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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Target binning in regression
I would like to find a predictive density for target variable via multi-class classification. Suppose we are given a set of features $\mathbf X$ and continuous target $\mathbf y$. Replace each $y$ ...
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Which error metric should I use for summed estimates?
I built an ensemble regression model (Random Forest + KNN + SVM) to predict biomass based on environmental conditions (biomass is strictly positive but continuous).
I now would like to use this model ...
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Confidence interval for (unobserved) sample mean
Suppose I take two samples, $a$ and $b$, from a population (or super population) but that I only observe $b$. However, I want to construct a confidence interval for $\bar{a}$, the average of the ...
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Quantifying uncertainty with RVM
I am reading about relevance vector machines as a potential methodology to address a regression problem with prediction of a continuous variable, where I more specifically want to work with a model ...
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How to compute a prediction interval from ordinary least squares regression output alone?
This question has been haunting me for a long time,
When I'm given an R output of linear regression, and asked to calculate 95% prediction interval, I feel there's something missing.
In this output, ...
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"Prediction interval" for a slope of a model fitted to new data
Problem statement:
I am using a simple linear regression with outcome $y$ and single predictor $x$ of the form:
$$
y_i \sim N(\mu_i, \sigma) \\
\mu_i = \beta_0 + \beta_1x_i
$$
I assume fitting $\...
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Logistic Regression - Intervals on Predicted Number of Cases
We have developed a logistic regression model for predicting the attendance at an event for registrants. We can use this model to predict the probability of attendance at future events for new ...
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Prediction interval for continuous positive data including zeros
I am trying to figure out given a set of positive continuous numbers (including zeros) what would be the most appropriate way to calculate a prediction interval, or a normal range, i.e. a range in ...
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Why is the prediction interval going way beyond the $100\%$ threshold? [closed]
Prediction interval in my forecasting is too high. It goes beyond the threshold of 100% of forecasting share of health spending as a percentage of total. This is the relevant data and the associated ...
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Convergent and Divergent Prediction Intervals in Time series models
My question is similar to this one Whether increasing the sample size influences the prediction interval? and it's also related with Rob Hyndman - Forecasting: Principles and Practice (2nd Edition), ...
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Prediction intervals for simple/baseline forecasts
I'm reading this, and I don't understand how the prediction intervals are calculated for the baseline forecast methods. I agree that we can estimate the SD of the sample from the known residuals
$$ \...
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How to calculate the forecast interval for time series prediction obtained by doing seasonal differencing before fitting arima
Here is the link of my previous question. How to forecast a time series which is generated by accumulating data of every five minutes and reset to 0 by the end of the day
I am working with a seasonal ...
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Prediction intervals in the case of changing variance
I derive a point estimate given value $x_0$ using an estimated linear regression as follows:
$$\hat{y_0} = x_0^T\hat{\beta}.$$
I know that a prediction interval for a given value $x_0$: $$\hat{y}_0\pm ...
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How are the confidence intervals calculated in the hw() function the the forecast package in R?
I have been using the hw() function from the forecast package to predict some timeseries objects. I've noticed for some of my timeseries predictions, the prediction interval sizes are almost the exact ...
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Few question on prediction intervals in forecasting
When can we construct prediction interval and we can't: What factor govern this?
One of the way to constrained forecast to an interval is using a log transformation.
For ex: if we want forecast to be ...
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How to use predict() function to compute confidence and prediction intervals other than 95%? [closed]
I want to compute a 90% confidence interval for a mean response at a specific x value, and a 90% prediction interval for the individual response at that same X value. The way I know how to do this in ...
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Probabilistic machine learning models: parameter uncertainty
Consider models such as DeepAR, ngboost and other frameworks to the general problem of predicting the parameters of some parametric distribution with some black-box function, call it f(X). The ...
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Election Predict Using Machine Learning
I want to predict the election results in a country. Firstly I want to check and specify probabilty. For doing this, I intend to use the election results of the past years and the estimation results ...
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How can I best get a prediction interval for future group or nested group means with LMM (lme4)?
I am building a linear mixed model of an experimental data set. The data can be grouped
into individual experiments, and further each experiment consists of clusters
within which a sample is observed ...
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How to represent the interval or uncertainty on regression predictions in an 'experimental vs predicted' plot?
Using an example similar to the one from R predict, simulate some independent variable ($x$) data, map them to an observed ...
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Get a range of values (val_1 to val_2) instead of one value in linear regression
So, the idea is that I use linear regression and I get an equation y = a * x + b. So when I give a value x I get a predicted ...
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Prediction interval for sum of weighted bernoulli random variables with estimated probability p
Suppose $X_1,...,X_n $ are independent bernoulli random variables with success parameter $p$, i.e. the common pmf is $f(x)=p^x (1-p) ^{1-x}$ for $x=1$ or $x=0$. I am interested in finding a prediction ...
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Why is my statistical prediction interval not as I'd expect? (statsmodels, python)
I am using the statsmodels python package to perform multivariate linear regression. I want to produce 80% prediction interval bands as part of my result.
The statsmodels package can produce ...
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Unexplainable cyclical patterns on prediction intervals for time-series forecasting using Extreme Gradient Boosting regressor
I am following the documentation of skforecast to make time-series forecasting using the Extreme Gradient Boosting regressor (i.e., ...
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What is the Formula for Prediction Interval in Multivariate Case? [duplicate]
I am using linear model to do prediction, and I would like to calculate my prediction's prediction interval, which, when there is only one predictor, is
However, my model has three predictors. What ...
