Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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13 views

Adjusting OverAll Time Performance using sectional Times

Assume I have two runners, Runner_1 is the average runner and Runner_2 is Usain Bolt. We let the two runners compete in 3 different races on a 100m distance. We assume that the benchmark time for 50m ...
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14 views

The performance of EM algorithm at different local maximas

Setup: Say I have a problem (any problem that can be modeled by a probabilistic model) to solve, this problem involves some unknown parameters to estimate. I model this problem in a probabilistic ...
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How do you compute the confidence interval for the product of two separate A/B tests?

I am trying to find the confidence interval of the end result of two A/B tests. As an example, lets assume that for test 1 I am looking at the click-through rate of a page and have a control and ...
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26 views

Testing multiple hypotheses multiple times

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I ...
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1answer
34 views

If two sample means of $X$ differ significantly and $X$ predicts $Y$, can it be inferred that the samples differ in their $Y$?

In the following model: $Y = \beta_0 + \beta_1 X + \epsilon $ $X$ is found to be significantly related to $Y$. Now, I observe $X$ within two groups. I compare the two means and find that the $X$ ...
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t-test to compare weighted means

I have an unbalanced panel of paired differences. That is, my panel consists of 100 firm time series of paired differences with varying length. I have tested wether the unweighted mean is different ...
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1answer
50 views

Most Efficient Estimator and Uniformly minimum variance unbiased estimator

I am studying Estimation theory from "Introduction to theory of statistics" by "Mood and Graybill". After completing I thought I understood UMVUE (uniformly minimum variance ...
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26 views

What statistical test to discriminate between within and between category with 2-dimensional data?

Let's say I have a multidimensional data with one axis indicating factors of a customer base (eg. income), and another axis could show some options (eg. fashion store A, fashion store B, fashion store ...
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20 views

Is there a formula for the expectation and variance of a ratio of sampling variances?

I know the formulas for the expectation and variance of the sample variance, difference between two sample means and proportions. Sample Variance $E(S^2) = σ^2$ $V(S^2) = 2\sigma^4/(n-1)$ Difference ...
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212 views

Testing Hypothesis with different alternatives

I want to test whether $\mu=\mu_0$ where $\mu_0$ is some fixed number. Consider the following two different testings. Hypothesis Testing 1: $H_0:\mu=\mu_0,H_1:\mu<\mu_0$ Hypothesis Testing 2: $H_0:\...
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1answer
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Is there a detailed explanation on why multiple population sampling distributions use difference for mean and proportion, while ratio for variances?

I think that it does make conceptual sense. For means and proportions, we want to compare the amount at which their values are apart. Which is why difference is used. For variances, the factor at ...
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1answer
32 views

Causal inference method for analyzing randomized control trial with covariates / pre intervention observations

I've got a seemingly easy situation, which turns out to be a little more complex than originally thought. Here's the Setup: We have a randomized controlled trial. Test and Control groups are the same ...
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Can someone explain to me the sampling distribution of sample variance in comparison to that of the sample mean?

I have read tons of things already about the sampling distribution of the sample variance but I can't get quite a good grasp of exactly what it is like in terms of the formulas of the measurements. ...
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2answers
32 views

How to compute the variance for a bayesian estimator

I can't figure out how to compute the variance of an estimator which is the mean of the posterior distribution let's say Gamma($\sum x_i+3, n+a$) How to find out the variance of this mean ?
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1answer
43 views

Type II error or no error?

I get stuck in the following question: You set up a two-sided hypothesis test for a population mean μ with a null hypothesis of​: μ=100. You chose a significance level of α=0.05. The p-value ...
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1answer
23 views

Why do the mean and proportion measurements take the spotlight in estimation?

Based on information I have read and from this website, sampling distributions do exist for statistic variants of measurements other than the mean. Sample ranges, maxima, minima, variance and ...
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In my study of Inferential Statistics, the following uses of inferences were mentioned. Could this be expanded upon?

