# Questions tagged [confidence-interval]

A confidence interval is an interval that covers an unknown parameter with $(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.

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### Penalized spline confidence intervals based on cluster-sandwich VCV

This is my first post here, but I've benefited a lot from this forum's results popping up in google search results. I've been teaching myself semi-parametric regression using penalized splines. ...
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### Confidence Intervals for AUC using cross-validation

I am analyzing the performance of a predictive model with the AUC, area under the ROC curve. I repeat several times cross-validation, and I have different estimations of the AUC in each folder. For ...
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### Computing a bootstrap confidence interval for the prediction error with the percentile and the BCa method

I have two related questions regarding the computation of a non-parametric bootstrap confidence interval for the prediction error. Setting: I have a sample S from a data population P and a learner L, ...
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### Calculating standard deviation from log-normal distribution confidence intervals

I have the results of a meta-analysis of 10 studies that reports a combined random effects odds ratio (computed using Woolf's method) and 95% confidence interval of an event happening in one group ...
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### Efficient nonparametric estimation of confidence intervals and p-values for nonlinear regression

I'm estimating parameters for a complex, "implicit" nonlinear model $f(\mathbf{x}, \boldsymbol{\theta})$. It's "implicit" in the sense that I don't have an explicit formula for $f$: its value is the ...
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### Contours containing a given fraction of $(x,y)$ points

I often need make $(x,y)$ scatter plots that have many ($>10^5$) points. I've experimented with different ways of representing this many points that capture the distribution while getting around ...
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### Comparing coefficients in multilevel models

Is it meaningful to compare the coefficients of two different predictors in multilevel model when the two are at different levels? Specifically I have two variables which measure the same construct ...
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### Using Fieller's theorem to calculate the confidence interval of a ratio (paired measurements)

If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio? An answer that was given to me, mentions ...
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### Why does uncertainty of the autocorrelation coefficient increase as lag increases?

The Python module statsmodels contains functions for ACF and PACF. Below is an example from the docs with a plot that shows the (zero-centered) confidence ...
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### How to construct confidence limits based on small stratified samples of finite populations?

Imagine a business wishes to audit its transactions. It has a database summarizing the transactions, which constitute a sampling frame for the population. It would be time-consuming and expensive to ...
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### Confidence interval for a linear combination of $\mu$ and $\sigma$

Given $n$ independent observations $X_1,X_2,\ldots X_n\sim\mathcal{N}(\mu,\sigma^2)$, where both the variance and the mean are unknown. How can I write down a confidence interval for $\mu+c\sigma$, ...
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### Calculating and plotting confidence interval for Theil-Sen estimator

I'm using Wilcox's R functions (specifically, regplot) to plot a Theil-Sen estimator with a single predictor. However, regplot ...
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### Difference between pointwise and uniform confidence sets

According to Wasserman's All of Nonparametric Statistics p.6, let $\mathfrak{F}$ be a set of distribution functions $F$ and $\theta$ some quantity of interest. A uniform asymptotic confidence set $C_n$...
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### Confidence Intervals for the Parameters of a Logistic Growth Curve

I'm using the growthcurver library to estimate the parameters from some bacterial growth curves. It fits a logistic equation of the following form: This returns ...
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### BCA bootstrap intuition

The papers below claims that BCa bootstrap improves bootstrap estimate accuracy over standard quantile bootstrapping, I think by adjusting for the underlying distribution's skew and bias. I am looking ...
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### Standard Error of the cumulative value for time series

I have two time series, as in the picture below. The data was gathered experimentally. A practical example could be a measured mass flow rate, where I measure the mass flow rate over a certain time ...
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### Has the reproducibility crisis affected confidence intervals as well?

The reproducibility crisis has given many pause over the value (?) of $p$-values to measure the relevance of statistical findings. Given the interpretation of a $p$-value and some knowledge of ...
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### Confidence interval for the restricted mean in survival analysis

What is the recommended way of calculating confidence intervals for the restricted mean in survival analysis? Here are some example data, taken from the paper Chris Barker (2009), The Mean, Median, ...
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### How to form a confidence band around the trend fitted from time series data

I have a time series data set. I can decompose it and get the trend but I would like to put confidence ranges around the trend (past) not the forecast-ed component. The decompose function also doesn'...
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### Error in estimation with continuous data

Is there a way to correlate error in a fit (MSD - mean squared displacement) to the error of the a calculation performed with the parameters associated with the fit? My specific problem is dealing ...
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### Confidence Interval for least squares estimator

There was a paper by Yasin-Abbasi-Yadkori https://arxiv.org/pdf/1102.2670.pdf titled Online Least Squares Estimation with Self-Normalized Processes. I am trying to give a brief context before asking ...
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### Implications of Different Bootstrap Procedures for Estimating Difference in Means

I'm having trouble understanding the difference between two bootstrap procedures to evaluate the difference in means between two samples. As an example, consider the following scenario: My goal is to ...
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### Predictive Accuracy of a Survival Model using Concordance

Is there a preferred approach for evaluating the predictive power of a survival regression model (e.g., Weibull Accelerated Failure Time)? The metric of choice, for now, is concordance or c-index. I'm ...
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### Why is a confidence ellipse based on multivariate-t tighter than one base on multivariate norm (R)

I want to draw a 95% confidence ellipse around my bivariate data. Using ggplot2::stat_ellipse() with type="t" (for a bivariate-t ...
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### Prediction intervals for generalized least squares model with heteroscedastic errors

I wanted to model some data with heteroscedastic errors using a gls model of the form ...
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### Confidence Interval vs Credible Interval for the Variance

I understand the conceptual difference between confidence and credible intervals. But I have difficulties applying these concepts to my application. I would like to know the concrete difference ...
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### Is it possible to produce a full confidence interval around a line using the Theil-Sen slope?

The numpy library will return the Theil-Sen slope and intercept from a set of data. It also provides a confidence interval on the slope. Is it possible to use this confidence interval along with the ...
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### What's the shape of confidence interval for linear regression estimated through TLS (total least squares)?

So, we know the shape of confidence intervals for vanilla linear regression estimated through OLS (ordinary least squares): Shape of confidence interval for predicted values in linear regression. In ...
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