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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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Confidence Intervals of not Gaussian functions

Is anybody know a good tutorial about how we calculate Confidence Intervals of not Gaussian functions? I give some example of what I kind of function I think about: 1st example: Let be $ X_1, X_2 \...
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Interpreting prediction intervals, and prediction intervals for a specific parameter?

Can someone correct my thinking if I'm off course here? Confidence intervals provide an estimate of precision$^1$ for a specific parameter, but they can also be used for a regression equation (i.e., ...
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How Confident Should I be

I have a question about confidence in a conversion rate. I have a sales page that had 1382 visitors, and 23 of them purchased the product. I know for that sample I had a 1.66% conversion rate. But ...
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How confident is my model? Is there a way to know?

I am interested in finding out how confident my model (say Logistic Regression) is in predicting the label of a new data point. For example, if it is not confident, I better abstain from making a ...
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Obtaining confidence over prediction? [duplicate]

I am facing a rather strange problem. Machine learning gives us a probability of a data point belonging to either class (classification) or the actual estimate of the dependent variable given ...
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Testing normality with Confidence Intervals

I've read an article that talks about transforming non-normal data to normal data. In the article it says: "In this case, normality clearly cannot be assumed; the p-value is less than 0.05 and more ...
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Unusual Confidence Interval

Let $X_1 , X_2 , ... , X_n$ be a random sample from a distribution with probability density function $\frac{1}{\theta}x^{\frac{1- \theta}{\theta}}I_{[0,1]}, \theta>0$. I want to find the 100$\alpha ...
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Confidence intervals on multiplication of two means with confidence intervals

I have survival probability 0.5 with a confidence interval around it. I have mean number of offspring 15.1 produced with confidence interval around it. I want to find species "fitness" by ...
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Associating a quality/confidence score with a regression model

Let's say I have a set of $N$ data points $x_n \in \mathbb{R}^M, \; n=1,2,\ldots,N$. Say I have trained a model $f:\mathbb{R}^M \mapsto \mathbb{R}$ on a separate training set (using linear regression, ...
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Prediction interval for XGBoost Classifier

I am reading this article https://towardsdatascience.com/regression-prediction-intervals-with-xgboost-428e0a018b where the author presented a method to calculate the prediction interval for XGBoost ...
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Calculate interaction effect confidence intervals in zero-inflated poisson regression

I'm conducting a zero-inflated Poisson regression using the pscl package in R. I've included interaction terms but am having an issue with interpretation. I am assuming an additive effect and summing ...
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What do we use variance of the error term for in regression analysis?

So I get that, for simple linear regression where Y = B_0 + B_1(x) + E, Var(Y|x) = Var(E). Variance of the mean response involves it, as does variance of future responses, but is this ever actually ...
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Getting prediction interval for xgboost prediction?

I am looking for a solution that can bring prediction interval for xgboost classification (https://xgboost.readthedocs.io/en/latest/), i.e. instead of output the probability that an instance belongs ...
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Confidence Interval help

2 1 The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows: 458, 450, 457, 456, 460, 459, 458, 456 a) ...
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Confidence Intervals help [duplicate]

The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows: 458, 450, 457, 456, 460, 459, 458, 456 a) Calculate a ...
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38 views

Linear regression - confidence interval for expected difference in $Y$ with respect to unknown values of $X$

Suppose I am given all of the necessary parameters about some linear model, but not the data itself. Namely, I am given $\hat{\beta}_1,\hat{\beta_0},\bar X, S_e, r^2$, etc. Also, I know that $X_1,\...
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Notation for confidence interval

Since P(lower bound estimate < true parameter < upper bound estimate) = 0.95 means that the series of random bounds contain the true parameter 95 percent of the times, then why not replace the ...
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Interpreting a Tukey - Kramer Confidence Interval Plot

In order to see if any statistically significant differences in the means of 4 particular diets exist, a post-hoc test is conducted i.e. Tukey – Kramer. Could someone please explain to me the plot ...
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Variance of unbiased estimator for the shape parameter of Pareto distribution

I'm interested in getting the error bounds of the unbiased estimator of the shape parameter ($\alpha$) using maximum likelihood method of Pareto distribution. The unbiased estimator is known to be ...
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Confidence intervals for multiple output values of a Markov process using covariance?

I have a Markov process (specifically the Wang-Landau algorithm) that produces a set of "weights" $w_i$ for $i=1,2,...,N$. The weights by themselves are actually meaningless, and what is actually ...
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Estimating true positive rate with a confidence interval given a classifier + unknown dataset truths

Let's say I've built a binary classifier - one that for instance, can classify whether a particular transaction is fraudulent or not. This classifier outputs a 1 or a 0, with a given degree of ...
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How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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Plot confidence interval of average polynomial fit from coefficients

I am studying the propagation of a wave and to do that I want to follow the position of my maxima over time. In order to do that I thought to fit a polynomial on the data of each replicate, then save ...
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CI for difference

If you build confidence interval for difference (for example, when you are comparing shares), and 0 is included, it means, that the difference is not significant. But can you say something about this ...
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How to compute 95% confidence interval bars and prediction interval bars of uniform data?

I need to compute the confidence and prediction interval of uniform dataset. import numpy as np Data= s = np.random.uniform(-10,10,1000) print(Data)
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Get better confidence interval by drawing multiple samples

Imagine that I have population of size N and I draw a sample of size n from which I compute a proportion $\hat{p}$ of a categorical variable. And I want to get a confidence interval of 95%. So I ...
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How much “ground truth” data do I need to evaluate a heuristic classification approach?