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What is the Matrix form of the prediction interval for Weighted Least Squares Regression
For ordinary least squares, I know the confidence interval is
$\hat{Y} ± t\cdot\sqrt{\hat{\sigma}^2 * x_{new}(X^{\top}X)^{-1}x_{new}^{\top}}$ and $X$ is the design matrix, n is the number of ...
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Using Confidence Intervals for finding confidence of forecasting model
My question is quite a general one.
Can I use the width of the confidence interval (let's say a 95% confidence interval) to find out how confident my model is while doing time series forecasting?
I am ...
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How much can I forecast in the future?
Given some time series data and a forecasting model (maybe conventional models like ARIMA, Prophet, etc, or deep-learning-based models like NBEATS, Transformers, etc), I want to find out how much in ...
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Is it possible to calculate prediction interval without info on the predictor x?
I can see from here that prediction interval for a new response Y (setting is simple linear regression) is
However I've read here that
Apparently, no calculation related to x is needed according to ...
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Prediction Intervals for a Two-Part Model?
I have fit a two-part model, where the first part is using a logistic regression to model the probability of seeing Y, and the second part is using a Gamma GLM regression with a log link to model the ...
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One tailed prediction intervals for Multiple Linear regression
After having fit a multiple regression model to my data, I am using it for predicting my dependent variable. I understand how one can predict and compute (using R) two tailed prediction intervals at a ...
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Substraction of predicted values: taking in to account prediction intervals
I'm trying to make a prediction of the number of annual flu hospitalizations.
In order to do so I'm trying to subtract the predicted number of hospitalizations when there is no flu from the predicted ...
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estimation of a yearly prediction interval for monthly data
I have a monthly time series and my objective is to provide my client with the next 12 point forecasts along with a yearly forecast. To obtain the yearly forecast, I simply summed up the 12 points ...
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Bootstrapping (aleatoric and epistemic) risk score uncertainty
I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk
$$r_i = f(x_i; \epsilon_i), \quad 0 \leq r_i \leq 1,$$
where $x_i$ is some ...
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Using remaining useful life predictions to assess model fit with right censored data
I am modelling time to failure of some units. All units are made my the same manufacturer and there are no recorded covariates to distinguish between the units.
This means that the central, $95\%$ say,...
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Prediction interval generalized estimating equations
Because I have time dependent covariates and the full covariate conditional mean assumption (Pepe and Anderson, 1994) does not hold, I have fitted a continuous longitudinal response with generalized ...
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Missing Prediction Intervals by R package autoTS
I'm using autoTS R package to fit automatic time series estimation and prediction to a very very large number of time series.
One of the outputs of the prediction function (my.predictions()) is a 95% ...
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Risk score uncertainty quantification
I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk
$$ r_i = f(x_i, \varepsilon)$$
where $x_i$ is some available information about the ...
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Bootstrapping with quantiles of data instead of SD*z?
I have recently been bootstrapping the confidence intervals of a neural network model estimated to data.
I execute the following psudo-code, which seems similar to previous bootstraps I have done:
...
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Intuition for confidence intervals vs prediction intervals for linear regression
I am having a bit of trouble understanding the difference between a confidence and prediction interval in the context of linear regression, and in what scenario we would use either of them. I've posed ...
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Is there a way to calculate prediction intervals for decision tree or extra trees regression models?
I only see examples of prediction intervals for random forest and linear regressions but do not see much about ensemble models. I'm not sure if my understanding about prediction intervals is correct.
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Distribution-free prediction intervals in linear regression
I've found some literature on the subject, but it is rather difficult to read. I am wondering if the following simplified method makes sense. My question is what part is correct in this methodology, ...
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How can we call difference between observed values and prediction interval?
As in the topic title. Is it correct to call difference between observed values and prediction intervals a "difference prediction interval"? Or should I go for "O-E prediction interval&...
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Parametric bootstrap *prediction* interval with heteroskedasticity and sandwich parameter covariance matrix
The sandwich estimator for OLS regressions where heteroskedasticity is suspected is
$$
var(\hat\beta) = (X'X)^{-1}X'ee'X(X'X)^{-1}
$$
If I want confidence intervals on predictions, I can just take ...
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Prediction interval: but instead, the probability that the next datum is above a fixed threshold?
I've been struggling with this problem, and I think I must be missing some important conceptual step. Imagine we observe $\theta_1 \sim N(\mu, \sigma^2)$, with unknown $\mu$ and known $\sigma^2$ (for ...
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Wide prediction intervals for short time series: how to fix that?
I have very small time series data(24 points) for sales for different-different regions. I need to build Range Forecast (Confidence/Credible Intervals) for sales around it for every region. I tried FB'...
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Confidence interval for the predicted values from normal distribution
Let's say I have some n samples of real values $y_{i}$ and predicted values $\hat{y_{i}}$. The predicted values were calculated from gradient boosting.
The things I know from this gradient boosting ...
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Aggregation of Interval Predictions
Given a montly time series, my objective is to provide my client with the next 12 point forecasts along with a yearly forecast. To obtain the yearly forecast, I simply sum up the 12 points forecasts. ...
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Real future value out of 95% predict interval for ARIMA forecast
When the predicted future value actually materializes, does it matter if it is outside the predict interval?
The value of prediction intervals is that they express the uncertainty in the forecasts. ...
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Getting the confidence interval or some sort of range for predictions from optimizations
I am trying to calculate range for my model predictions after performing optimization and getting values of the optimized parameters.
I am aware that we can get a standard error of the optimized ...
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