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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62 views

Forecasting costs with forecast interval using past performance

I'm trying to adopt a model for project cost forecasting in agile. Consider the following table of previous costs per sprint, along with story points completed: ...
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Simple method of forecasting number of guests given current and historical data

I am trying to predict the number of guests a restaurant might serve in a meal period based on the volume of business that same day from prior years (3-5 years of data), trends for the same day of the ...
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307 views

Prediction Interval for Regression Models with Weights

Courtesy Prediction Interval for Neural Net With Hessian :: nnet in R I would like to understand how to manually derive a point-wise prediction confidence interval applicable to neural models. ...
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283 views

Find error interval of linear relationship

I have two sensors of different quality capturing the same process, where one of them is much more accurate than the other. Hence, I want to find out how much better. Let us for example say that the ...
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1answer
570 views

Forecast R function : prediction interval is not symmetric across mean

Using forecast function in Forecast package, I am trying to get mean and prediction interval for forecast period (h = 8). But I could not understand why prediction interval are not symmetric across ...
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Sampling from forecasting interval

Suppose I have an ARIMA model with $n$ step ahead forecasts and forecast intervals. If I want to sample from those forecasts: One way to look at is: take one observation from the prediction ...
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524 views

Are predictive distributions supposed to be distributions of future data?

In frequentist analysis, we define a 95% prediction interval as an interval that will contain the next observation 95% of the time under repeated sampling of the entire experiment and prediction. If ...
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1answer
133 views

ARIMA forecasting using exogenous variables with their own forecast intervals

Suppose model <- Arima(y , xreg=cbind(x1, x2), order=(p,d,q)) If I am forecasting $x_1$ and $x_2$, then for forecasting $y$: 1) If I use expected forecasts ...
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636 views

Disadvantage of prediction interval vs confidence interval

I have a linear regression model μ = 4.7937 - 0.0627t with Y ~ N(μ, σ^2), where t is temperature and μ is the expected number of accidents that happen. At t = 50, μ = 1.66 and the confidence ...
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977 views

Heteroskedasticity in a VEC model, adding robust standard errors and plotting forecasts

I'm dealing with a data set which required me to log and take first differences of it to induce stationary. A VECM as a result was prodouced. Everything seemed fine until I checked for ...
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113 views

Calculate original data forecast interval from differenced data forecast interval

How to calculate original data forecast interval from differenced data forecast interval? Please provide formulas or bibliographic reference.
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Time series: Getting from monthly to semi-annually data by summing - how to determine the forecast interval? [duplicate]

I have to forecast some monthly timeseries 1.5 years into the future and then sum them up to get 3 semi-annual counts. The forecasts give forecast intervals, but how do I get from the 6 monthly ...
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419 views

How to provide CI for prediction for mixed model? lsmeans vs predictInterval

I have a linear mixed model, say: $$y \approx x_1 + \cdots + x_n + (1\,|\ \text{person})$$ I would like to have a Confidence interval for the prediction, so I would like to say: if $x_1=3\ $ and $\ ...
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Predicting Uncertainty in Random Forest Regression [duplicate]

Scenario: I'm trying to build a random forest regressor to accelerate probing a large phase space. I'm using python/scikit-learn to perform the regression, and I'm able to obtain a model that has a ...
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244 views

Determine Accuracy of Prediction Interval

I have two time series models and I was wondering the best way to determine if prediction interval for Model A is more accurate than the prediction interval for Model B relative to the actual value at ...
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How to make correct predictions of probabilities and their uncertainty in Bayesian logistic regression?

In the context of Bayesian logistic regression, outcomes $y$ are binary (discrete) and covariates $X$ are given. We assume in particular: $$ p(y | x, \theta) = Bin(n,\theta) \newcommand{\new}{{\rm ...
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Choosing data points for multiple regression

I am building a regression model from simulation data. Specifically, I can choose which data points to sample and want to minimize my average prediction interval in the prediction space $[L,U]$. In ...
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1answer
564 views

metaprop in R: same results for random effects, fixed effects and prediction interval [closed]

I am using the metaprop function in R to obtain estimates for a fixed effects model, a random effects model and a prediction interval. I've done this many times, without any issues, but I'm puzzled ...
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1answer
411 views

Is a confidence interval symmetric when constructed on an inverse prediction of a logistic regression?

