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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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Does UMVUE of $\frac{\theta_{x}}{\theta_{y}}$ exist? X $\sim$ exp($\theta_{x}$), Y $\sim$ exp($\theta_{y}$)

I have got the following variables. $$ X\sim exp(\theta_{x_{i}}), \ Y \sim exp(\theta_{y_{i}}) $$ and want to find the UMVUE of $$ \frac{\theta_{x}}{\theta_{y}}. $$ As the complete statistics ...
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Neyman–Pearson lemma in hypothesis testing [on hold]

as i have been working for hypothesis testing , i found a NPL(Neyman–Pearson lemma) i know about all things like non-randomized and randomized test , most powerful test , critical region etc. but i am ...
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Which corrections should I use? T-test for differences in means with different sample sizes and standard deviations

I have two samples, coming from different populations. One sample has 8,000 records, a mean of 5 and a sd of 0.5 The second has 1,500 records, a mean of 7 and a sd of 1.5 The distributions are close ...
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Bayesian Inference - determining probability of win [on hold]

We're running an experiment on our landing pages, showing different variants to users. We want to know which variant (page) performs best. We need 100,000 users for our experiment. That's going to ...
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Can one make statistical inferences from 6 patients?

Is it conceptually correct to make statistical inferences from a very small number of patients (even when using exact methods like Fisher's test, etc)? What do I have to look out for: power or p-value?...
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What statistical method will I use if I want to compare 10 caloric values of rice samples to a suggested amount?

We've conducted a comparative study on the caloric values of rice sample from different food stalls found within our university and we want to compare it to a suggested caloric value of per-meal rice ...
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Effective Sample Size for Weighted Samples

I have an MCMC sampler with weighted samples and I want to compute effective sample size at every step to determine sample degeneracy. I am using the following formula: $ESS = \frac{(\sum_{i=1}^N{w_i}...
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use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
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K - means, expected shape of the curve [closed]

I want to understand what happens as we increase the number of clusters using k- means, what is the expected shape of the curve showing the average distance between points and their assigned clusters? ...
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Maximum likelihood estimator of the parameter of randomness in Watts and Strogatz's model (1998)

According to the paper Menezes, M. B., Kim, S., & Huang, R. (2017). Constructing a Watts-Strogatz network from a small-world network with symmetric degree distribution. PloS one, 12(6), e0179120,...
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How is the posterior tail-area probability calculated?

I am currently using the CausalImpact package for some research and in this context I need to know and be able to explain, how the posterior tail-area probability is calculated in order to reproduce ...
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Inference and prediction with skewed response

Here below 2 questions. A typical linear model assumption says that the error terms are normal, which implies that the conditional distributions of Y given X=x are normal. The unconditional (marginal)...
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Missing data from an 2 arm AB test and proper inference methods

Suppose in a 2 arm AB test designed to assess the increase in spend caused by a promotional offer, we randomize customers to either test or control (i.e no offer or promotional offer). During the ...
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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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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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Consistency in uniform distribution

I know what consistency is but in options C and D both U and V are given whose covariance is quite difficult to find.
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Finding a critical region for a simple test, with PDF $f(x) = (\frac{x}{\theta} + \frac{1}{2}) \space \mathbb{1}_{(-1,1)} (x)$

I'm dealing with a simple inference problem which involve a PDF I've never dealt with before. We have $X_1, ..., X_n$ iid variables where $X_i$ has a PDF $$f(x) = (\frac{x}{\theta} + \frac{1}{2}) \...
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What if errors (residuals) follow other distribution rather than linear regression?

At first, sorry for the bad english. I'm not good at english because I'm a Korean. Recently, I'm studying linear regression. I've heard that errors always follow normal distribution because they are ...
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Checking if a coin is fair

I was asked the following question by a friend. I could not help her out but I hope someone can explain it to me. I could not find any similar example.Thanks for any help and explanation. Q: Results ...
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A question about selection of appropriate test procedure in Testing of Hypothesis

Q. Let (X, Y) be a paired response measured in continuous scale and obtained by administering a a certain drug on a patient. Let 'm1' and 'm2' denote the expected responses. Under suitable assumptions,...
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determine cutoff for independant variable based on outcome

I have very limited understanding of statistics so have failed to find the correct question to ask, let alone the answer. I have put multiple samples through a series of experiments where for each ...
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60 views

Probabilistic model: what's the probability of this model?

The above model is from Berkeley cs294-112 Page 23. It is said that $$ p(O_{1:T},s_{1:T}, a_{1:T}) =p(s_1)\prod_{t}p(s_{t+1}|s_t,a_t)p(O_t|s_t,a_t)\tag 1 $$ I'm quite confused about this solution: ...
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A question about Testing of Hypothesis

Q. Suppose for an experiment, the test for normality of an underlying population is accepted on the basis of a data set. To cross check the result, the experimener repeated the test with another ...
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39 views

Distribution function of a biased estimator

$f(y) = ay^{a-1}/θ^a, 0<y<θ$ $ \hat{\Theta} = max(Y_1, Y_2, . . . , Y_n).$ How do I find the $E[\hat{\Theta}]$ ? I'm trying to show that it's a biased estimator, then I'm going to find ...
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Sample from known function

I am wondering how is it possible to not be able to sample from a function that is known. E.g. suppose the expression of $f(x)$ is known but we need to approximate it in order to sample from it, why ...
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Bayesian Statistics -Prior and Posterior distributions

Please is it ever possible for the prior distribution to contain more information about parameter(s) than the posterior distribution? If yes, when can that occur? Is it the same concept as the ...
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Definition for lifted inference

