# Questions tagged [confidence-interval]

A confidence interval is an interval that covers an unknown parameter with $100(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.

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### Moving block bootstrap to get CI arou d first derivative of trend

I have a time series and I want to know the rate of change of the nonlinear trend component. To do this I want to take the first derivative of the trend but I need a confidence interval around it. I ...
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### Confidence interval for superiority/inferiority tests

I am looking into superiority/non-inferiority tests and my understanding is that the null hypothesis for a superiority test is $$H_{0}: \epsilon \leq \delta$$ where $\delta \geq 0$ and $\epsilon$ ...
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### confidence interval over point estimate given regression parameters?

In Bayesian analysis, the poster distribution is often sampled when the PDF is not intractable (often). If the samples are of length $n$ then every index in $range(1,n)$ corresponds to a valid sample ...
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### Confidence interval for a normal RV that its std is the mean of a different normal RV

Question: Suppose $X\sim\mathcal{N}(\mu_X,a),Y\sim\mathcal{N}(\mu_Y,b\cdot\mu_X)$ where $a$ and $b$ are known, but $\mu_X$ and $\mu_Y$ are not. What confidence bounds can we give for $\mu_Y$ from one ...
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### Difference between a comparison of independent variables t.test and linear regression model of one category?

The thing is I am trying to obtain confidence intervals of several variables (food, blood chemical analysis...) of patients who are divided in two groups according the intervention. Until now I was ...
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### Confidence intervals around treatment effect in stratified experiment

Suppose you conduct an experiment, where a population is randomized and treatment is given to the treatment group and you are interested in covariates (stratification has been employed) and their ...
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### Estimating Confidence in Feature Rankings from Multiple Experiments with Non-Normal Data

Hello dear Cross Validated Community, I am a new doctoral student in bioinformatics, and I am working on a project involving multiple experiments, each generating a single numerical result for each of ...
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### Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
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### When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
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### Forecasting positive time series with missing values and few observations

I am working on forecasting a positive time series dataset of prices with missing values and only a limited number of observations. Specifically, I have 150 observations, one per week, and I need to ...
1 vote
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### How to calculate and plot a confidence interval for a bivariate normal distribution?

I have a two-dimensional normal distribution (with correlations). I do not have data points, but only the 2D mean and the covariance matrix. I want to draw the 68, 95 and 99% confidence intervals ...
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### Calculation of confidence intervals in linear regression model - normal or student?

I am working with a pretty simple linear regression model, in which I was asked to work with confidence intervals instead of p-values (classic) The thing is I was trying two approaches to get ...
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### Standard error for optimal solution of a convex optimization problem

Suppose I'm given a sample of IID pairs $\{(x_i, y_i)\}_{i=1}^n$ of non-negative numbers from some distribution $\mathcal{D}$ having a finite mean and covariance matrix. Moreover, I'm given a strictly ...
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### Finding a Pivotal quantity

0 I am working on this problem for class, where the setup is the following: Let X be a single observation from the beta(θ,1) pdf. (b) Find a pivotal quantity and use it to set up a CI having the same ...
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### Abnormally large confidence interval with binomial gam when p->1 at max of predictor range

I am running a gam (mgcv in R) to model a non-linear effect of time on a binomial reponse (positive or negative sample). This is a minimal example of such a model: ...
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### Transformation of a Random Variable

I am working on this problem for class, where the setup is the following: Let X be a single observation from the $beta(\theta,1)$ pdf. (a) Let $Y=-(logX)^{-1}$. Evaluate the confidence coefficient of ...
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### Compare bootstrap auc confidence interval using t-test

In order to choose between a machine learning model when the number of features is 5 and a machine learning model when the number of features is 6, I want to bootstrap the auc of the model to obtain a ...
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### Proof of Azuma-Hoeffding inequality for Martingales in MAB

Suppose in an MAB problem, $X_t=\mu+\epsilon_t$ represents the reward values at each period (for a given arm). If $\mathcal{M}(t)$ shows the set of periods until $t$ where a specific arm has been ...
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### Heteroscedasticity-consistent (robust) standard errors complemented by i) confidence intervals for beta, ii) Tolerance and iii) VIF values in R?

