# All Questions

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### Identifying the correlation between a slope and a level

Throughout this post, I assume at least second moments exist. Consider a heterogeneous linear treatment effect model of the form: $$Y_i = \alpha_i + \beta_i X_i$$ where $\alpha_i, \beta_i$ are ...
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### What core topics would all statisticians be required to know?

I would like to know what topics are considered 'core knowledge' for a statistician. Please keep in mind I know very little about statistics. At my university, I hear statistics students discuss ...
92 views
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### On random variables made up of independent random digits

Some random variables can be expressed as a binary expansion whose digits are chosen independently at random; this is called a convolution. One example of this kind of random variable is the one for ...
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### Testing predictive power of a set of features

This is perhaps a typical setup in Bioinformatics: we need to build a model to predict a dependent biological variable (say $y$), given a large set of (usually genomic) features $X$ (which might not ...
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### Converting Categorical Data to Numerical by Sampling

Suppose I had sampled $1000$ individuals from a population in order to learn about two different questions, both of which had categorical, binary answers. (For the sake of this hypothetical, let's say ...
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### Identification of correlated errors with multinominal probit

Consider the multinational probit model where we observe $Y_i \in \{1, \dots, K + l\}$ with  \begin{align*} Y_i = l \Leftrightarrow Z_l&\geq \max(Z_1,\dots Z_{K +1}\} \qquad l \in \{1, \dots, ...
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### R - generate deviate using probability based on known occurrence of event

In R, I want to simulate an event using a probability $p$ based on a known occurrence $k$ of the event. If I have a population of $n = 100$ individuals in a given area, and I know over a period of ...
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### Bayesian Regression- Expectation Maximization

In Bayesian regression, we have $y_i=x_i^{T}w+\epsilon_i$ where $w \sim \mathcal{N}(0,\alpha)$ and $\epsilon_i \sim \mathcal{N}(0,\frac{1}{\beta})$. Inference of $\alpha$ and $\beta$ is done by ...
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### Is censoring data necessary to calculate the hazard ratio between 2 KM curves?

I would like to know if censoring data is necessary to calculate the hazard ratio between 2 Kaplan Meier (KM) curves. Censoring data is typically represented by small vertical bars atop of the curve ...
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### Let $X_t$ be a solution of a SDE. Does the set $\{X_t \in \{p\}\}$ has null measure?

This question was previously posted on https://math.stackexchange.com/questions/3981156/let-x-t-be-a-solution-of-a-sde-does-the-set-x-t-in-p-has-null-meas. I think this question is easy. However, I ...
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### Estimating the errors in parameters in the ordinary least square

I am reading the book An Introduction to Error Analysis by John R. Taylor. In Ch8: Least-Squares Fitting, he has derived expressions for parameters $A$ and $B$ in fitting the line $A+Bx$ to the set of ...