I have a dataset with a continuous variable paired with a binomial response. We want a one-sided confidence bound to determine at what value of the continuous variable would we get a desired ...
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1answer
342 views

Simulation based on BSTS model

Currently I'm fitting different time series models and produce combined n-step-ahead forecasts. As finding prediction intervals (analytically) for combined forecasts is quite a hassle, I decided to ...
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What is "Forecasting the most probable following value"

I am reading the book, "Machine Learning in Java" published by Packt publishing, and written by Boštjan Kaluža; and there is a paragraph at the book, and I can not understand. At the book, there is ...
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1answer
49 views

Interpret forecast output - standard error?

I ran the function forecast to get predicted values from a seasonal arima model. Please see the picture. What are the values in the left column? I guess they are the standard error? How are the ...
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108 views

How to get different forecasting values with Seasonal ARIMA?

thanks for the help in my previous post which describes my issue. I fitted a seasonal ARIMA model to my daily temperature time series. My goal is to run the forecast lets say 10,000 times in order to ...
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1answer
476 views

Estimating white noise distribution for a AR(1) process in R

I have a time serie and I want to compile some scenarios following a AR(1) process. I have used the package forecast from R to compute the coefficient with : <...
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How to incorporate uncertainty of actual historical data into forecast prediction intervals?

I wonder how we can incorporate uncertainty of the actual historical data into forecast prediction intervals. In other words, we would have for example 95% range instead of the data points for ...
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469 views

Python forestci.random_forest_error return negative value

After running a out sample prediction using randomforestregressor, I need to construct a confidence interval for the predictions. The rational behind it is to give the business side a sense of what ...
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How to analyze a prediction interval inside another prediction interval

For those who know something about statistics, I'm wondering how to analyze a prediction interval encompassing other prediction intervals. To provide some background, I'm not talking about confidence ...
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138 views

What happens if we set the prediction interval and confidence interval around the regression line at ".9999999"

Below, I'm showing a hypothetical simple linear regression case. There are $5000$ datapoints in each of the 4 sub-populations stacked over the top of each predictor value. Each subpopulation is ...
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3k views

Points Outside Linear Regression Confidence Band

I have done a linear regression of predicted measurements (of my model) vs. observed measurements and plotted the confidence band. Can I draw any conclusions about the points that lie outside the band?...
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718 views

Why do we include the variance of $\epsilon$ for the variance of predicted values? (normal linear models)

Suppose I have a normal linear model $Y = X\boldsymbol{\beta}+\epsilon$, $\epsilon \sim N(0,\sigma^{2}I_{n})$. Given covariates $x_{*}$ and estimated parameter vector $\hat{\boldsymbol{\beta}}$, I ...
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62 views

Credible/Confidence intervals for fitted values

I fitted some models using MCMC using different link functions like $$\text{Logit}:\qquad \hat{y_i}=\frac{e^{x_i^T\hat{\beta}}}{1+e^{x_i^T\hat{\beta}}}$$ $$\text{Probit}: \qquad \hat{y_i}=\Phi(x_i^T\...
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408 views

Extremely wide prediction interval

I am fitting a linear model to a data set with a lot of variance. Basically, I have sales for the first few months of similar, but not exactly the same objects, and am trying to predict sales a year ...
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Is chaining neural networks in this way a good way to estimate a prediction interval?

Suppose you want to predict the outcome of some real valued function $f$. The details of the function are unknowable and it also has a stochastic component. You identify some variables $\theta$ which ...
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593 views

How do I interpret prediction interval and point prediction?

Consider a simple linear model: I have obtained a prediction interval of $(37, 66)$ and a point prediction of $52$. (the problem behind is not a concern I reckon, for the sake of the question). Now ...
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1answer
123 views

Prediction Interval, linear regression - why is a future response a random variable but other responses are not random variables?

