Sekamalli

Sekamalli is a Finnish term used to describe statistical models that represent data as arising from a mixture of several underlying subpopulations. In a sekamalli, the overall distribution of the observed data is expressed as a weighted sum of component distributions, with each component having its own parameters. A latent (unobserved) variable indicates which component generated each observation. This framework allows modeling heterogeneity in the data without requiring explicit knowledge of subpopulation membership.

Commonly used components are Gaussian, yielding a Gaussian mixture model, but other families such as Poisson, Bernoulli, or exponential distributions can be employed depending on the data type and application. Finite mixture models assume a fixed number of components, while more flexible, nonparametric variants (often called Dirichlet process mixtures) allow the number of components to grow with the data.

Estimation and inference in sekamallit typically rely on iterative algorithms. The expectation–maximization (EM) algorithm is widely used to estimate mixing proportions and component parameters, given a specified number of components. Bayesian approaches using Markov chain Monte Carlo methods provide alternative inference, including uncertainty quantification for the number of components. Model selection involves choosing the number of components using criteria such as AIC or BIC, or through cross-validation.

Applications of sekamallit are broad, including clustering, density estimation, anomaly detection, image and speech processing, and genetics. They enable probabilistic assignment of observations to subpopulations and can accommodate complex data structures with flexible component distributions. Sekamalli is distinct from mixed-effects models, which account for random effects in hierarchical data, representing a different modeling paradigm.