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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13 views

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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64 views

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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35 views

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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17 views

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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90 views

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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28 views

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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120 views

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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1answer
144 views

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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27 views

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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1answer
51 views

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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60 views

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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145 views

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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28 views

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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59 views

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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35 views

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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44 views

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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87 views

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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1answer
55 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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26 views

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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124 views

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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43 views

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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37 views

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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308 views

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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146 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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