We have a new observation $x_0$, whose response will be $Y_0 = \beta_0+\beta_1x_0+\epsilon_0$. We want to predict $Y_0$. The estimator that we use is $\hat{Y}_0 = \hat{\beta}_0+\hat{\beta}_1x_0$. ...
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277 views

Confidence vs prediction intervals

I try understand the difference between prediction and confidence intervals. Say we want to predict the winning time of the 100 m race in the Olympics 2020. We have fitted a linear regression model of ...
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1answer
40 views

Using clusters to estimate model variance

I am working with a blackbox prediction model which takes known inputs and outputs a single mean response. I know this model's residuals to be heteroskedastic, but also can assume the error term of ...
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1answer
660 views

ARIMA model with extremely small estimated $\sigma^2$ in log-transformed data

I analyzed a time series data set using ARIMA model. And if I fit an ARIMA model using the original data, the estimated $\sigma^2$ is in the normal range, say 100. But when fit the same model using ...
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166 views

Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $n$

I'm working on a problem which has the following qualities. The available data $x$ is numerous - on the order of $10^6$ The CDF $F_X$ has support over nonnegative real numbers. I don't know $F_X$. We ...
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Difference between estimation and prediction in simple linear regression model?

Here is what my notes say about estimation and prediction: Estimating the conditional mean We need to estimate the conditional mean $\beta_0+\beta_1x_0$ at a value $x_0$, so we use $\hat{Y_0}=\hat{...
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898 views

Predictive maintenace model to identify indication of failure before it happens

Situation I'm working on a problem where I'm using sensor data to predict machine failure before the failure happens and I need some advice on which methods to explore. Specifically, I want to ...
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693 views

Bootstrapped prediction intervals: Quantile, median, SE...?

I am trying to construct prediction intervals for a non linear model via Boostrap. What I do is to apply the usual bootstrap procedure, here you have pseudo-code for 1000 iterations: ...
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1answer
340 views

What is a "valid interval" in a prediction?

Learning about linear regression, I was teached that when a linear regression is calculated for a set of points, I can only make predictions with this linear model on the interval setted by the first ...
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1answer
2k views

"ARIMA" versus "ARMA on differenced data" gives different prediction interval

I have seasonal time series (with frequency of 30). I am fitting ARIMA models using R library forecast. My first ARIMA model would be (1,0,1)(1,1,0)[30] with ...
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2answers
208 views

Prediction interval for single future response

I know the following results: $\frac{RSS}{\sigma^{2}} \sim \chi^{2}_{n-r}$ where $r = rank(X)$ and $k$ is the degrees of freedom. Then, for any $c \in \mathbb{R^{p}} $, and when X has full rank, i.e. ...
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1answer
98 views

When calculating a meta-analytic prediction interval is it appropriate to report the back-transformed mean of that distribution?

The Problem I have been working on an epidemiological meta-analysis of prevalence values, measured as proportions but analyzed in logit-space. The conditions I study are quite rare (<5%) so all ...
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1answer
46 views

simple linear regression (predictor)

Consider a simple linear regression model $Y = X\beta + \epsilon$ $ \ $. Let $Y_O$ be the least square predictor of $Y$ at $X = x_o$ , based on $n$ observations $ (X_i ,Y_i) $and $\overline X$ = ...
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4k views

Which formula does the forecast package in R use to calculate variance/ standard error for prediction intervals?

I am trying to compare a manual computation for the prediction interval for a forecasted value (one step ahead, at 95% confidence) on this data set, to the given prediction interval from R's forecast ...
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1answer
5k views

Linear regression : from parameters with standard error to prediction interval

I have the slope and intercept of my model as well as their respective standard error but not the data from which it was estimated (I retrieved it from the literature). I would like to plot the ...
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105 views

Standard error of the mean of several values of y predicted from a multiple regression

I have a multiple regression equation that predicts a trait of interest ($y$) from two measured traits ($x_1$ and $x_2$). I want to measure $x_1$ and $x_2$ for $k$ individuals of a certain plant ...

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