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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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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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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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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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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, ...
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Regression when the independent variables are counts by age group

I want to run a regression where the independent variables are counts of number of people in different age buckets (size 10 e.g 25-34, 35-44 etc...) and the objective is to understand the effect of ...
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How do you model a null hypothesis? [on hold]

I understand that, in hypothesis testing, the idea is that you create a sampling distribution under the null hypothesis and then you conduct an experiment. Your value falls on some part of that ...
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Does heteroskedasticity matter when estimating a regression using the entire population?

The F-statistic, t-statistics, p-values and standard errors of the estimated coefficients will all be incorrect in the presence of heteroskedasticity. However, does this even matter if I am working ...
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In the presence of heteroskedasticity, is quantile regression more appropiate than OLS?

..for understanding the relationship between a dependent and independent variables, given that quantile regression makes no assumptions about the distribution of the residual.
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How to infer difference of population proportion between two groups when proportion is small?

I have a dataset where the issue is of this form. There are two groups, Group A (N=5000) and Group B (N=1000). Let's say 5 people in Group A develop a certain disease, and only 2 in group B do. Then ...
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Approximate the critical region such that the size of the test tends to $\alpha$

Consider this question, Suppose $X_1, X_2, . . . , X_n$ is a random sample from an exponential distribution with mean $\lambda$. Assume that the observed data is available on $[X_1], . . . , [X_n]$,...
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Before using CV-selected Regression model for Inference, shouldn't model performance be evaluated on unused test set?

I just came across a biokinesiology paper that used some Machine Learning methods, but I think there is a flaw in their methodology. The authors had data on stroke patients and used Lasso regression ...
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Find UMVUE of $p^3$

Let $X_1, X_2, ..., X_n$ be a random sample from $Binom(1, p)$. I'm trying to find the UMVUE of $p^3$. Some thoughts: Apparently, $\bar{X}^3$ is not the answer, although it's the MLE of $p^3$. For ...
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MLE of the unknown radius

Consider this question, Suppose that $(X_1, Y_1),(X_2, Y_2), . . . ,(X_n, Y_n)$ are the coordinates of $n$ points chosen independently and uniformly at random within a circle with center $(0, 0)...
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Why is degree of freedom so important? [duplicate]

As far as I'm concerned, the degree of freedom is simply the number of linear equations need to be satisfied. However, it seems closely related to the statistical deduction. For example Dividing by ...
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Hypothesis testing with matrix of measurements

I need to test if a treatment has taken effect in a certain group of patients for which I make a measurement of the relevant variables before doing the treatment and afterwards. Usually, I would do a ...
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1answer
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Chi Square Analysis Throws Error - The internally computed table of expected frequencies has a zero element at (0,)

I am trying to see the association between two variables. I used Chi-Square analysis in Scipy package in Python. Here is the crosstab result of the two variables: ...
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If 'B is more likely given A', then 'A is more likely given B'

I am trying to get a clearer intuition behind: "If $A$ makes $B$ more likely then $B$ makes $A$ more likely" i.e Let $n(S)$ denote the size of the space in which $A$ and $B$ are, then Claim: $...
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Why is the maximum risk of an estimator independent of a prior distribution over the parameter?

One way of choosing an estimator $\delta(x)$ for data $X$ distributed as $P_{\theta}(X)$, where $\theta \in \Theta$ is: $$minimize \sup_{\theta \in \Theta} Risk(\delta(x), \theta)$$ In this case why ...
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How to Calculate the Most Important Customer Journeys

I have data that includes customers journey(essentially a path) towards either a conversion(home-loan application) or non-conversion(no application) or both. For example: ...
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1answer
51 views

Best Course of Study for Data-Science/Statistician Interviews [closed]

This is my first question here, so please pardon my gaffes. I am currently working as a Data-Scientist, a position which I worked up from Junior Analyst position.My bachelors is in Computer Science ...
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Does the UMP exist?

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 $g(λ)=\lambda(1 - e^{-λ})$ Is there a UMP (...
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High dimensional linear regression inference

I am reading through high-dimensional literature currently but I got confused. Especially about statistical inference with LASSO, anyone can clarify me the main difference among Van De Geer(2014)ON ...
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How do I estimate probability of success with no successes? [duplicate]

My $6$ friends and I tried buying tickets to a popular event. Everyone who wanted a ticket got a random number and if your number is less than or equal the number of tickets available, you can buy a ...
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Bayesian inference on binarized Poisson distribution

I have a variable that is Poisson distributed. Let's say I have a number of boxes each with a number of balls inside according to a Poisson distribution, with $\lambda=0.4$, (the average number of ...
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1answer
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Posterior predictive: what happens to integral over parameters?

Question I don't understand how when integrating over the parameters in the posterior predictive, the integration "disappears". It's hard for me to ask simply because I am confused, so here is an ...
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Optimizing multiple objectives with different scales

I have multiple objectives, such as $f(\mathbf{x})$, $g(\mathbf{x})$, and $h(\mathbf{x})$. I would like to find a set of $x$ that can $\underset{\mathbf{x}}{argmin} [ f(\mathbf{x}) + g(\mathbf{x}) + ...
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Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)

Example (the numbers are just for illustration). If A redhead is 3 times more likely to get skin cancer than a non-redhead. Redheads are 7% of the population. Then What percentage of skin cancer ...
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1answer
53 views

Binomial distributed random sample: find the least variance from the set of all unbiased estimators of $\theta$

Let $X_{1},X_{2},\ldots,X_{n}$ be random sample from $X\sim\text{Binomial}(2,\theta)$. (a) Find the least variance from the set of all unbiased estimators of $\theta$. (b) Find a sufficient ...
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1answer
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Normal distributed random sample: find the least variance from the set of all unbiased estimators of $\theta$

Let $X_{1},X_{2},\ldots,X_{n}$ be a random sample from $X\sim\mathcal{N}(0,\sigma^{2})$. (a) Find the least variance from the set of all unbiased estimators of $\sigma^{2}$. (b) Find a sufficient ...
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Exponential Distribution - Memoryless and examples

In several (introductory) statistics books we can see that they use an Exponential Distriubtion to model the time of failure of an electronic component. I understand that it got the appealing property ...
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Is there a standard way to Determine Sample Size when doing Bayesian Inference?

