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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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Tradeoff between Prediction Interval Accuracy & Mean Squared Error

My goal is to quantify the prediction uncertainty in a model regressing climate covariates against GDP. I start with a model with temperature as a third degree polynomial, country fixed effects ($\...
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How to generate 95% prediction interval around predictions from ML model?

I have predictions from an ML model and would like to generate 95% prediction intervals around each prediction generated from the model such that I can claim that these are the plausible range of ...
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Using Bootstrapped Residuals to Estimate Time Series Prediction Intervals

I am working with a very simple forecasting "model" which is not a standard statistical model. I am trying to use the methodology described in Hyndman's textbook under the section "...
Justin Furlotte's user avatar
11 votes
1 answer
180 views

Prediction bands for weighted linear regression

For a linear regression of $x_i, y_i,$ we know that the confidence intervals are: $$\hat{y} \pm t \cdot s \sqrt{ \frac{1}{n} + \frac{(x - \bar{x})^2}{\sum (x_i - \bar{x})^2} }$$ and prediction bands: $...
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Confidence int. expands much more rapidly than prediction int. as we depart from $\bar X$

In this post we see a regression plot (pasted below) with a confidence interval (CI) and a prediction interval (PI). The CI is expanding fairly noticeably as we get further away from the mean of $X$ (...
Richard Hardy's user avatar
1 vote
1 answer
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Difficulty simulating prediction interval for quasipoisson GLM in R

I fit a quasi-poisson model (with pretty severe over-dispersion, as I understand it) summarized here: I'd now like to obtain fitted values and 95% prediction intervals. After some searching, I came ...
josephfsexton's user avatar
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Why Do AR-NN Models Have Tighter Confidence Intervals Compared to Linear AR Models?

I have conducted a forecast for the following data series using different autoregressive models: Intercept-only, AR1, AR2, ARIMA BIC, ARIMA AIC, and AR-NN. Using the point forecasts, the AR1 model is ...
george1994's user avatar
1 vote
1 answer
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How do I calculate estimated variance for an ensemble forecast?

I have several (n) different forecasts of comparable quality for a variable, based on the same data but using wildly different statistical models. For each, I have generated an estimate for m periods ...
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Prediction Intervals for forecasts vs Probabilistic Forecasting

In the context of time series forecasting, there a relationship between these 2? Are prediction intervals are type of probabilistic forecasting?
a12345's user avatar
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Why are the prediction intervals for my DNN regression model horizontal lines?

I am working on developing prediction intervals for deep reinforcement learning. Therefore, I am following the instructions given over here. I ran a small example using a simple deep-learning model to ...
desert_ranger's user avatar
6 votes
1 answer
174 views

Gaussian Process: confidence interval vs prediction interval vs credible interval

Let a distribution over functions be described by a Gaussian Process (GP) prior, following the notation of Rasmussen and Williams: $$ f(\mathbf{x})\sim\mathcal{GP}(m(\mathbf{x}), k(\mathbf{x},\mathbf{...
abc's user avatar
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3 votes
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How do I develop prediction intervals for Reinforcement Learning?

I recently learned about the concept of prediction intervals (for regression) and I would like to apply them to my Deep Reinforcement Learning algorithm. I am working with a Model-Free RL algorithm ...
desert_ranger's user avatar
1 vote
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Prediction vs confidence intervals using random forest / an ensemble of estimators

Given a random forest (or any other ensemble) where each of the $i=1..n$ trees/base estimators is trained by minimizing the mean squared error, then each tree/base estimator prediction $\hat{Y}_i(x) =...
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Defining Prediction Interval (exercise 10 from the chapter 13 of All of Statistics)

I am struggling with the exercise 10 on the prediction interval from the Wassermann's "All of Statistics" book. In a) the aim is to show that $$ P(-2 < N(0, 1+\frac{\sigma^2}{s^2}) < ...
Jedrek369's user avatar
1 vote
2 answers
94 views

Interpretation of posterior predictive distributions

QUESTION UPDATE due to the comments I have received so far. The data, the example and the results below are fictitious, as I am interested with the correct interpretation of these results. Suppose I ...
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Point-level prediction intervals in LightGBM models

I would like to compute prediction intervals for LightGBM at the sample level. In other words, given a certain row to be classified (supervised classification, not regression), what is the upper bound ...
Tiago Melo's user avatar
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ETS Confidence Intervals in R are several orders of magnitude larger than the time series itself?

