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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Jeffreys Interval Calculations and Sample Size

I have a rough understanding of bayesian statistics and of the Jeffrey's Interval/priors. I understand that the Jeffrey's interval takes the form: p|x ~ Beta(x + 0.5, n - x + 0.5) I am interested in ...
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Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions?

Simple problem of estimating: $$ y = f(x) + \epsilon $$ Where I use your standard Nadaraya-Watson Regression to guess $f(x)$. This is relatively fast and works well even in an online setting. Now I ...
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what is the estimated variance of predictions from mixed model?

I have fitted the following lmer model (assume it is "correct") with lme4: Y ~ X1 + X2 + X3 + (1 | year) + (1 | site) + (1 | site:year) where X1-X3 are ...
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11 views

Sample size determination for estimating a count

I want to estimate a simple variable: "**how many times my website is visited in 2015?". Suppose that I cannot count all visits to my website (it is expensive!), but I can count the connections on ...
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Uncertainty in parameter estimates when fitting distributions

I used the fitdist function from the "fitdistrplus" package in R to estimate the parameters of my data. Once I get the parameters, I must get the confidence ...
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404 views

Hypothesis testing. Why center the sampling distribution on H0?

A p-value is the probability to obtain a statistic that is at least as extreme as the one observed in the sample data when assuming that the null-hypothesis ($H_0$) is true. Graphically this ...
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1answer
39 views

Removing undefined (NaN) values during log-likelihood maximization

I am trying to maximize a Poisson likelihood function for an array of values, of the form llhij = -mij + kij*ln(mij/kij). (where I use the numerical approximation ln(k!) ~ k*ln(k)). For my ...
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40 views

Given a 1-Sided Lower Confidence Bound value, How to determine target failure rate

$R(t)$ = reliability = 1 - unreliability (probability that item is still operational for a given time t) unreliability = Cumulative Distribution Function (CDF) = (...
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Confidence and Prediction Intervals for Multiple Linear Regression Model

I am looking for a derivation of confidence and prediction intervals for a multiple linear regression model. I have seen that for a given vector of predictors $(x^*)$ and $X$ denoting the design ...
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17 views

Relationship Between Percentile and Confidence Interval (On a Mean)

This question came up at work when someone asked me what the relationship was between a percentile and a confidence interval, and I had a very hard time articulating my thoughts. The context was a ...
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How to combine/pool binomial proportion confidence intervals after multiple imputation?

After I multiply imputed my dataset m times I wanted to calculate a binomial proportion confidence interval. I did that formerly using the Hmisc::binconf() function ...
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1answer
42 views

Can we use bootstrap samples that are smaller than original sample?

I want to use bootstrapping to estimate confidence intervals for estimated parameters from a panel dataset with N=250 firms and T=50 month. The estimation of parameters is computationally expensive (...
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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 ...
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1answer
47 views

Bootstrapping a sample from a finite population

Can someone point me to some reference for theory on bootstrapping a sample took from a population of known size? I am used to use Bootstrap to calculate confidence intervals of a sample when the ...
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1answer
34 views

How do I find confidence interval for a function of multiple parameters?

I need to estimate the confidence interval for the efficiency η which is a function of 5 parameters $P1-P5$, $η = f(P1,…P5)$, with all parameters $P1-P5$ having normal distributions . I know the mean ...
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1answer
35 views

combining RMSE for multiple cross-validation procedures

I have implemented a leave one out cross validation to calculate errors between daily forecast and observed values for spatio-temporal data taken in a given season (summer say). I have further ...
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36 views

Obtaining confidence intervals from covariance matrix?

I have performed a simple linear regression on two variables - age $a$ and price $p$ - which has given me the gradient and y-intercept (price depreciation $\frac{dp}{da}$ and initial price $p_0$.) I ...
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48 views

How to calculate prediction confidence intervals for estimated mixed model change scores varying per a continuous predictor, using “lme4” in R

The Setup I am employing a linear mixed model in R using the packages "lme4" and "lmerTest." In modeling my predicted variable, I have two time indicators set as fixed and random effects: one time ...
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Interpreatation of ratio of variances in random effects model - ICC-like quantity

I was reading this question and answer, and I was curious about a different ratio of variances than the ones described. Using this random effects model: $$ Y_{ijk} = \beta_0 + \eta_{i} + \theta_{j} +...
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Error Rate Confidence

I have a very basic understanding of statistics and have the following question: Given a test that can be run and give either a Pass or Fail result, how do I calculate how many times I must run the ...
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32 views

How am I going to understand this bootstrapping?

I already feel like I'm spamming this site! However, after several days of scratching my head and thinking things over, I cannot really answer this myself. I want to get a confidence interval of the ...
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1answer
18 views

Why confidence interval is important when point estimator is close to zero? [duplicate]

When the point estimator is relatively small numbers, a confidence interval is likely to contain zero, be fairly wide and include both positive and negative values. Basically, when CI contains zero ...
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Confidence interval sum fitted probabilities GLM

Let CI$_i:=logit^{-1}(\hat{\mathcal S}_i \pm 1.96*$ SE$(\hat{\mathcal S}_i))$ denote the $n$ Wald confidence intervals of the fitted probabilities $\{\hat{p}_i\}_{i=1,\dots,n}, \hat{p}_i:=\hat{p}_i(x|\...
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What fraction of repeat experiments will have an effect size within the 95% confidence interval of the first experiment?

Let's stick to an ideal situation with random sampling, Gaussian populations, equal variances, no P-hacking, etc. Step 1. You run an experiment say comparing two sample means, and compute a 95% ...
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1answer
78 views

The true meaning/difference of alpha values and p-values

EDIT: I may have been confused by the confusion of others. In any case, it helped a lot when I came to know that the $p$-value is stochastic. It does make sense, given the $p$-value is a ...
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From successive samples of increasing size how do I measure “variability is within the error band” for a particular confidence level?

