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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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How to show a UMVUE exists only if $g(p)$ is a polynomial of degree at most $n$?

Let $X\sim Bin(n,p)$. The problem is to show that a UMVUE can only exist for $g(p)$ if $g(p)$ is a polynomial in $p$ of degree at most $n$. For the case when $g(p) = \frac{1}{p}$ we can show that it'...
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Relation between prior odds and the prior distribution of each parameter

When comparing models using Bayes factors in Bayesian statistics, one typically present the prior probability of each competing model in odds form. How do those prior odds compare to the prior ...
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Can you perform statistical inference in a multi-armed bandit scenario?

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Multi-armed bandit is a technique to try different options and sample more ...
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Can sampling from a truncation of a random variable, rather than the original variable be more Blackwell-informative?

Suppose you are interested in finding the mean of a random variable. You have some prior belief of it and before sampling 1 observation, you can decide whether to sample from the original random ...
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16 views

Ratios and Probability

So I had this question in one of my classes and I wrote a super simple version of it and what I did. The only reason I'm asking is because either this question was super easy and I did it right, or I ...
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8 views

How can I find underlying relations between the entire set without using correlations? [duplicate]

These simple correlations show how each two variables are related, but this leaves open the question as to whether there are any underlying relations between the entire set. Give an example of how ...
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Consistent estimation and valid inference when performing regressions on data with differing levels of granularity

Imagine that a dataset has a combination of variables of differing levels of granularity (e.g. an international sample of firms containing both firm-level and country level information). There are $K$ ...
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For Granger Causality, what inference can be made if p is < 0.05 for ssr based chi2 test, but larger for everything else for a specific lag?

I am running a Granger causality test using statstools in Python, but am struggling to interpret the results correctly. It is my understanding that if the p value < 0.05, one can assume high ...
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20 views

Minimal sufficient statistics: how should we define and interpret it? [duplicate]

Through my studies of statistics inference, I came into the concept of minimal sufficient statistics. However, I find it a little bit cumbersome. Could someone provide me its definition and how should ...
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How to assess “reliability” for a non-stationary time series compared to a reference

I have two arterial pressure measurement devices, one of which is the reference. My goal is to assess reliability compared to the reference and the variables (demographics, passing time, etc.) ...
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27 views

relation among loss function / MLE / Bayesian estimation

I have read a lot of stuff on the relation between minimizing a loss function / maximizing the likelihood / choose a centrality measure of the posterior (Bayesian estimation); but I cannot see a clear ...
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47 views

Question about the equality of variances of two populations

When finding the confidence interval for the mean difference between two groups of sample, under which assumption about the equality of their population variances should we take if no information ...
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23 views

Find $k \in R$ such that $P\left(\max\left\{\frac{{S_x}^2}{{S_y}^2}, \frac{{S_y}^2}{{S_x}^2}\right\} > k\right)= 0.05$

Let $\overline{X}$ and $\overline{Y}$ sample means and ${S_x}^2, {S_y}^2$ unbiased estimators for the variance of 2 independent random samples of size 7 with normal distribution with mean unknown and ...
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20 views

Finding a confidence interval for shifted exponential distribution

Let $X_1,\ldots, X_n$ are i.i.d. random variables such that: $$f(x;\sigma ,\theta)=\frac{1}{\sigma}e^{\frac{-(x-\theta)}{\sigma}}, x\gt \theta$$ where $\sigma \gt 0 $ and $\theta \in R$ . a) if ...
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1answer
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If $X_i \sim U(\theta-\frac{1}{2};\theta+\frac{1}{2})$, show that $[X_{(1)},X_{(n)}]$ is a confidence interval [closed]

Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. a) Show that $[X_{(1)},X_{(n)}]$ is a confidence interval for $\theta$. b) Compute the ...
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20 views

Posterior convergence in expectation vs probability

Let's assume that we are doing approximate Bayesian inference and compute the convergence of our posterior estimate to the true value of the parameter using Wasserstein distance. Why posterior ...
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How does the most fitting methods for controlling for confounding variables depend on the nature of the dependent variable? [closed]

As far as I understand, people often adopt linear regression to regress out confounding variables (by fitting a linear model). Is this the right thing to do if the dependent variable is not continuous?...
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How can we cast an optimisation problem as an inference problem?

