Bayesian methods

A machine learning thing. Related to Naive Bayes classifier.

It's one way to approach a classification problem.

BTW, terminology is varied. The term classifier can be meant as:

1. a mathematical function that maps input data to a category
2. an algorithm that implements classification, esp. in a concrete implementation

In stats, classification is often done via logistic regression, speaking of explanatory/independent vars, and the possible categories are termed outcomes. In ML, observations are often known as instances, the explanatory vars as features, and the possible categories are termed classes.

Bayesian methods

datacolada.org/78

This is an alternative to classical hypothesis testing. You can select models based on Bayes factor.

The aim of the Bayes factor is to quantify the support for a model over another, regardless of whether these models are correct.

When the two models are equally probable a priori, so that node:internal/modules/cjs/loader:1228 throw err; ^ Error: Cannot find module 'katex' Require stack: - /home/kept/private-dotfiles/.config/emacs/texToMathML.js at Module._resolveFilename (node:internal/modules/cjs/loader:1225:15) at Module._load (node:internal/modules/cjs/loader:1051:27) at Module.require (node:internal/modules/cjs/loader:1311:19) at require (node:internal/modules/helpers:179:18) at Object. (/home/kept/private-dotfiles/.config/emacs/texToMathML.js:1:15) at Module._compile (node:internal/modules/cjs/loader:1469:14) at Module._extensions..js (node:internal/modules/cjs/loader:1548:10) at Module.load (node:internal/modules/cjs/loader:1288:32) at Module._load (node:internal/modules/cjs/loader:1104:12) at Function.executeUserEntryPoint [as runMain] (node:internal/modules/run_main:173:12) { code: 'MODULE_NOT_FOUND', requireStack: [ '/home/kept/private-dotfiles/.config/emacs/texToMathML.js' ] } Node.js v20.18.1 , the Bayes factor is equal to the ratio of the posterior probabilities of M₁ and M₂.

When the priors are different, it is the following ratio. Pr(M₁|D) is simply the aforementioned posterior probability of M₁.

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an advantage of the use of Bayes factors is that it automatically, and quite naturally, includes a penalty for including too much model structure.[6] It thus guards against overfitting. For models where an explicit version of the likelihood is not available or too costly to evaluate numerically, approximate Bayesian computation can be used for model selection in a Bayesian framework,[7] with the caveat that approximate-Bayesian estimates of Bayes factors are often biased.[8]

Other approaches are:

• to treat model comparison as a decision problem, computing the expected value or cost of each model choice;
• to use minimum message length (MML).

Bayesian methods

The Bayesian structural time series (BSTS) model is a statistical technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other applications. The model is designed to work with time series data.

Difference-in-differences models[1] and interrupted time series designs[2] are alternatives to this approach.

The model consists of three main components:

1. Kalman filter. The technique for time series decomposition. In this step, a researcher can add different state variables: trend, seasonality, regression, and others.
2. Spike-and-slab method. In this step, the most important regression predictors are selected.
3. Bayesian model averaging (ensemble learning). Combining the results and prediction calculation.