In the section 5.6 of book Data Preparation for Data Mining, by Dorian Pyle it states This is a complex subject, and it is easy to confuse what actually has been captured here. In the example ...
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56 views

Can confidence intervals for predicted probabilities be interpreted similarly to confidence intervals for means?

I've made a bar plot and I calculated confidence intervals by hand, (+/- 1.96*std_error)+predicted_probability and I want to be sure that it's interpretable. ...
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Sample Size Formula for Wilson Score, Clopper Pearson, and Jeffrey's

I am interested in finding the sample size formulas for proportions using the Wilson Score, Clopper Pearson, and Jeffrey's methods to compare with the Wald method. Also if anyone has code to replicate ...
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67 views

How do I interpret Standard deviation or 95% CI to describe the population?

When reading scientific articles I see different approaches for summarising continuous variables in describing the study population. For instance, if I want to describe the mean age of study ...
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33 views

When is it considered a repeated and independent experiment in chemistry?

Sorry for the somewhat confusing title. I was wondering about the use of confidence intervals in the context of chemical and biochemical experiments. The experiments must be repeated and the data have ...
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21 views

Interpretting Confidence Interval Questions

Q.In a survey conducted by a mail order company a random sample of 200 customers yielded 172 who indicated that they were highly satisfied with the delivery time of their orders. Calculate an ...
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1answer
24 views

scipy.stats.poisson.interval - what confidence interval

What kind of confidence interval does scipy.stats.poisson.interval return? Is it normal approximation? I went on GitHub, but could not look it up in the code. How ...
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34 views

R, glmer(), plot bootstrapped CI in graph

Using the glmer() function in the LME4-library in R I computed logistic models, of the form: Y ~ cat1 * cont1 + (1|Subject) where, obviously, Y is the binomial outcome variable (0 or 1), cat1 is a ...
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How can I combine a survey of a population and a survey of a sample of a population?

I have a question about combining survey results that involve a measure of a population and a measure of a sample of a population. Here is what I have: 1) In a given state, I surveyed recycling ...
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Making a Bayesian prior from a frequentist result

How should one go about turning a frequentist result into a Bayesian prior? Consider the following pretty generic scenario: An experiment was conducted in the past and a result on some parameter $\...
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74 views

Error bars on bar graphs: Is reporting confidence intervals really better than reporting standard errors of the means?

I have heard this advice repeatedly however recently when I was looking at my own graph with CIs I had a panic attack because the error bars overlapped, yet my analysis told me the difference between ...
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1answer
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Extracting Standard Errors for a combination of factorial predictors in binomial GLM

Suppose I run a binomial GLM (in R) with response variable [0,1] and 2 predictor variables that are both categorical. Let's call them a and ...
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Calculating error on subject-level predictions in repeated measure study

Introduction Suppose I observe 30 subjects attempt a given task in 3 separate occasions and I give them a score. To analyse each subject's performance over time, I can use a multilevel / mixed effect ...
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38 views

Real meaning of confidence ellipse

Reading about the true meaning of 95% confidence ellipse, I tend to come across 2 explanations : The ellipse that contains 95% of the data Not the above, but the ellipse that explains the variance ...
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32 views

What mean should be used for the variables that are involved in a linear regression model in a log-transformed space?

This has been bothering me for a while. Both $X$ and $Y$ are material properties. They can be described using a linear regression model built in the log-transformed space, i.e., $\log Y=a \log X+b$. ...
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37 views

When can't a confidence interval be constructed?

In one of my econometrics assignments, we were asked to consider the effect of measurement error in the dependent variable of a simple linear regression. And I was just wondering, under what ...
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What is the difference between coverage probability and confidence coefficient?

Casella-Berger provides the following two definitions for an interval estimator [L (X), U(X)] of a parameter $\theta $ :- Coverage Probability: probability that the random interval [L (X), U(X)] ...
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39 views

confidence interval with logistic regression [closed]

I have data which consist of 0,1,-1 values somethink like this. x:{1,1,1,-1,-1,0,0,0,0,0,1,1,1,1,1,1,1,1 ......} y:{1,1,1,0,0,0,1,1 ......} I need to ...
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Identify outlier usage intervals in time-series data

I want to find outliers in power consumption in real-time, at hourly rate, i.e., at the end of the hour, I should say whether power consumption in current hour was outlier/anomalous or not. Approach: ...
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18 views

Problem Calculating Standard Error

I have a set of individuals categorized into two classes as follows: ...
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28 views

How to calculate a confidence interval for a trimmed mean

I try to get the sample size that presents the population, I averaged randomly the 10 and then the 20 readings then I used the formula CI = 1.96 * std/root n, that gave me the CI at any (n), but how ...
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42 views

Role of Central Limit Theorem in creating confidence intervals and hypothesis testing

How is central limit theorem useful in creating confidence intervals as well as its role in hypothesis testing around the population parameter.
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22 views

Confidence Interval for Regression Line (simple linear regression)

So I've constructed a confidence interval for my regression line. However, because I have 2500 data points it is a very, very narrow interval (I can barely see it next to the regression line when I ...
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Using confidence intervals with Simple Linear Regression

So simple linear regression is performed on 3000 data points, and 1000 data points are withheld. How can we use confidence intervals, along with the withheld data points, to assess the predictive ...
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How to obtain a confidence interval or a measure of prediction dispersion when using xgboost for classification?

How to obtain a confidence interval or a measure of prediction dispersion when using xgboost for classification? So for example, if xgboost predicts a probability of an event is 0.9, how can the ...