Stats Vocabulary / Short Notes
TBA
Table of contents
Group
In hypothesis testing, we often compare two groups of data.
- Control group: the group that does not receive the treatment
- Treatment group: the group that receives the treatment
Memorylessness
When a probability distribution modeling a “wait time” is memoryless, the probability of “waiting” for a certain amount of time until an event occurs is the same regardless of how much time has already passed.
$$ P(X > s + t | X > s) = P(X > t) $$
For example, if time $s$ has already passed, you’d think that the probability of waiting for another $t$ time until an event occurs would be different from the probability of waiting for $t$ time until an event occurs.
However, if the distribution is memoryless, the probability of waiting for $t$ more time until an event occurs is the same regardless of how much time has already passed.
Two common distributions that are memoryless are:
Parametric Models
A model is a set of distributions.
A parametric model is a set of distributions that can be parameterized by a finite number of parameters.
When $\theta$ is a vector of parameters in the parameter space $\Theta$, we denote parametric models:
$$ \mathcal{P} = \{ f(x; \theta) : \theta \in \Theta \} $$
Parameters of Interest and Nuisance Parameters
When we do statistical inference, we are often interested in only the subset of parameters (e.g. the mean of a Gaussian) which are called parameters of interest.
The remaining parameters that defines the distribution but are not of our interest are called nuisance parameters.
Regression Function
In supervised learning, we have pairs of data $(X_i, Y_i)$ for $i=1,\dots,n$.
A regression function is a function that maps the predictor variable $X$ to the response variable $Y$:
$$ r(x) = \E[Y | X=x] $$
Estimating the regression function is the goal of regression.
Prediction vs Classification
For a new predictor $X$, we want to predict the response $Y$.
If $Y$ is a continuous variable, we call it prediction.
If $Y$ is a categorical variable, we call it classification.
TBA
- skewnewss
- kurtosis