Monte Carlo methods are computational techniques that use a very large number of random samples to approximate results that are hard to calculate analytically. A system is simulated thousands of times with randomly varied assumptions, and the distribution of outcomes is analysed. Organisations use this for risk analysis, project scheduling or portfolio valuation. In AI, the methods are used in reinforcement learning and in tree search for games, among other areas.
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.
Reinforcement learning is a branch of machine learning in which an agent learns by trial and error. It acts within an environment, receives rewards for good outcomes and penalties for bad ones, and in this way develops a strategy that maximises its overall reward. Well-known examples include programs that master board games such as Go, robot control and the fine-tuning of language models based on human ratings.
Predictive modelling is the technical core of predictive analytics: example data with known outcomes is used to build a model that predicts a value or class for new cases. Common methods include regression, decision trees, random forests and neural networks. A model might, for instance, estimate a property price from floor area, location and year of construction. Before deployment it is tested on held-back data to detect overfitting.
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.