I am currently doing Bayesian Inference by using the BayesAB R library. I've observed that that sample size has a big impact on the posterior distribution. When doing Frequentist Hypothesis Testing ...
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Statistical technique to assess change in drug events over time - Interrupted time series analysis?

I have a dataset of the number of drug related events (e.g. arrest, non-fatal overdoses) a population of individuals have had. My aim is to see if a certain policy intervention that occurred on 1 June ...
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1answer
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Does bootstrapped regression allow for inference?

Assuming a linear model of $$ y = \beta_0+\beta_1x+\epsilon $$ I can construct a bootstrapped confidence interval for the estimate of $\beta_1$ by sampling with replacement from all of the $(x_i, y_i)...
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Multivariate Taylor series for moments of a random variable

In the expectation propagation for the generative aspect model, Minka uses Taylor series for the parameter estimation of the topics $p(w\mid a)$ eq 31. I am a little confused in the last equation. He ...
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Maximum likelihood parameters deviate from posterior distributions

I have a likelihood function $\mathcal{L}(d | \theta)$ for the probability of my data $d$ given some model parameters $\theta \in \mathbf{R}^N$, which I would like to estimate. Assuming flat priors on ...
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1answer
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Problem on conducting a hypothesis test with sample data

I'm trying to perform a statistical tests for the sample data(n=63) which is the effect of smoking for time(measured in minute) to fall asleep. First, I set a null hypothesis, there's no effect of ...
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If $X_1, \ldots X_n \sim N(\mu, \sigma^2)$ and we only observe $(X_1 - \bar{X}, \ldots, X_n - \bar{X})$, can we learn about $\mu$ or $\sigma^2$?

Suppose $X_1, \ldots X_n \sim N(\mu, \sigma^2)$ and we only observe $(X_1 - \bar{X}, \ldots, X_n - \bar{X})$, such that each observed point is now mean centered. Can we still learn about $\mu$ or $\...
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In Bayesian inference, why are some terms dropped from the posterior predictive?

In Kevin Murphy's Conjugate Bayesian analysis of the Gaussian distribution, he writes that the posterior predictive distribution is $$ p(x \mid D) = \int p(x \mid \theta) p(\theta \mid D) d \theta $$ ...
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Covariance Matrix: Unit Vectors

If you have a random vector X = [X(1), X(2), ..., X(n)], dimension dx1. The probability of any vector to be like: X(1) = [1, 0, 0, 0..., 0] is equal to 1/d. I'm trying to calculate the Covariance ...
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Understanding walds test output

In order to understand walds test Ive created a smoking dataset to check if gender or age has a greater impact on wether a person smokes or not. This code : ...
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29 views

Statistical test to compare the grades of students in different course-sections?

If we have multiple sections of the same course, and each section is being taught by a different instructor, what statistical test should we use to answer the following question: Are the grades of ...
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1answer
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How to derive the asymptotic distribution of t-statistic?

Let ${X_n}$ be an IID sample such that ${X_i} \sim N(\mu,\sigma^2)$. When both $\mu$ and $\sigma$ are unknown, we construct $t(\hat{\mu},s)=\dfrac{\sqrt{n}(\hat{\mu}-\mu)}{s}$, where $s$ is the sample ...
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How to solve the estimate population characters with sample text-mining?

I've recently learning text-mining, but none of my textbooks talk of inferential statistics; they talk about how to analyze collected data but hardly deal with how to estimate population data through ...
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Does Levy distribution has a conjugate prior?

I have searched a lot but can not find the conjugate prior of Levy distribution.
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estimate mean and standar deviation from proportions

I have normal distributed data but i don´t know the mean neither the stdv. What i know is that 67.9% of my data points are below 2500g and 0.21% are over 3000g. How can I estimate the mean and stdv ...
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Why is sufficient statistics/data reduction normally taught in Statistics?

In most upper-level classes on statistical inference, data reduction and sufficient statistics are normally taught, but without too much motivation. I understand sufficient statistics are important ...
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60 views

T Test or Chi Square?

There are 2 variables, City and No Of Matches won. Variables: 1City Sydney Canberra 2No Of Matches Won? Sydney: 200 out of 300 Canberra: 210 out of 300 Question: Is team Canberra ...
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How to statistically infer common pattern in text

Am trying to solve a problem where I need to infer common patterns in text for example, the data below, with bare eyes it can be noticed there is a pattern and that is ...
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Sufficiency of $|X|$ when $X\sim N(0,\sigma^2)$ without using Factorization theorem

Question: Given, $X\sim N(0,\sigma^2)$. By means of conditional approach show that $|X|$ is a sufficient estimator for $\sigma^2$. My Attempt: This problem is very easy if we use Fisher–Neyman ...