logistic Sigmoid function (previously: Finding the prediction interval for logistic regression) Update 2: This paper describes what I am looking to implement. Update: ...
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Implementing Bayesian Linear Regression using PyMC3

I am learning a Bayesian Approach towards implementing Linear Regression. The motivation is that Bayesian Approach gives you a range on predictions which might be useful when investing money in ...
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(G)LM prediction interval with heteroscedasticity

I am trying to get prediction intervals from some non-linear data which also exhibits heteroscedasticity. ...
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Prediction and confidence intervals interpretation for nonlinear data and linear model

I have a bunch of features that have an approximately simliar pattern. I've plotted a confidence interval and a prediction interval for one of them and I wonder weather CI and PI are meaningfull for ...
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32 views

Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. https://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...
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Predictions on transformed series post intervention analysis

I have taken this logged data and performed an intervention analysis: ...
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Regarding Hyndman's approach to estimating prediction intervals for forecasts generated by neural networks

I'm currently looking for ways to estimate prediction intervals from an LSTM generated forecast. Several advanced methods are suggested in the literature (e.g. SQF-RNN), but as a first pass, I'm ...
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Upper 95% Prediction Bound

I understand calculating a two-sided 95% confidence interval for Beta1 of a simple linear regression model. Now I am stuck trying to calculate an upper 95% Prediction bound for y_star at the value of ...

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