I have a heuristic approach to a de-duplication problem: There are about 300 million unknown data points. I attempt to match each data point with one of about 4 million independently known data ...
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Confidence intervals specified for a t-test in R

I am new to statistics with R. While doing a one sample t-test with R with population mean specified, I find the results on confidence levels given by R are misleading. Instead of giving confidence ...
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Using Hoeffding's inequality to determine testing data size

Suppose one needs to perform binary classification on a dataset with 300 records of a random numerical variable, and need to ensure error rate on future data will not exceed the error rate on test ...
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Drawing 95% ellipse over scatter plot

The context is regression analysis using Eviews, but first I wanted to create a few scatter plots and overlay error ellipses on them. Eviews doesn't support that kind of graph ornamentation so I am ...
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Confidence Interval of shifted exponential

. I know what confidence intervals are but can a confidence interval of given size have different lengths?
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How to calculate a prediction interval for the mean of multiple new responses

I am using a Neural Network to estimate Ecosystem Respiration (ER) and Gross Primary Productivity (GPP) from Net Ecosystem Exchange (NEE) observations where. NEE = GPP + ER I've used the model to ...
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Bonferroni confidence region for shifted Laplace parameters

Consider the shifted Laplace distribution with the density: $f(y)=\frac{\theta}{2}e^{-\theta|y-\mu|}$ $y\in \Re$ Using the Bonferroni method, construct a $100(1-\alpha)\%$ confidence region for $(\...
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Calculating a Confidence Interval for a Proportion for a Sample of Different Size

I'm interested in a (preferably analytic) solution or approximation to the following problem: Let $s_1$ be a sample from an unknown distribution of size $N_1$ and with proportion of successes $p_1$. ...
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How can I calculate $\mu_x/\mu_y$ using Jackknife?

I have difficulties in calculating confidence interval using Jackknife. Suppose that I have two independent samples and I do not know both their population distributions. I understand how to ...
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Confidence interval for sum(observed) (continuous, right-skewed) divided by sum(expected) (continuous, right-skewed)

I need confidence intervals for an o/e metric based on a continuous variable (observed days/ expected days) sumed up for all the people in the population.
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Error on mean from measurements made from a distribution with a possible long tail

I am using Langevin dynamics simulations to measure a first hitting time of particles leaving a region in parameter space. I would like to measure the mean first hitting time (and not the median for ...
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1answer
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how to present results for two group success rate with confidence interval

I have two groups A and B, and for each data point I have two possible outcomes, success and failures. For each group, I have calculated the success rate, and the confidence interval for a binomial ...
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Confidence interval of fit parameter

First of all: I am quite new to statistics, so please don't tear me apart. ;-) I am currently trying to calculate a confidence interval for a fit of a curve to measured data points. I have done this ...
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Reporting models: Add intercept from fixed effect including confidence intervals

Suppose I have a fixed effect model where I investigate a time series of measurements. My estimate + CI gives me the changes from intercept and a p-value. So stage 1 is baseline and the output gives ...
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Linear regression: slope (b) confidence interval and R^2

Possibly quite a basic question: I am unsure of the relationship between the confidence interval for a regression coefficient (b) and R^2. That is, is the width of the confidence interval directly ...
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confidence limits on model parameters : Monte carlo vs chi-square

I performed a non-linear fitting on experimental datas to determine model parameters using least square methods ($\sigma$ is the same for all the experimental datas). And now, I want to determine ...
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Confidence on the median for a weighted empirical distribution

I have observation data $x_1, \dots, x_n$ with associated positive weights $w_1, \dots, w_n$ such that $\sum_i w_i = 1$, representing a "weighted" empirical distribution with CDF $$ \hat{F}(x) = \sum_{...
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why to compute distribution when I need to extract the confidential interval of my data?

I need to compute confidence interval for regression intercepts.To summarize: 1\ I extract all intercept of my data based on linear regression [a1,a2,a3,..,an] 2\ ...
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1answer
43 views

Uncertainty and confidence in classification

I have a multi class classifier with 30-40 different classes. When i predict a class i would like to get an estimation about how certain my model is with its own prediction of that single sample . i....
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Is there a probability distribution with unskewed confidence intervals for quantile estimation?

The so-called process capability index Cpk is often used to express the yield Y in a production, e.g. for a given upper specification limit x. Mathematically it is based on fitting a normal ...
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1answer
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What to do in meta-analysis if confidence interval not symmetrical?

I'm about to make a meta analysis of a particular topic. I'm using Comprehensive Meta-Analysis (CMA) ver. 3.0 for that reason. However, after I input all the necessary data, the software refused to ...
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Are confidence intervals useful?

In frequentist statistics, a 95% confidence interval is an interval-producing procedure that, if repeated an infinite number of times, would contain the true parameter 95% of the time. Why is this ...
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Building a confidence interval

How do I know when to use the +/- alpha/2 and when do I use the alpha/2 on one end and 1-(alpha/2) on the other end when building a confidence interval? Does it depend on the distribution the ...
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Profile likelihood confidence interval proof

I have read that for null hypothesis $H_0 : \beta = \beta_0$, the likelihood ratio statistic from profile-likelihood is $$LR = 2 (\log L_p(\hat{\beta_p}) - \log L_p(\beta_0))$$ where $\hat{\beta_p}$ ...