# 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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### How to compute confidence interval in ANOVA with repeated measures?

I made a model using repeated measures univariate ANOVA in R. ...
334 views

### Validity of confidence interval for $\rho$ when $X\sim N_3(0,\Sigma)$ with $\Sigma_{ij}=\rho^{|i-j|}$

Suppose $X\sim N_3(0,\Sigma)$, where $\Sigma=\begin{pmatrix}1&\rho&\rho^2\\\rho&1&\rho\\\rho^2&\rho&1\end{pmatrix}$. On the basis of one observation $x=(x_1,x_2,x_3)'$, I have ...
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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. ...
7k views

### 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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### 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 ...
3k views

### 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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### 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 ...
664 views

### 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 ...
4k views

### 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 ...
227 views

### 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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### Generalization of degrees of freedom for t distribution for coefficients after multiple imputation

Donald Rubin has shown that regression coefficient estimates have fatter tails after multiple imputation and has provided a formula for the degrees of freedom to use as a t-distribution approximation ...
872 views

### 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 ...
297 views

### 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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### 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 ...
664 views

### 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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### 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 ...
201 views

### Linear Regression - Confidence interval for mean response vs prediction interval

I understand the concept of a confidence interval for the mean response (fitted line) for simple linear regression $y$ = $\beta_{0}$+$\beta_{1}$$X_{i}$. It is that taken over many times, with 95% ...
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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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### Simulating Monte Carlo with different standard deviations and interval confidence

I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties. From what I understand Monte Carlo accepts random numbers of each input variable of ...
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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'...
750 views

### 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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### Stop collecting data when our confidence interval is sufficiently narrow?

I am running an experiment that is unpleasant and time-consuming, so I want to minimize the number of times I have to do it. I have done a sample size calculation to determine that I need $100$ ...
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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 ...
913 views

### 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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### Calculating a confidence interval for a weighted sample

In a nutshell, I'd like to compute a confidence interval for some weighted sample day where the final value I'm seeking is a sum of different weighted samples. Illustrated here with a toy example set ...
807 views

### Prediction intervals for HTS forecasting

So I have a lot of time series with a hierarchical structure, and need to produce forecast for each base series and its aggregates by the hierarchical structure. I have decided to produce forecast ...
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### Election fraud detection: the statistics of Quick Count

I’m reading the book Quick Count and Election Observation (chapter 5). I’m interested in understanding the statistics used in Quick Counts. Quick Counts is a methodology for verifying official ...
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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 interval for proportions

I have some data like this: id pop var 1 593 51 2 592 31 3 346 20 4 1214 70 5 1063 66 6 1370 71 each ...
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### Binomial mid-p value

I've been under the impression that the mid-$p$ values generally control the Type I error, and consequently confidence intervals based on mid-$p$ values control the coverage. However I have checked ...
288 views

### Confidence interval for the biggest difference between means

I have a number of samples $X_1,\ldots,X_n$ from Gaussian distributions centered at $\mu_1,\ldots,\mu_n$ respectively. I need to construct a confidence interval for the biggest difference between ...
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### Confidence interval about a multivariate normal probability

From a given sample $x_i \underset{\mathrm{iid}}{\sim} {\cal N}(\mu, \sigma^2)$ it is possible to get a confidence interval about the probability $\Pr(x_i \geq a)$ for any number $a$, by "inverting" ...
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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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### Is there a way to add sample confidence interval to regression?

I have the following situation. We want to measure if animal weight has an influence on their home range size (measured as an area). However, there is inherent error measuring an animal home range. ...
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### How to explain the difference between confidence and credible interval?

The key difference between Bayesian statistical inference and frequentist statistical methods concerns the nature of the unknown parameters that you are trying to estimate. In the frequentist ...
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### Does distance from the decision boundary suggest higher confidence that the class prediction is correct using SVM?

Does further distance from the decision boundary threshold suggest higher confidence that the class prediction is correct when using SVM with probability estimates enabled? This is not a question ...
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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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### Density estimation for big feature space

let's say I have a data set with 100 features and a couple million of samples. Whenever I get a new sample, I would like to estimate how many samples would have been around it in the original set (let'...
289 views

### Calculating confidence interval for ratio of sums

I have a problem where I need to calculate a confidence interval for a ratio of two sums. I have code below which calculates this stat using a bootstrapping method, but I would much prefer a closed ...
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### A question on Bayesian credible interval vs frequentist confidence interval

The difference of Bayesian credible interval (BCI) and the frequentist confidence interval (FCI) is well explained with a nice example in this answer. Here is my own summary of the situation in the ...
222 views

### Meta-analysis using bootstrapped confidence intervals (non-normal data)

I have the results of two studies (my own and a previous study). I want to perform a small meta-analysis to obtain a better estimate of the effect size. For the two studies I have the means and 95% ...
288 views

### inverse.predict chemcal package

I have noticed that the inverse.predict function (chemCal package) does not take into account all the degrees of freedom of the ...
2k views

### Confidence Intervals with Propagation of Uncertainty

Lets say I'm trying to make a measurement of the area, $A$ of an object imaged in a large number of noisy gray-scale image, and I want to include uncertainty quantification to some confidence interval,...
865 views

### 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 ...
310 views

### 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 ...