In order to solve heteroscedasticity in my data, I ran a regression with heteroscedasticity-consistent ("robust") standard errors. I would also like to report i) standardized betas together ...
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### Finding a specific reference on the construction of a confidence interval where by inspection we can see it does contain the parameter

I realise this is a long shot but I am trying to find a reference to a specific example of a construction of a confidence interval which I came across in the past. My memory on this is hazy and I may ...
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### when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero?

when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero? I know this can be done with GAMS as shown in this ...
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### Select classification model using nested cv and bootstrap auc confidence interval

My goal is to find the best 1 model out of 55 classification models. I first ran nested cv on 55 models to see which model had better generalization. The AUC score was used as an evaluation indicator. ...
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### Statistical significance of non-overlapping 1-sigma confidence intervals

Is this logic correct or not? Given two random variables, each with its own estimate of the mean and a 1-sigma (z=1, 68%) confidence interval that do not overlap with each other: The probability of a ...
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### I want to find the coverage of a bootstrap confidence interval of a ratio of means [closed]

I want to answer this question Explore coverage of the above four types of confidence intervals. For this you should simulate data from X ∼ N(2, 1), Y ∼ N(1, 1) and calculate coverage of the different ...
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### Bootstrap on samples with different precision

Imagine the following setup: I have N specimens that come from the same population (e.g., they are from the dame material) For each specimen i, I have a single estimate of a given property in terms ...
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### Confidence interval for binomial distribution [duplicate]

I'm developing a simple application for memorization, for personal use. The user gives responses corresponding to prompts, and each prompt belongs to some category. At the end, we have for each ...
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### What is the difference between Confidence intervals and precision intervals? [closed]

I've tried searching but I cannot even find a definition for a "precision interval" anyway. I am completing a meta-analysis and the package in R that I used to create my figure put both ...
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### How to proceed when the observed effect is smaller than the Minimum Detectable Effect?

Given an A/B test with an already defined sample size and variance, a power analysis was conducted to estimate the Minimum Detectable Effect (MDE) of a proportion. After the experiment was concluded, ...
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### How to read and use equations for confidence interval from sequential testing

in the book "Group Sequential and Confirmatory Adaptive Designs in Clinical Trials" by Wasmer and Brannath - they explain on p.85 how to calculate a confidence interval. They consider a ...
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### Point-level prediction intervals in LightGBM models

I would like to compute prediction intervals for LightGBM at the sample level. In other words, given a certain row to be classified (supervised classification, not regression), what is the upper bound ...
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### Confidence and prediciton intervals for power law fit

I would like to determine confidence intervals and prediction intervals for a noisy dataset that follows a power law distribution. I have a dataset that (to my eye) follows power law behavior in the ...
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### Calculating confidence intervals in R

I am curious as to why I am getting two different 95% confident intervals in R, given a mean of $0.008$, an SD of $0.1035697$ and $n = 39$ (normal distributed). When I use the code: ...
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### Can a result be statistically significant if the null value is one of the 95% confidence intervals?

I'm reading a paper on the effect of 2 different drugs on mortality. The results are reported as RR 0.96 (0.94-1.00), p=0.03. The p value indicates significance but the upper 95% limit is 1.00. Am I ...
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### Should I use a one-sided or a two-sided confidence interval?

Context: I am teaching a subject and I prepared a multiple-choice quiz for my students. To have a feeling for which is an acceptable grade I decided to compute a baseline score, which is the score ...
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### How to use variance-covariance matrix to estimate the confidence interval of regression coefficient? [duplicate]

guys I'm interested in multivariate regression and I basically understand the maximum likelihood method to get the point estimation of regression coefficients. However, it still has not been figured ...
1 vote
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### Interpretation of incidence rate ratio

The incidence rate ratio (and 95% confidence interval) of rotavirus gastroenteritis for the vaccine group compared to the placebo group is $0.67 (0.55, 0.82)$. I want to know approximately how many ...
1 vote
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### Question about using the RFpredInterval Package: How to calculate the standard deviation of data points in same terminal node as test data point

I am using the RFpredInterval package (specifically the rfpi function) to obtain prediction intervals for a random forest. I ...
In the setting of Huber's paper, the true density is $y\sim f_0$, and the density under consideration is $y\sim f(\cdot|\theta)$. If we choose to maximize $y\sim f(\cdot|\theta)$, we will find that $\... • 345 0 votes 0 answers 19 views ### Dealing with covariance Within my dataset, I employ a variable termed "Instagram reach," quantifying the audience size exposed to a particular post. Simultaneously, "engagement" denotes the count of ... 0 votes 0 answers 12 views ### Bootstrapped Confidence Intervals controlling for FWER? I'm currently using the bootci package in MATLAB to compute bootstrapped confidence intervals. I have data for two variables and I'm interested in comparing differences in means of these variables. ... 1 vote 1 answer 40 views ### What is the distribution of the model prediction and the expectation of the model prediction in linear regression? What is the distribution of$E[Y|X]$(=$X\hat{\beta}$) and$X\hat{\beta} + \epsilon\$ in a multivariate linear regression There are several places this question has been answered implicitly or ...
I recently learned about confidence interval for proportion now let's say i use a Z score and get the confidence interval of 95% as follows: $$C.I = \hat{p} \pm Z_{(1-0.95)/2} \sqrt{p(1-p)/n}$$ now ...