Bayesian networks are graphical models that represent variables as nodes and their probabilistic dependencies as directed arrows. Using Bayes' theorem, they show how new observations change the probability of other events. One example is diagnostic support: estimating the most likely cause from observed symptoms. Their strengths are transparency and the ability to handle uncertain or incomplete data.
Causal inference covers methods for deriving cause-and-effect relationships from data rather than merely identifying correlations. It answers questions such as 'What would have happened if we had not taken this measure?'. Tools include randomised experiments such as A/B tests, causal graphs and statistical techniques for observational data. Example: checking whether a discount campaign actually increased sales or whether they would have risen anyway for seasonal reasons.
Naive Bayes is a family of simple classification methods based on Bayes’ theorem. They are called “naive” because they assume all features are independent of one another, which is rarely true in practice but often still produces good results. The methods are fast, need little training data and are particularly well suited to text. A classic example is the spam filter that sorts emails based on typical words.
A hidden Markov model (HMM) is a statistical model for sequences in which the actual states are hidden and can only be inferred from observable signals. It describes the probability of one state following another and of each state producing a given observation. HMMs were long the standard in speech recognition and part-of-speech tagging; today they are still used, for example, in bioinformatics and time-series analysis.
An expert system is a computer program that stores the know-how of human specialists as rules and facts and draws conclusions from them. It typically consists of a knowledge base and an inference engine that applies the rules. Expert systems shaped AI in the 1970s and 1980s, for example in medical diagnosis or configuring technical equipment. Their ideas live on today in rule-based checks and knowledge graphs.
