3.1.P Philosophy of Data Analysis

Classical (Frequentist) Statistics

A statistical paradigm that defines probability as the long-run relative frequency of an event over an infinite series of identical, repeated trials.

Population Parameter

A true, fixed numerical value that describes a specific characteristic of an entire population.

Sampling Distribution

A theoretical probability distribution of a statistic obtained through infinitely repeating a sampling process from a population.

Bayesian Statistics

A statistical paradigm based on Bayes' Theorem that treats probability as a conditional measure of belief or evidence strength, treating parameters as random variables rather than fixed constants.

Prior Probability

The initial probability assigned to a parameter or hypothesis before any new empirical data is observed.

Posterior Probability

The updated probability of a parameter or hypothesis calculated after incorporating new empirical data.

Washing Out of the Prior

A phenomenon where the mathematical impact of an initial prior distribution diminishes as sample sizes grow, because big data overwhelms the prior's influence.

Exploratory Data Analysis (EDA)

A data-driven approach to analysis championed by John Tukey that prioritizes uncovering patterns, trends, and anomalies directly within the data rather than checking rigid theoretical assumptions.

Ensemble Methods

Data science techniques (such as bagging and boosting) that integrate predictions from multiple distinct models to improve overall prediction accuracy and robustness.

Positivism

A philosophy pioneered by Auguste Comte asserting that valid knowledge comes only from empirical observation and sensory experience, rejecting metaphysics and unobservable phenomena.

Anti-Realism / Instrumentalism

The stance that scientific theories do not necessarily describe an objective reality, but are merely useful instruments for organizing observations and making practical predictions.

Scientific Realism

The philosophical belief that an objective reality exists independently of human perception, and that successful scientific theories accurately describe both observable and unobservable entities in that reality.

Critical Realism

A branch of realism that accepts an objective reality exists but acknowledges that human perceptions, models, and theories of it are inevitably flawed, fallible, and approximate.

Structural Realism

The belief that scientific theories accurately capture the objective mathematical and structural relationships of the universe, rather than its underlying individual entities.

Entity Realism

The belief that unobservable entities (like atoms or causal mechanisms) objectively exist if we can manipulate them in experiments to consistently bring about predictable effects.

Fallacy of Affirming the Consequent

A logical fallacy taking the form: "If A then B; B is true, therefore A is true." In statistics, it refers to assuming a hypothesis is true simply because the observed data matches its predictions.

Deductive Reasoning (Deduction)

A top-down, rule-based approach to logic where specific conclusions are derived from a general premise or overarching law. If the premises are true, the conclusion must be true.

Inductive Reasoning (Induction)

A bottom-up approach to logic where general conclusions or parameters are inferred from specific observations, carrying an inherent "leap of faith" that the future will resemble the past.

Confirmation Theory

A subfield of philosophy exploring the logical rules and quantitative measures determining the degree to which empirical evidence confirms or supports a scientific theory.

Abductive Reasoning (Abduction)

A logic of discovery introduced by Charles Sanders Peirce that starts with an observed, surprising phenomenon and generates the most plausible, qualitative hypotheses to investigate further.

Inference to the Best Explanation (IBE)

A logic of justification developed by Gilbert Harman that evaluates a set of competing, rival models or hypotheses at the end of an inquiry to select the most coherent and accurate explanatory account.