Currently an undergraduate engineering student studying Statistics. My source has cited three major uses of inferences: Types of Inferences Estimation - The value of a parameter is estimated. Testing ...
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1answer
29 views

Differences between Mann-Whitney U and chi-square tests for if two-samples come from same distribution

In a textbook, it introduces the chi-square goodness of fit test to test independence between two variables (organized in a contingency table), which can also be used to test if m samples are likely ...
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1answer
47 views

Regression's population parameters

Suppose I've specified a linear regression model: $$ Y = \beta_0 + \beta_1 X + \epsilon $$ where $\beta_0$, $\beta_1$ are the population parameters. My question is: why are these parameters ...
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19 views

Survival Analysis for recurrent events

Not my exact setup, but for easier explanation imagine I'm working on a project that looks at user session data on a website (like netflix). The idea is to understand how video playback errors might ...
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9 views

How to handle strong ceiling effects in an repeated measurment experiment?

i am trying to analyse some old data. It's an between-within subject experiment with 4 experimental conditions and 2 points of measurment. The question is, if there are differences in effect of the ...
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1answer
38 views

What is the relationship between VAE and EM algorithm?

What's the relationship between Variational Autoencoders and the Expectation Maximization Algorithm? I know that the EM algorithm is used in latent variable models, specifically to do maximum ...
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49 views

The seven scientists: Difficulties with maximum likelihood

I'm working on the exercise 22.15 - the seven scientists - in the book by David Mackay where he claimed that Maximum Likelihood method might have difficulties with. However, when I applied the maximum ...
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Compute standard-error/deviation for an aggregated/ fractional metric

I have a dataset, where I want to visualize an aggregated efficiency over time (t), while also showing the variation/ uncertainty in the data. The target metric is computed as the fraction of the ...
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1answer
20 views

What is statistical meaning of testing of machine learning model on new data?

Any machine learning model, normally, is applied on new data for testing. If the accuracy of the model is below a certain threshold, the model is rejected. But why? This is just a random sample, the ...
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36 views

Independence of the sample mean and sample variance

For $X_i \stackrel{indep}{\sim} N(\mu_i, 1)$, I have to show that the sample mean $\bar{X}=n^{-1}\sum_i X_i$ and $S_{XX}=\sum_i (X_i-\bar{X})^2$ are independent the theory of random projections onto ...
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2 x 2 x 2 design

I'm doing a 2 x 2 x 2 design. To be specific, it's a 2 (BETWEEN-subjects variable) X 2 (WITHIN-subjects) X 2 (WITHIN-subjects) factorial design. And three Dependent Variables I know MANOVA is the one ...
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1answer
29 views

How to tell if there is strong evidence one brand is preferred over another?

Two new varieties of cheese, V1 and V2, are to be compared. In order to establish if there was a significant/real overall difference in consumer response to the two varieties, a study was conducted. ...
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26 views

What is the similarity and difference between signal recovery and parameter estimation?

As per inferential approach both are estimation problem. But, in signal recovery, we estimate our input signal from the measured (noisy or noise free) observations. And, in parameter estimation, we ...
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Estimate standard error of interaction based on stratified models

Is it possible to estimate the standard error of an interaction term based on summary statistics from the corresponding stratified regressions? For example, I am interested in the difference of the ...
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13 views

How to interpret coefficients from regularized cox regression?

I have computed regularized coxph model with LASSO penalty, some of the covariates are thus omited. But I got some non-zero betas. Is it possible to interpret these values, in some similar way as ...
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8 views

How are clustered standard errors and Newey-West errors related

As the question says, how are the two concepts related? As far as I understand, both approaches correct for heteroscedasticity and autocorrelation. Yet, they are different. Would applying one of the ...
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1answer
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Should I reword the Factor if it shows all negative loadings?

I've seen very similar questions but none really address my issue. I ran a PCA on 29 items to identify different factors of stress and worry. All items were on a scale from 1 to 3 and none of these ...
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How to estimate cut off percentiles to classify cost per metric?

I work at an ad agency and one of our key performance metrics is what we call "cost per outcome". Right now I have advertisements grouped by type of advertisement, lets say type "A"...
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23 views

Is this problem related to statistical inference from two population parameters? If so, why does my approach not give the right answer?

