A prediction interval is an interval that covers the future (or otherwise unknown) value of a random variable with some prespecified probability.

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what is the estimated variance of predictions from mixed model?

I have fitted the following lmer model (assume it is "correct") with lme4: Y ~ X1 + X2 + X3 + (1 | year) + (1 | site) + (1 | site:year) where X1-X3 are ...
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18 views

Confidence and Prediction Intervals for Multiple Linear Regression Model

I am looking for a derivation of confidence and prediction intervals for a multiple linear regression model. I have seen that for a given vector of predictors $(x^*)$ and $X$ denoting the design ...
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1answer
62 views

Fixed Prediction Interval

I want to place a Multiple Regression model into a production system and use the Prediction Interval as a threshold for anomalies. I've seen how I can calculate the Prediction Interval two ways: $$...
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19 views

Robust estimation of multivariate reference bands

I have a subjectivly healthy population of approx 1200 individuals with three measurements on the continous scale, we can call them y1, y2 and y3. All of these are strongly related to age in a non-...
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33 views

Identify outlier usage intervals in time-series data

I want to find outliers in power consumption in real-time, at hourly rate, i.e., at the end of the hour, I should say whether power consumption in current hour was outlier/anomalous or not. Approach: ...
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1answer
23 views

Confidence and Prediction Intervals and Cross-Validation

So suppose, I have 5000 points of data. I hold out 1000 for validation testing, and conduct simple linear regression on the first 4000 points. How can I determine if the linear model: y = a + bx + e,...
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15 views

Prediction intervals for Model II regression RMA

I'm using the lmodel2 package in R in order fit a linear regression that takes into account the measurement errors in both x and y. I'd like to plot the prediction interval as well. For OLS, the ...
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13 views

Tolerance interval vs Prediction interval, which one is wider?

Let say we have a 95% prediction interval, versus 95%/99% tolerance interval, which one is wider? A. PI always wider than TI B. TI always wider than PI C. Depends on sample you get Thanks!
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14 views

Topics needed to learn to for predicting future of a data set?

I am planning to work this summer by writing a code which will eventually become an app, that has the ability to predict what the prices will be atleast 6 month ahead of time. I have a data set of the ...
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1answer
36 views

Prediction interval, forecast error for a function of a forecast

I have two variables $X$ and $Y$. For each variable I created a forecasting model (using time series) and estimated $X_{t+1}$ and $Y_{t+1}$ and the prediction interval and the error for each. I have ...
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20 views

Prediction interval for multi step forecast

I am using the "drift method" to make a multi-step forecast. The formula for the forecast is $y_T = \frac{h}{T-1} \sum (y_t - y_{t-1})$, where $h$ is the forecast horizon and $y_T$ is the last ...
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19 views

How to obtain the equation of a predictive interval around the regression line in R? [duplicate]

I have a some data set on which I fit a linear regression model using the lm function in R. I can also visually obtain the prediction Interval around that regression line using predict. My question is ...
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22 views

Forecasting intervals linear extrapolation with time as independent variable

I want to do a forecast with linear extrapolation, and I want to make prediction intervals with it. I see a lot of prediction interval explanations, but I don't see how to use this for my kind of data....
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41 views

Confidence/prediction intervals for total least squares regression

I am learning the ropes of total least squares regression and I found this thread How to perform orthogonal regression (total least squares) via PCA? where the answer by @amoeba, together with some R ...
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1answer
90 views

Forecasting Poisson, accuracy and prediction intervals

I'm trying to forecast Poisson data, divided in groups, of 1-26 months of data, depending on the group. Of the pooled data ...
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18 views

Prediction Intervals when the Noise/Error is not Uniformly Normally Distributed?

Suppose I've done a linear regression, I've got $\hat{y}=Ax+b$ (where $x$ is probably a vector and $y$ may be a real or a vector). So our actual assumption is the model $y=Ax+b+e$, where $e$ is ...
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8 views

Confidence Intervals for Outputs of Regression? [duplicate]

Suppose I have some reasonably sized dataset and I do linear regression on it, so now I have a model, say $\hat{y}=Ax+b$, where $y$ is real (or perhaps a vector, but let's say real for now), $x$ (my ...
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48 views

large Bayesian prediction uncertainty for gam (mgcv) logistic regression

I'm running across an interesting case where the estimated uncertainty based on the Bayesian simulation approach outlined in Simon Wood's book (Generalized Additive Models (2004), section 4.8; as ...
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21 views

Probability distribution over predicted probabilities in multinomial logistics regression

I am currently wondering (and cannot get my head around this) how to get a probability distribution (or something similar to a prediction interval in OLS) for the predicted probabilities of a ...
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69 views

Non linear time series analysis using complex systems theory

I have been working on non linear time series analysis using complex systems theory. Currently I am using recurrence plots to analyze recurrences and also performing recurrence quantification analysis ...
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16 views

Prediction interval of 3d data

I have a data set consisting of 3 columns: $x$, $y$ and $z$. I am analyzing the influence of $x$ and $y$ on $z$: I have managed to find a surface fit of the form $z=10^{a+bx+cx^2+d\log{y}}$ in ...
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6 views

Distibution of the pdf as a random variable when evaluated at samples generated from itself

Let $x_i \sim p$ for some probability density function $p$ with respect to Lebesgue measure on $\mathbb{R}$. Then each of $p(x_i)$ is a random variable taking values in some interval $[0,c]$ from some ...
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69 views

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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3answers
156 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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51 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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30 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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27 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 y0....
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98 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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66 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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28 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
70 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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10 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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34 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
73 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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75 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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29 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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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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60 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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63 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
71 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
240 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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32 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
36 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
232 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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37 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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1answer
87 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
50 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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160 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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82 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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23 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, ...