## Top new questions this week:

### Intuitive explanation of "Statistical Inference"

What is the cleanest, easiest way to explain someone the concept of Inference? What does it intuitively mean? How would you go to explain it to the layperson, or to a person who has studied a very ...

machine-learning inference intuition

### How can the square of an asymptotically normal variable also be asympotically normal?

The Delta method states that, given $$\sqrt{n} (X_n - \mu) \xrightarrow{d} N(0, 1)$$ then $$\sqrt{n} (g(X_n) - g(\mu)) \xrightarrow{d} N(0, g'(\mu))$$ I'm surprised that this can be true. As a ...

delta-method

### Linear Mixed Effect Model - random intercept and slope? Identifiability problems

I have a question regarding model building for a large dataset including about 5000 Subjects. I want to fit a LMEM including multiple variables and I have repeated measurements in time. But for some ...

mixed-model

### Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$

Question: Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$ My attempt has been by modifying the answer from this question: The Poisson distribution is a ...

estimation inference exponential-family umvue

### Bayesian interpretation of logistic ridge regression

Most textbooks (also this blog) cover the fact that ridge regression,  \hat y = \hat \beta X; \\ \hat \beta = \underset{\beta}{\text{argmin}}\ \ \frac{(y-\beta X)^T(y-\beta X)}{\sigma^2} + \lambda ...

### Exchangeability and joint distribution

The definition of an exchangeabilty for a finite sequence says that, if we have random variables $X_1,\ldots,X_n$, then for each permutation $\pi: \{1,\ldots,n\}\rightarrow\{1,\ldots,n\}$, the joint ...

self-study bayesian mathematical-statistics exchangeability

### Doubt regarding mixed modeling format

Say, I have a dataset that looks at how many times my 5 babies chases a cat around the house . I'm trying to estimate 'y' which is the number of times the cat runs one complete round around the house ...

regression mixed-model lme4-nlme modeling multilevel-analysis

## Greatest hits from previous weeks:

### Amazon interview question—probability of 2nd interview

I got this question during an interview with Amazon: 50% of all people who receive a first interview receive a second interview 95% of your friends that got a second interview felt they had a good ...

probability bayesian conditional-probability

### Why does a time series have to be stationary?

I understand that a stationary time series is one whose mean and variance is constant over time. Can someone please explain why we have to make sure our data set is stationary before we can run ...

regression time-series stationarity

### How to deal with Z-score greater than 3?

In a standard normal distribution how do I deal with a $Z$ value greater than 3? I know that z-score ranges form -3 to 3 Consider this one ... mean = 70, standard deviation = 4 I need to ...

normal-distribution

### What should I do when my neural network doesn't learn?

I'm training a neural network but the training loss doesn't decrease. How can I fix this? I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my ...

neural-networks deep-learning

### What's the difference between a confidence interval and a credible interval?

Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would ...

bayesian confidence-interval frequentist credible-interval fiducial

### Cohen's kappa in plain English

I am reading a data mining book and it mentioned the Kappa statistic as a means for evaluating the prediction performance of classifiers. However, I just can't understand this. I also checked ...

classification data-mining cohens-kappa

### What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?

continuous-data discrete-data

## Can you answer these questions?

### How do you train a clustering model?

This should've been a pretty simple question, but I still have a few questions so I decided to bring the discussion here. The thing is, I have a group of products, and the historical dataset looks ...

clustering algorithms unsupervised-learning

### Can use pseudo maximum likelihood method with mixed continuous and discret data in copula

For copula models there are different estimation ways. One of them, is Pseudo maximum likelihood method. In this method, the margins are estimated using empirical cumulative density function. Then ...

copula empirical-likelihood pseudo-likelihood