What I tried was use the statistic z = pbar1 - pbar2 +- z of a/2 * SQRT[{pbar1*(1-pbar1)}/n1 + {pbar2*(1-pbar1)}/n2 ] pbar1= 37/88 = .235 n1 = 88 n2=102 pbar2=.235 z = .42045-.235 +- 1.96 * SQRT[{....
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19 views

Stats test to compare two distributions of proportions?

I am struggling for a statistical test to compare two distributions of proportions i.e. my control group and experimental group. Exp design is as follows: 40 samples (1 sample = 1 tree) each for ...
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1answer
21 views

Cramer-Rao Lower Bound Proof (fuzzy step)

The following is the derivation of the Cramer-Rao lower bound as detailed on p.336 of Casella and Berger's Statistical Inference: $\frac{d}{d\theta}E[W(\bf{X})|\theta] = \int_{\chi}W(\bf{x})\left[\...
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How does pymc3 posterior simulation work in this simple case without having the full conditional distributions?

I'm trying to estimate the posterior distribution of the gamma parameters alpha and beta given that my data comes from a gamma distribution and the priors I chose come from two uniform distributions. ...
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63 views

proof of Cramer-Rao lower bound

I am trying to understand the proof for this theorem from the book Casella and Berger (2nd ed.) page 336. $W(X)$ if any estimator for samples $X_1,\ldots,X_n$ on distribution $f(X|\theta)$. I notice ...
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How to normalize data which has started at different time periods?

So I have to review our business producers and have a long list of ones which have been signed up since 2017 with the company. We have continually hired more producers throughout the past three years. ...
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Variance estimator using mixture of scaled and unscaled data

Given two datasets: $X_1, \dots, X_n \sim N(1, \sigma^2)$ and $X_{n+1}, \dots, X_N \sim N(1, 2\sigma^2)$ My proposed estimator for $\sigma^2$ is simply a scaled combination of both classical ...
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20 views

Question about probability vs inferential statistics

I'm currently struggling with a question involving probability and statistics. I have this dataset of sales, and I was trying to make a probability of sales based on that dataset and the data that it ...
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How to obtain equation for evidence given equation for joint density of latent and observed variables (Variational Inference)

I am working through the following review paper: https://arxiv.org/pdf/1601.00670.pdf and would like to gain some insight into arriving at the formulae for joint density of latent and observed ...
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11 views

Causal Inference of Between-Group Differences in Time Series Data

I'm relatively new to time series data/causal inference (am working my way through Mostly Harmless Econometrics as we speak). Though, I'm still not sure how to appropriately test between-group ...
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7 views

Comparing countries with different proportions of available data and missing values

I have 200 countries, and each country has various subcategories with different number of data points and missing values. For example, I have a country with 100 data points, 40% of which are missing ...
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Does it make sense to build 2 models - one for prediction and one for inference?

I am considering using a Generalised Additive model for prediction and a Generalised Mixed effects model for inference to explain the relationship between variables, so I can play to the strengths of ...
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23 views

How to estimate differences between two normal means when variances are tested to be unequal

Let $X_1 X_2...X_n, Y_1 Y_2...Y_n$ be $\sim N(\mu_x$, $\sigma_x^2$), $\sim N(\mu_y, \sigma_y^2$). I want to estimate ($\mu_x - \mu_y$) and have used F-test to see that $\sigma_x^2$ $\neq$ $\sigma_y^2$ ...
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2k views

What are the worst (commonly adopted) ideas/principles in statistics?

In my statistical teaching, I encounter some stubborn ideas/principles relating to statistics that have become popularised, yet seem to me to be misleading, or in some cases utterly without merit. I ...
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1answer
28 views

Gamma-Poisson conjugate prior, posterior exploding?

I've been looking for simple code that can model ad clicks per day. Notionally, gamma-poisson would be a good conjugate prior. However, I'm finding that for slightly large daily click rate values, the ...
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Is there a metric for the gains curve?

as we do have a ROC AUC metric, I was wondering if there is a specific metric to evaluate the gain curve?

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