I am forecasting a time series with confidence intervals using the ets model in R. Here is the time series: Running the following R code: ...
Justin Furlotte's user avatar
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Confidence and prediciton intervals for power law fit

I would like to determine confidence intervals and prediction intervals for a noisy dataset that follows a power law distribution. I have a dataset that (to my eye) follows power law behavior in the ...
Robert Zinke's user avatar
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19 views

Potential evaluation based on the coherence of predicted value with actual data

I have the following data over time: that means data collected for a single variable like CPU usage in lowest, highest, and average mode over time every 5 mins (data granularity = 5mins) like the ...
Mario's user avatar
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1 vote
1 answer
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What is the distribution of the model prediction and the expectation of the model prediction in linear regression?

What is the distribution of $E[Y|X]$ (=$X\hat{\beta}$) and $X\hat{\beta} + \epsilon$ in a multivariate linear regression There are several places this question has been answered implicitly or ...
figs_and_nuts's user avatar
1 vote
1 answer
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Confidence box for coefficients of linear regression?

I am learning linear regression and I am trying to create a visualisation. Say I want to estimate a power model $y=ax^b$ using linear regression. I take the logarithm to get $$\ln(y)=\ln(a)+b\ln(x)$$ ...
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3 votes
1 answer
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Forecasting excess mortality with ARIMA model

I am using the forecast package by Prof Hyndman, and have had success fitting ARIMA models to excess mortality (from the COVID-19 pandemic) data. I am currently trying to produce plots for cumulative ...
Jina A.'s user avatar
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3 votes
1 answer
55 views

Prediction Intervals and Alternatives to NHST for testing forecast accuracy between models

Here Rob Hyndman says In the predictive approach to statistics (McLean, 2000), problems of statistical analysis are viewed as prediction problems, and the central theme is a statistical (probability) ...
pandashelp's user avatar
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Prediction interval as per probability

I am practicing the regression problem using the sci-kit learn dataset. The dataset is about housing prices. When we use a regression model, it predicts a number. Based on the predicted value and ...
Bad Coder's user avatar
2 votes
1 answer
96 views

Evaluate upper bound prediction results using classic error calculation instead of PI metrics

I have the following data over time: that means data collected for a single variable like CPU usage in lowest, highest, and average mode over time every 5 mins (data granularity = 5mins) like the ...
Mario's user avatar
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0 votes
0 answers
31 views

Inference for Binomial proportion with estimated p but unknown N

Let's say I own a bakery that, among other desserts, sells one really tasty chocolate cake. It's so good that I've estimated that I've estimated 80% of my daily customers will buy a piece of cake, ...
stharms's user avatar
1 vote
0 answers
28 views

Prediction Interval Construction

At my organization, we use a deterministic formula mid-month to predict an end-of-month value. We have some data on the historical performance of this prediction. We know the value of the average ...
Dan's user avatar
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1 vote
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40 views

Compare two classifier performances by prediction interval and probability coverage

Following a previously asked questions on prediction intervals for a logistic regression classifier, I'm currently experiencing a conundrum. I want to test a procedure to reverse-engineer the ...
D.K.'s user avatar
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4 votes
1 answer
91 views

OLS Forecasting Intervals

currently studying for my econometrics exam and struggling to understand the difference between these two forecasting intervals. xf are new observations added to the sample. Could someone please ...
Quack's user avatar
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1 vote
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70 views

Why are Prediction Intervals (usually) based on the Average Observation?

This is something I have been thinking about for a while - suppose we fit a regression model and then plot the prediction interval for a given variable vs the response: https://strengejacke.github.io/...
Uk rain troll's user avatar
1 vote
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41 views

Which prediction interval to use - meta-regression selected using LOOCV

I have a research paper that conducted a meta-regression using multiple predictor variables in metafor. They did a meta-regression for all combinations of variables and then used LOOCV to select the ...
Aaron Simmons's user avatar
3 votes
1 answer
76 views

Prediction interval for linear regression on seasonal data in R

I am using the following code to perform a generalized linear regression which produces a satisfying prediction for this highly seasonal time series. i am just not very satisfied with the prediction ...
bgp2000's user avatar
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0 answers
33 views

Calculating prediction interval from data available in publication

I have a publication that provides a linear multiple regression equation from a meta-analysis. LOOCV was used to select the explanatory variables included in a final model from all possible models. A ...
Aaron Simmons's user avatar
0 votes
0 answers
27 views

