# 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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### Testing significance of a random effect glmmADMB model

Below is the output from a model of novel object test scores fit with the nbinom1 (quasi-Poisson) option in glmmADMB. I used ...
719 views

### Finding UMVUE of $\theta e^{-\theta}$ where $X_i\sim\text{Pois}(\theta)$

Suppose $X_1, X_2, . . . , X_n$ are i.i.d Poisson ($\theta$) random variables, where $\theta\in(0,\infty)$. Give the UMVUE of $\theta e^{-\theta}$ I found a similar problem here. I have that the ...
182 views

### How to go about selecting an algorithm for approximate Bayesian inference

I am wondering if there are any good rules of thumb for how to go about selecting an approximate inference algorithm for a problem/model (specifically when exact inference is intractable)? When you ...
755 views

### Simple linear regression with a random predictor

We understand a SLR model as $$y_i = \alpha + \beta x_i + \varepsilon_i$$ with $\varepsilon_i$ i.i.d with equal variance. Suppose I have two instruments measuring a common entity, say, density of ...
198 views

### Resampling within a survey to account for missing data

Suppose I have survey responses that look like this: ...
317 views

### Does sampling from a large dataset lead to correct inferences?

Say we have some population, and we obtain a "representative" random sample of that population, $(y_i, x_i)_{i = 1}^n$, where $n$ is very large (millions) and $x_i = (x_{i1}, x_{i2}, ... x_{ip})'$ is ...
816 views

### Intuitive explanation of desirable properties (Unbiasedness, Consistency, Efficiency) of statistical estimators?

From literature I understand that the desirable properties of statistical estimators are Unbiasedness - we want the estimator to give the correct parameter value theta, on an average, irrespective of ...
143 views

### Drawing conclusions of several inferences with the same data in one study

In a sample size of 100, we identified the existence of two attributes A and B. Our goal is to assess whether there is any ...
485 views

### What is the problem with overdifferencing a long memory time series?

Suppose I have a long memory time series and instead of using fractional differentiation I take a first difference. What kind of problems am I going to run into? Is there any advantage to doing the ...
134 views

### Time series forecasting using statistical tools

I'm building a system which needs to poll some feed of articles in a smart way. When polling, I can only know the number of new articles (could be $0$ - no new articles). I don't have the info when ...
5k views

260 views

### Sufficient statistics for $\mu_1 - \mu_2$

If $X_1, ..., X_n$ is a random sample from $X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $\sigma^2$ is known,...
128 views

### Explanatory variables may bias predictions

I' m asking this question out of sheer curiosity, my teacher was not able to explain it. If I'm using logistic regression with categorical variables they are coded like {1,2,3}. I guess it wouldn't ...
120 views

### Likelihood function when $X\sim U(0,\theta)$

Let $X_1, ..., X_n$ be $i.i.d$ random variables, uniformly distributed over $(0,\theta)$. Derive the likelihood function given the sample $x_1, ..., x_n$. Answer The likelihood function is: \begin{...
231 views

### Unbiased estimator of $\lambda(1 - e^\lambda)$ when $x_1,\ldots,x_n$ are i.i.d Poisson($\lambda$)

Suppose $x_1, x_2, x_3,\ldots, x_n$ are i.i.d. random variables with a common Poisson$(\lambda)$ distribution. I was trying to find an unbiased estimator for $\lambda(1 - e^\lambda)$, but I could not ...
650 views

### Differences between prior distribution and prior predictive distribution?

While studying Bayesian statistics, somehow I am facing a problem to understand the differences between prior distribution and prior predictive distribution. Prior distribution is sort of fine to ...
3k views

### How to infer correlations from correlations

I have a question regarding correlation inference. Consider, I have two sets of variables X and Y. For an x element of X I know the correlation to an unknown variable z. I also have the covariance ...
167 views

### Definition of Statistic

I keep seeing conflicting definitions of a statistic. Is a statistic a random variable such that it is a function of the random variables of a random sample? Or is it the value of the function of the ...
1k views

### Bayesian vs. frequentist estimation

I don't really understand the connection between bayesian to "normal" frequentist estimation. Suppose we want to estimate the expected value of a population given a sample. In frequentist statisics ...