What is the definition for lifted inference? As per my current knowledge, lifted inference is an inference technique that uses the rules of first-order logic. Is it true?
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Appropriate follow-up test in a 2-way within groups ANOVA

I have a 2 (time1 vs time2) x 2 (drug blood concentration: resting vs. post-exercise) within subjects design. I want to know if the difference between post-exercise and baseline is different at each ...
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Estimating the values of unknown subpopulation areas with only the known total population values in R

I probably should have posted it here first, but I have the full details listed on stackoverflow. https://stackoverflow.com/questions/54414182/is-randomforest-appropriate-to-figure-out-if-i-drop-a-...
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Hypothesis testing in non-parametric regression

Say I have two processes/time series, $X = (X_{t_{1}},X_{t_{2}},\dots , X_{t_{n}})$ and $Y = (Y_{t_{1}},Y_{t_{2}},\dots , Y_{t_{n}})$ observed at times $t_i$ for $i=1,2,\dots, n$ where $0 < t_1 <...
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Understanding probabilistic inference graphs

I am having trouble understanding inference graphs. In the diagram below I understand the graph on the left (forward graph) where the arrows describe the direction that data flows when training for ...
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Statistics of Diff in diff with optimal group

I am trying to run a diff in diff to measure the impact of a feature. I want to run the experiment per geo region and I have 90 regions. To run a proper diff in diff I should split in have the ...
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1answer
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Find Conditional probability distribution given conditions - Bayes Network

I'm taking a course on bayesian statistics and I'm having trouble with one assigment, it goes like this: Construct an example in which two variables have a common effect, and the presence of one of ...
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How to prove theoretically that Treatment Sum of Squares + Error Sum of Squares = Total Sum of Squares using the formula below?

How to prove theoretically that Treatment Sum of Squares + Error Sum of Squares = Total Sum of Squares using the formula in the picture?
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Sufficient set of features for distinguishing items [duplicate]

My input is a set of objects having different values with respect to a set of features (F1, F2, F3, F4, F5). The output should be a set of minimal features allowing to distinguish all these objects or ...
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Cramèr-Rao lower bound on the variance of an unbiased estimator

When is the variance of an unbiased estimator lower than the Cramèr-Rao lower bound ??
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Is it possible to estimate a population mean from a convenience sample?

I have data for which I can compute a sample mean. These samples are certainly not random. Is there any way to make an estimate of the population mean from a single biased sample?
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How do you reconcile a statistically insignificant logistic regression with a significant AUC?

Suppose I run logistic regression with one continuous predictor. The Wald tests of significance show a p-value that is not significant at the 5% level. Looking at the receiver operating ...
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How to determine a probability function that best represents the cost? [closed]

I have: 38 14020 38 16881 27 10679 36 15870 48 17608 So I have cases and total costs. How do I determine a probability function that best ...
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Existence of UMVUE of $\theta$ for sample from $\small{\frac{\ln\theta}{\theta-1}\theta^x\,\mathbf1_{0<x<1}}$?

Suppose $X_1,X_2,\ldots,X_n$ is a random sample drawn from a distribution with pdf $$f_{\theta}(x)=\small\frac{\ln\theta}{\theta-1}\theta^x\,\mathbf1_{0<x<1}\quad,\,\theta>1$$ Does there ...
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1answer
11 views

index and base year

I am creating a league table of a group of people with the aim to track their performance on 5 KPIs using indices. Base month value is set to 100. Out of 5 KPIs, an increase in 3 indices means good ...
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Stochastic Differential equation: CAPM

Let $R = (R_1, \dots , R_M)'$ denote a vector of excess returns of $M$ assets observed at $n$ time points, $0 < t_1 < t_2 < \cdots < t_n < T$, within a time span $T > 0$. We wish ...
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1answer
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Clustering circles with different radii with Gaussian Mixture Models

I am interested in clustering $N$ circles in the plane with varying radii using a Gaussian mixture model. The radius of each circle is an integer number $R_i\in\mathbb{N}$ determined from observation. ...
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INTERPRET A REGRESSION MODEL WHEN OUTCOME VARIABLE IS LOG TRANSFORMED [duplicate]

I have used a linear model between a log-transformed outcome variable and a group of predictor variables. In this model, the dependent variable is in its log-transformed state, and the independent ...
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Should I use statistical inference on this “sample”?

The dataset gets its data from thousands of individuals throughout the US who update the same spreadsheet of about 5000 rows. This dataset contains address for individuals and is updated by the ...
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Large datasets, deviations and noise/signal

The below excerpt mentions that 'large deviations' are more attributable to variance than to information. What does the author mean when he says 'deviations'? Deviations from what? And why would it be ...
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How to fit a superimposed distribution (\eg a Gaussian distribution + a Uniform distribution)

Suppose we have a set of independent observations of a random variable X, which is a Superimposition of two mutual independent random variables (i.e. X = Y + Z), Y follows a uniform distribution, ...
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Mann whitney u or independent t test?

I had to compare whether the two groups is somehow of the same distribution the problem is I only have 3 samples from each group in millimeters, say, Group A is 29mm, 32mm and 31mm while the other ...
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39 views

Bayesian hypothesis test: Type I and II errors

In a Bayesian hypothesis test between two alternatives A and B, what is the probability of making a type I and type II error? This question has been asked many times on this forum in various formats: ...
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Is expectation maximization an approximation algorithm?

Is expectation maximization an approximation algorithm? Does it give the exact solution?