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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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 ...
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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
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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 used SPSS, but to my current knowledge that is only able ...
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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 ...
Tintswalo Shivambe
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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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Calculating confidence interval in linear mixed effect model
Consider a simple linear mixed effect model (LMM)
$$Y_{ij}=b_{i}+X_{ij}\beta+\epsilon_{ij},$$
where $b_i\sim N(0,\sigma_b^2)$, $\epsilon_{ij}\sim N(0,\sigma_e^2)$.
Typically, one can estimate $\...
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False Discovery Rate-Adjusted Multiple Confidence Intervals after p-value-adjustment
I apologize in advance if my question is incomprehensible, I am very new to this topic.
My data consists of 6 dependent variables (DV1-6) and 5 independent variables (IV1-5) of interest. For reasons ...
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Confidence intervals for proportions and independence
Suppose a company sells various products at different prices. I would like to compute confidence intervals for the contribution of each product to overal sales, preferably in terms of currency (e.g., ...
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What do One-Sided Confidence Ellipses Look Like?
To make things concrete, take a simple linear model:
$$E[y \vert x_1, x_2] = \alpha + \beta_1 x_1 +\beta_2 x_2$$
In a one-sided hypothesis test, like $\beta_1 \ge k$ vs. $\beta_1 \lt k$, the ...
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Questions about how to proceed when residuals of linear regression are not exactly normally distributed
I have done a linear regression analysis on some data and I want to construct confidence intervals on the coefficients. I have read that it is necessary for the residuals to be normally distributed to ...
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Assessing deviations between actual and expected mortality rates with GAM models and confidence intervals
I'm currently using a Generalized Additive Model (GAM) aimed at modelling mortality as a binary response (1 if the person has died and 0 otherwise). My primary goal is to compare the actual mortality ...
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Can anyone work out the P value from this graph?
Can anyone work out the p value just based on the graph below? I cannot understand how this is calculated and what additional information I would needs to work it out.
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Confidence interval of MLE variance estimator (Normal Distribution)
May I use Fisher information for constructing confidence interval for MLE variance estimator?
Fisher information should be: $I(\theta) = E[I_0(\theta,Y)] = E\left[ \frac{m}{2(\sigma^2)^2} \right] = \...
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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 ...
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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 ...
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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 ...
Rachel Tumbleson
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QMLE and Confidence Intervals
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 $\...
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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 ...
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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. ...
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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 ...
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Proportion C.I confidence level with a change of variance
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 ...
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What is the connection between z* and a z distribution?
I'm a student in AP Stats and our teacher just told us that z* is the critical value used for calculating a confidence interval, but I was wondering where it actually came from. Like is there a ...
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Understanding the significance of a few results derived in the course of linear regression
I am reading up on linear regression from 18.650 MIT. In the way of explaining it, the professor derives a few results and I have attached them in the image
The first result gets used along with the ...
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Confidence box for coefficients of linear regression?
I am learning linear regression and I am trying to create a visualisation. Say I want to estimate a power model $y=ax^b$ using linear regression. I take the logarithm to get
$$\ln(y)=\ln(a)+b\ln(x)$$
...
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Interpretation of $\sigma$ in Gaussian mixture
I have a distribution of a variable that was normalized with plt.hist and then fitted with a sum of gaussian curves $g_M = \displaystyle\sum_i\frac{w_i}{\sigma_i \...
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Understanding the multicollinearity issue in relation to linear regression
There are 2 issues that multicollinearity in linear regression leads to
Interpretability goes for a toss
Parameter confidence intervals are wide and it is difficult to find a parameter significant
I ...
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