The main idea of variational methods is to cast inference as an optimisation problem. In the paper Junction Tree Variational Autoencoder for Molecular Graph Generation, the authors state that the ...
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11 views

Extracting likelihoods from generative model

I am looking for papers dealing with the extraction of explicit descriptions of probability distributions from a generative model. My use case is the following: I trained a GAN to generate samples ...
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12 views

How to find the p-value for this hypothesis test for two proportions?

I can't find the answer for this problem. In the answersheet it suggests that the Z-score is -20.5, but I can't understand how it's been calculated. : A 2012 survey of 2,254 American adults ...
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1answer
17 views

What is a factor in the context of Bayesian networks and inference?

I have come across the term "factor" in the context of Bayesian networks and inference (which I am not very familiar with). I've also heard of the expression "factor graph", which is an undirected ...
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Is my model selection procedure problematic for inference?

I'm not sure if this is "step-wise" model selection, but here is what I'm doing Decide a handful of models through exploratory data analysis. Fit the models to the data, and calculate their AIC. Pick ...
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1answer
54 views

Two-sided UMP test for exponential densities?

I'm struggling with a problem from Lehmann & Romano's book *Testing Statistical Hypothesis." Suppose $X_i$ is a random sample from $$f(x) = \frac{1}{b}e^{-(x-a)/b}\mathbf{1}_{x>a}$$ The ...
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18 views

Gaussian process where the output is constrained to be 0 or greater

I am trying my hand at simple GP regression and in my case, the output variable can be greater than or equal to zero. How can one constrain GPs, so that the predictions always stay in the specified ...
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23 views

Best statistical method should I use to calculate p value?

I'm comparing two different populations with unequal variances and non normal distributions using python. For sample #1 I'm drawing a random sample of n=30 from a population of 200. For sample #2 I'...
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12 views

How to infer the distribution of a statistic (Bayesian inference?)

I have a list of approximately 30,000 venues in a major US city. These venues hold all kinds of events, sports, conferences, concerts etc. I want to know the distribution of the 'capacity' of these ...
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25 views

How to compare two small sample proportions using R?

All the data is in the attachment below& The question is: Do these data provide convincing evidence that there is a difference in how good people are at recognising the backs and the palms of ...
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32 views

Why does this improper prior = constant?

MacKay has an exercise on using Laplace's method for a Poisson model: $$ p(r \mid \lambda ) = \frac{e^{-\lambda} \lambda^r}{r!}, \qquad p(\lambda) = \frac{1}{\lambda} $$ And he asks the reader to ...
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Conflicting unilateral and bilateral tests. Which one should I base myself on?

Suppose I have $H_0: \beta = 0$ vs $H_1: \beta \neq 0$. My data tells me that I don't reject the null, with a p-value of approximately 0.06. Then out of curiosity, since by the scientific theory one ...
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27 views

How does the frequentist approach to probability estimation work when the number of outcomes is greater than 2?

I've read Checking_whether_a_coin_is_fair and I'm trying to find a resource which generalizes the frequentist approach to the case where there are $k$ distinct outcomes and $n$ trials. Can someone ...
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1answer
41 views

Model performance and statistical inference

I want to build a statistical model with the aim of answering what is the effect of x1 on y. Even though my aim is statistical inference, I'll keep a separate test set. Let's say I estimate the ...
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Unbiased estimator ( Integral Issue)

$X_1, ... , X_n$ are iid with pdf $f(x|\theta) = e^{-(x-\theta))}I_{(\theta, \infty)}(x)$ it is easy to find the sufficient statistic which is $X_{(1)}$ $E_{\theta}[g(X_{(1)})]=$ $\theta$ (...
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1answer
34 views

How to find if people's preference is significant

I am trying to find out the wheither people prefer ads on Instagram or Facebook. As in are they more likely to choose x or y? Each person is given if you had to choose from and they pick x or y. ...
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38 views

