Intervals which cover the (future or otherwise unknown) value of some random variable with some prespecified probability. See https://en.wikipedia.org/wiki/Prediction_interval

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Combine multiple independent variables into one variable in a GLM/GAM/GAMLSS model

In the R package gamlss there is a function centiles that according to the documentation is ...
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67 views

Forecast accuracy metric that involves prediction intervals

I'm in the process of generating a time series forecast for a company's product revenue and am looking for some way to show accuracy over time - e.g. after say 6 months they want to see how the actual ...
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13 views

Should I use 'sample standard deviation' for 'prediction intervals' and 'standard error of the mean' for 'confidence intervals'?

I just want to make sure I am getting this right. When I am concerned about the "result" of any particular new datapoint I should use prediction intervals not confidence intervals. When I am concerned ...
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22 views

Distribution of the estimate inside the prediction interval while performing linear regression

I would like to clarify how to interpret the prediction interval (PI) that we get while performing linear regression. I realize that PI provides us the uncertainty in our estimate of y when X = x, ...
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3 views

merTools predictInterval() for model with nested random effect [migrated]

Does predictInterval() from the merTools package not like nested random effects? For example, using the ...
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13 views

confidence score for predicted value using a regression model?

I have trained a regression model which predicts value y = f(x). I need some way to measure confidence that predicted values are true values. Specifically, in runtime, given x0, I have a predicted ...
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1answer
89 views

How can I use bayesian reasoning to explain a Scrum team if they initial estimates were right or wrong and if the project is currently delayed or not?

Imagine a software development team estimates they are going to be able to complete 80 user stories in 5 sprints using Scrum: Sprint 1: 16 stories Sprint 2: 16 stories Sprint 3: 16 stories Sprint ...
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31 views

How to Calculate Standard Error and Prediction Intervals for ARMA Forecasts on Transformed Data?

I have been recently learning about the Box-Jenkins process for ARMA modeling, and I ran into a bit of a wall when it comes to error analysis. In a lot of my data sets, I have to apply a log ...
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17 views

Spline regression with variable variance of residuals

I am running a natural spline regression x vs y, like in figure (there are also some dummy variables but it doesn't matter here). It happens that I have a lot of heteroskedasticity, i.e. mutable ...
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1answer
42 views

Calculating prediction intervals from heteroscedastic data

What is the standard method for generating a 95% predicton interval (not confidence) for a linear regression given heteroscedastic data? Let me be more specific with an example: ...
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4 views

Prediction interval of multi-step investments with varying but known mean and variance

I am constructing forecasts for retail investment portfolios. A portfolio has periodic contributions of varying amount per period, and varying return characteristics over time. The variable of ...
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24 views

Prediction intervals for forecast from aggregated cases

I have data on $N$ individuals that were followed for some time. Variable $Y$ that describes accumulation of some goods by the individuals. For each individual there is some number of records ...
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1answer
55 views

R's lm prediction interval vs simulation

I was trying to simulate the prediction interval for lm model in R, but I found out that my prediction interval is consistently biased. I've attached the code, and a sample figure below. Any idea why? ...
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35 views

How to get prediction interval given non normal data?

I'll start by saying that I have very little background in statistics and that my question title above is probably worded incorrectly. If I need to change the title to more accurately reflect my ...
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0answers
24 views

Calculate the PDF given a list of values and a list of correlated

The question itself is simple; I have a list of event/values and another list of values correlated with the first one. Let's say something like that: ...
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7 views

How many raters do I need to determine reliability of agreement on stimulus classification?

I have a stimulus set comprised of 147 videos, each with one of seven labels (hidden from raters). I want to determine how reliable label assignment is for each stimulus -- that is, I want to be able ...
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49 views

Precision of Prediction Intervals for Multiple Linear Regression

As discussed in 33433, the prediction interval for single linear regression is most precise at the mean of the $x$ values. Does this also hold true for multiple linear regression, that is: the ...
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43 views

How to calculate prediction intervals based on Chebyshev inequality?

I have recently read the article by Gardner (1988) who proposes Chebyshev inequality-based prediction intervals for forecast: suppose we have a model selected on the usual basis of one-step-ahead ...
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1answer
48 views

Gaussian process prediction interval

How can the prediction interval of a Gaussian process be evaluated? I don't know how to estimate this interval though I can find a 95 % confidence interval for the mean line.
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2answers
206 views

Do confidence intervals and prediction intervals shrink to a point for a very large sample size?

My question applies to regression estimates. The formulae for confidence interval: $$ \hat y \pm t_{\alpha/2, n-2} \sqrt{MSE} \sqrt{1/n + \frac{(x-\bar x)^2}{\sum (x_i - \bar x)^2}} $$ and prediction ...
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0answers
25 views

Obtaining uncertainties from an errors-in-variables machine learning algorithm

In my field, every value reported comes with a 1-sigma uncertainty value. I'm using random forest regressors to estimate a value. All of my inputs have 1-sigma uncertainty information with them. ...
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1answer
30 views

Combining prediction intervals

I'm using ML regressors (neural networks and random forests) to predict some numbers. I can put in my inputs and get out a value and its prediction interval. The inputs to my regressors are noisy, ...
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3answers
144 views

Prediction Intervals with Heteroscedasticity

I am using R to perform linear regression. I have seen ways to calculate prediction intervals, but these depend on homoscedastic data. Is there a way to calculate prediction intervals with ...
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33 views

Prediction intervals for levels using a VAR model in second differences

Given a VAR model for the second differences of a vector time series, $\Delta^2 y$, how to obtain the one-step-ahead (and possibly $h$-step-ahead) prediction intervals for the series in levels, $y$? ...
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49 views

how does predicted median go above 95% prediction interval when using GBM with quantile loss function

I was checking out how to create prediction intervals with Gradient boosted regression trees using Scikit-learn. If you set the alpha at .95 or .05, you can get the 95% prediction interval around the ...
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1answer
39 views

How can I calculate the PI of (simple) exponential smoothing?