Prediction Interval formula for WLS regression

I have been unable to find a non-matrix notation formula to calculate prediction interval for a weighted least squares regression. For OLS, I have $$y = \hat y \pm t\times \sqrt{\left(\textrm{MSE}\...
Laurie's user avatar
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0 answers
47 views

Estimating variance by regressing squared residuals

For a linear regression, one way to estimate the range of a prediction for a new observation is to calculate the prediction interval for the new observation. What if, instead, the squared residuals ...
Albeit's user avatar
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0 answers
24 views

Using OLS regression with time-series data and measuring its uncertainty

Imagine I have two cities situated near each other. People have buying patterns in both cities so similar that the number of a company's sales per day is very closely correlated. My goal is to ...
Антон Бугаев's user avatar
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0 answers
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Bayesian inference on an interval probability

I am an engineering student and grappling with some statistical concepts for my research study. I would like to get some suggestions on how to tackle this problem properly. Problem description (see ...
ian's user avatar
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2 votes
0 answers
48 views

How to elicit prediction intervals from clients?

When I prepare probabilistic forecasts I am often left with a choice of what percentage highest-density region to choose for prediction intervals for clients. This matters for reporting uncertainty to ...
Galen's user avatar
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0 votes
0 answers
39 views

How to find prediction interval or visualize q-q plot for log pearson type III distribution

In flood analysis, return period and streamflow values are estimated using log person type III distribution. And we use different libraries to do that, but I can't find how to plot the prediction ...
Atreyagaurav's user avatar
1 vote
0 answers
30 views

Needing help with sample size calculation [closed]

I am doing a doctoral thesis in which I will try to use a standardized protocol to detect children with neurodevelopmental deviations in the general population (meaning children who do not have any of ...
Beky Bekic's user avatar
1 vote
1 answer
143 views

How to understand this coefficient in a linear regression confidence interval?

I'm working on a situation (with computations made by someone not involved anymore), where we have a linear regression and a confidence interval (of shape given in Shape of confidence interval for ...
Basj's user avatar
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0 answers
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How can I determine the potential intersection point of two gaussian time series predictions?

Sorry if some of my terminology is off, I hope I can make the problem clear. I have two (independent) time series on the same plane, one trending slightly upwards and one slightly downwards, towards ...
Mick's user avatar
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1 vote
1 answer
92 views

Forecast monthly mean from daily time series using latest forecast package syntax

I am trying to forecast the mean of a month of daily time series data. I need to forecast the mean of the current month (meaning we have partial data) as well as the next month(s) (meaning I need to ...
Adhi R.'s user avatar
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3 votes
1 answer
98 views

Prediction intervals and bias-variance tradeoff

I was looking for literature which connects prediction intervals with the bias-variance trade-off. Obviously both concepts deal with describing a mean squared deviation: the bias variance tradeoff ...
Ggjj11's user avatar
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0 votes
1 answer
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Prediction Interval for back-calculation when observation has variance

Given an existing regression curve, how do I properly account for the known variance of the dependent variable when back-calculating for the (nominally) independent variable? If I had an observation $...
azabell's user avatar
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1 vote
1 answer
53 views

Prediction intervals practical use cases in time series

i've been encountering a lot prediction intervals in regression and time series analysis to evaluate uncertainty about predictions , i'm using it in my time series forecasts , and i wanna know ...
John mcmillan's user avatar
0 votes
1 answer
131 views

Interpretation of prediction intervals in a random-effects meta-analysis when tau^2 is 0

I'm reading a meta-analysis that compared the risk of an adverse outcome in the intervention and control group. The meta-analysis yielded a summary effect size (risk difference) of +3.9%, with a 95% ...
Clueless's user avatar
0 votes
0 answers
39 views

Calculate non linear regression (nls()) prediction interval without a library

I wouldlike to know how to calculate a prediction interval manually, without using a library. Ultimate goal is to write some formula in a spreadsheet based on the model params that would let me ...
Doug Fir's user avatar
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1 vote
1 answer
153 views

Prediction Interval when independent variable has variance

Given an existing regression curve, how do I properly account for the known variance I have in some new value of X? If I had an observation $x_{new} = 700$ with a variance $\sigma_x^2 = 150$ then how ...
azabell's user avatar
  • 21
4 votes
1 answer
286 views

In Beta Regression we obtain predictions of the mean response, do we therefore assume that the response is B(mu, var) around those predictions?

The title question here is a bit awkward because I'm really asking if this illustration I've drawn is true: Suppose we have a Beta Regression of one predictor, X, which is used to model both the ...
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