Advantages of Wasserstein barycenters

Which are the advantages of using Wasserstein distance when averaging many probability distribution estimates? How does uncertainty of each affects the computation of the barycenter? Does the ...
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1answer
44 views

Unbiased Estimator based on Sufficient Statistic

suppose $X_1, ... , X_n$ are iid with pdf $f(x|\beta) = e^{-(x-\beta))}I_{(\beta, \infty)}(x)$ and the pdf of ( the smallest order statistic) $X_{(1)}$ is given by $f_{X_1}(x)$ = n $ *$ $e^{n(\...
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2answers
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If a group is more likely to do something, does that mean that individuals in the group are more likely to do something?

I have some large amount of people take test A. Based on the scores on test A, I assign them either to group A1 or to group A2. A1 are the people with scores at least 50% on test A, and A2 has people ...
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1answer
27 views

Interaction term to deal with heteroscedasticity

The variance in my dependent variable changes with a changing value in an important independent variable and is hence probably distorting the measured effect of the treatment. Can I combat this form ...
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Karlin Rubin Theorem UMP (Uniformly most powerful test ) Is it correct?

Suppose $X_1, X_2, X_3,\ldots, X_n$ are i.i.d. random variables with a common Poisson$(\lambda)$ distribution. $$X=(X_1, X_2, X_3,\ldots, X_n)$$ and $g(λ)=\lambda(1 - e^{-λ})$ , with $(λ>0)$ ...
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108 views

Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$

Given a random variable $X\sim Bin(n,p)$, where $p$ is known $p\in (0,1)$ , $n$ is an unknown positive integer and $x\in\{0,1,2,....n\}$, what is the maximum likelihood estimator of $n$? I ...
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23 views

Conditional Expectation of Poisson

Suppose $X_1$,$X_2$,$X_3$,.....,$X_n$ are i.i.d. random variables with a common pmf poisson(λ) (t = a value) How would you calculate the below without using intuition (I would appreciate if you ...
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6 views

model for regression with restricted dependent and independent variables

I am working on grade prediction. I have previous grades from the students and am planning to predict their future scores. Both past and future test scores are restricted from 0 - 15. When i run ...
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3answers
76 views

How to infer the parameter $p = f(n)$ of different Bernoulli distributions $X_{n}$?

I have a dataset corresponding to the results of independant Bernoulli trials. Each trial is associated to a number $n \in ]1;+\infty[$ and follows a Bernoulli distribution with parameter $p=f(n)=b + ...
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1answer
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50 views

Regression with bounded non-normal dependent variable

I'm wondering what a suitable regression model would be to predict a bounded, continuous, non-normally distributed dependent variable from a binary explanatory variable with partially crossed data. I'...
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1answer
38 views

Is a Type III statistical error just a subset of Type I or II error?

I have recently come across the idea of a type III error through discussion with colleagues. The definition they gave me was something along these lines: "Type III error occurs when you correctly ...
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1answer
29 views

Paired vs. Pooled Inference… When is it okay to pair samples?

I understand that paired tests are usually done on sampling distributions that have some sort of linkage. But is there a definitive way to differentiate when to use a paired t test vs. pooled? The ...
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29 views

Choosing appropriate statistical tests

I am trying to run stats on medical treatment data and would like your guys and girls help Goal: Comparing two trends of annual percentages for statistical significance. Is one decreasing due to the ...
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1answer
19 views

In the study of causal inference on networks, what implications does assuming unconfoundedness have on homophily?

I read in a book on causal inference on networks that: The unconfoundedness assumption does not rule out the presence of homophily, that is tendency of individuals who share similar ...
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1answer
20 views

Is the resulting function of plotting two variables imply that all other factors are being held constant?

Say, for instance, I plot two relationships (separately): (a) Share of income spent on food vs. household income; and (b) No. of houses in a unit vs. population of a city Then, for both (a) and (b),...
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Minimum variance of logit(p)

Let's say that we have $X_i \in Bin(n,p), i=1,...,n, iid$. How can we find the minimum possible variance of an unbiased estimator of $logit(p) = \log(\frac{p}{1-p})$ ? My thought is the following, ...