Guozhen AIGlobal AI field notes and model intelligence

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English editions of Guozhen AI articles. The text is localized for global readers while the original diagrams, screenshots, and code examples remain aligned with the Chinese source.

Simulate coin flips

Don’t stop learning probability theory at rote memorization of formulas. The most effective approach is to validate your intuition with small simulations—and then interpr...

20. Probability for AI Beginners: Summarizing Model Evaluation & Selection + Further Learning Resources

Model selection shouldn’t simply chase the highest score. To identify a robust, production ready solution, you must compare baselines, validation strategies, error prone...

Load dataset

Model evaluation is itself a probabilistic problem: prediction scores, decision thresholds, and misclassification costs jointly determine whether a model is fit for use.

Define x-axis (conversion rate from 0 to 1)

When implementing Bayesian methods, the most critical step is to clearly separate prior assumptions from empirical evidence—and then assess whether the resulting posterio...

17. Bayesian Updating: Priors and Posteriors

Bayesian updating is not a one time formula—it is an ongoing process of assimilating evidence. Today’s posterior can serve as tomorrow’s prior.

Understanding Bayes' Theorem

Bayes’ Theorem updates beliefs in light of new evidence. It combines three key elements: what we believed before seeing the evidence (prior), how strongly the evidence su...

15 Practical Applications of the Central Limit Theorem

The Central Limit Theorem (CLT) explains why sample means from many distributions tend to approximate a normal distribution. It forms the theoretical foundation for confi...

Set random seed for reproducibility

The Law of Large Numbers tells us that, given a sufficiently large number of repetitions, the sample average will gradually converge toward the theoretical expectation—bu...

Compute variances

Covariance measures whether two variables change together ; correlation removes the influence of scale. A high correlation does not imply causation.

Define random variable X

Variance measures how much outcomes fluctuate around their expected value. Two models may share the same expectation, yet differ markedly in variance—leading to entirely...

Die face values

The expected value is the long run average weighted by probabilities—it need not be an outcome that actually occurs in any single trial. It serves well to measure overall...

Set parameters

The geometric distribution models how long we must wait until the first success . It is appropriate for “waiting time” problems—not for counting how many successes occur...

Compute Poisson probability

The Poisson distribution is well suited for modeling the number of occurrences of an event within a fixed interval of time or space—such as arrivals, clicks, or failures.

Set mean and standard deviation

The normal distribution is centered at its mean and characterized by its standard deviation, which quantifies dispersion. Many types of measurement errors and sample mean...

Visualize the binomial PMF

The binomial distribution applies to a fixed number of repeated trials, where we care specifically about how many times success occurs . Its key requirements are:

Set parameters

The PDF describes density ; the CDF describes cumulative probability . In continuous distributions, the density value at a single point does not equal the probability of...

Simulate 1000 die rolls

For discrete variables, we examine the probability at each point ; for continuous variables, we examine the area under the curve over an interval. The computational metho...

Define possible values of random variable X

A random variable transforms uncertain experimental outcomes into computable numbers. It serves as the bridge from events to distributions, expectations, and model evalua...

Set seed for reproducibility

Conditional probability is not merely ordinary probability with an extra symbol—it redefines the scope of discussion given that a particular event has occurred.

Define the sample space

The sample space comprises all possible outcomes of an experiment; an event is a subset of that space. For many probability problems, the main difficulty lies not in comp...

Define counts

Probability first addresses a fundamental question: Among all possible outcomes, how likely is a particular event to occur? To make sense of probability formulas, we must...