statistics

The essence of statistical inference:
Given observed data $X$, we want to learn about the unknown parameters $\theta$ that generated it.

Two fundamental quantities:

• Likelihood $P(X\mid \theta )$ - probability of observing data given parameters
• Posterior $P(\theta \mid X)$ - probability of parameters given observed data

The posterior is what we’re after - it tells us what parameter values are plausible given our observations. We compute it using Bayes Theorem: posterior $\propto$ likelihood $\times$ prior.

Statistics is all about building models and testing them, separating signal from noise.

---

Descriptive/deductive: summarize data you have.
Inferential/inductive: generalize from a sample to the population.

Scale levels

• Nominal: Identity/Categorical
• Ordinal: Rank (1-5 stars - the diff between 1/2 stars is not necessarily the same as 4/5)
• Metric: Distance (meaningful distance - counts, …)
  • Interval: No true zero (10°C is not twice as hot as 5°C)
  • Ratio: True Zero, meaningful ratios (10K is twice as hot as 5K)

---

Humans are face are detectors with very high sensitivity and a bias towards false positives.

References

mathematics