I would like to calculate the prediction intervals of exponential smoothing. In R there is a function (ses in a forecast package) which calculates the point forecast and also the prediction intervals. ...
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91 views

R: Calculating prediction intervals (95%, seasonal naive and holt winters)

Could somebody explain to me the theory behind how R calculates the 95% prediction intervals for my 12 step ahead forecasts in (1) a seasonal naive model and (2) a Holt-Winters forecast. My code is ...
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68 views

Calculation for variance of slope for linear model in R predict function

I'm looking through the code for the predict.lm function in R, and am confused about one of the calculations. I believe it is the calculation used to determine the ...
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19 views

Confidence band for mean of means

This is sort of a stats theory question, and I can't really convince myself of the correct way to view things: In normal regression, the confidence band (or interval) gives the bounds on the mean, ...
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2answers
307 views

What non-Bayesian methods are there for predictive inference?

In Bayesian inference a predictive distribution for future data is derived by integrating out unknown parameters; integrating over the posterior distribution of those parameters gives a posterior ...
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1answer
42 views

Arbitrary prediction interval with random independent variables

I have a equation with the parameters determined from multiple linear regression: $$ Y = \beta_0 + X_1 \beta_1 + X_2\beta_2 $$ I would like to forecast the distribution of $Y$ numerically, in other ...
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1answer
46 views

Identity of residual distribution, and identification of correct model in multiple categorical linear regression

I am using R for this analysis, and so examples and graphics will be produced in this language. I am willing to provide equivalent examples in similar languages if it will help someone, and am willing ...
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79 views

Should I ignore negative prediction values?

I have the following time series of count data: ...
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67 views

understanding and reporting results from monte-carlo simulation

I apologize upfront if the the question is vague. Basically I have results from monte carlo simulation and I'm trying to understand how to present the results and importantly the "why" part of the ...
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104 views

Prediction intervals for forecasts using spectral analysis

I have circadian data which typically have a period of around 24 hours so using spectral analysis seems appropriate. I've used spectrum resampling which is quite robust to changes in period which ...
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2answers
40 views

Making predictions using a Prediction Interval

I have a group of observations with measured variables: A, B, c and d. I want to predict A using: $f(A)=\beta_0c+ \beta_1d$. I usually get a prediction interval ($PI_\hat{A}$) using bootstrapping. I ...
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38 views

Prediction intervals for kNN regression

I would like compute prediction intervals for predictions made by kNN regression. I can't find any explicit reference to confirm, so my question is - is this approach to computing prediction intervals ...
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22 views

What is the mathematics behind the GAM prediction intervals?

From the R gam function available in the gam and mgcv package there is the option to obtain ...
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1answer
30 views

Testing and validating a limit for experimental data

I have found some similar questions to the one I pose here, but the answers are either over my head, or seem to be slightly off point to what I am trying to accomplish. If it's a true repeat, I ...
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2answers
67 views

How to generate confidence bands for $\hat{Y}$

Suppose I run a linear regression model. I am interested in generating prediction intervals. The predicted values are easy to compute, but how can I compute the standard deviations for each of the ...
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255 views

Empirical Prediction interval for time series forecast based on quantile regression

As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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56 views

Is it possible to get a prediction interval for logistic regression via a latent variable?

carbocation asked how to compute prediction intervals for logistic regression. The answer was that prediction intervals don't make sense for logistic regression because the response variable only ...
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126 views

How does R calculate prediction intervals in the forecast package?

I have a large dataset with different factors that I want to forecast to the future. These forecasts I will then later on use as inputs for a Monte Carlo simulation. My idea would be to use arima ...
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1answer
319 views

R: glm(…,family=poisson) plot confidence and prediction intervals [closed]

I could not find many information on how to plot a confidence interval and a prediction interval for a Poisson regression (for example with glm()). What are some ...
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29 views

Why does the upper prediction interval region gets larger than lower prediction interval when data are transformed?

I present here two examples one with transformed data and the other without any transformation. In the transformed data case, the upper interval gets enormous large, whereas not in the untransformed ...
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101 views

ensemble of three regressors to find pointwise prediction intervals in instance-based online learning setting

Here is my online learning scenario: Data point $x_n$ arrives Response of the data point, $\hat{y}_n$, is predicted. Real response, $y_n$, is obtained Regression algorithm is updated incrementally ...
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142 views

Derivation of prediction interval for simple linear regression

For simple linear regression $y_i = \beta_0 + \beta_1 x_i + e$, how does one derive the prediction interval for some $x$? I thought the prediction error was just the mean square error for regression ...
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93 views

Multiple regression model and prediction/confidence interval for two values of a coefficient

Hi i've been working on this model of house prices based on multiple independent variables. I got the out put out throught gretl. ...
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1answer
78 views

Using predict() in R to predict the y-value for multiple occurrences of the same x-value

If I have a linear model and want to use predict() to predict the mean and confidence interval of multiple ($m$) new observations of a given x-value ($x_h$), how do ...
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80 views

Restricting a set of predictions to a range of values of non-negative numbers

I am not even sure how to even phrase this question so if anyone could help that would be great. I am analyzing facebook activity and I wish to predict a particular activity (comments, for instance). ...