The philosophy of statistics involves the meaning, justification,

utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophe ...

, use and abuse of statistics and its methodology, and ethical and epistemological issues involved in the consideration of choice and interpretation of data and methods of statistics.

Topics of interest

Foundations of statistics The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist ...

involves issues in theoretical statistics, its goals and optimization methods to meet these goals, parametric assumptions or lack thereof considered in nonparametric statistics,

model selection Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the ...

for the underlying

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

, and interpretation of the meaning of inferences made using statistics, related to the

philosophy of probability The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one be ...

and the philosophy of science. Discussion of the selection of the goals and the meaning of optimization, in foundations of statistics, are the subject of the philosophy of statistics. Selection of distribution models, and of the means of selection, is the subject of the philosophy of statistics, whereas the mathematics of optimization is the subject of nonparametric statistics. * David Cox makes the point that any kind of interpretation of evidence is in fact a statistical model, although it is known through Ian Hacking's work that many are ignorant of this subtlety. * Issues arise involving sample size, such as cost and efficiency, are common, such as in polling and pharmaceutical research. * Extra-mathematical considerations in the design of experiments and accommodating these issues arise in most actual experiments. * The motivation and justification of

data analysis Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, enc ...

and

experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

, as part of the scientific method are considered. * Distinctions between induction and

logical deduction Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false ...

relevant to inferences from data and evidence arise, such as when frequentist interpretations are compared with degrees of certainty derived from

Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...

. However, the difference between induction and ordinary reasoning is not generally appreciated. * Leo Breiman exposed the diversity of thinking in his article on 'The Two Cultures', making the point that statistics has several kinds of inference to make, modelling and prediction amongst them. * Issues in the philosophy of statistics arise throughout the

history of statistics Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. In early times, the meaning was restricted to information about states, particularly demographics s ...

Causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the ca ...

considerations arise with interpretations of, and definitions of, correlation, and in the theory of measurement. * Objectivity in statistics is often confused with truth whereas it is better understood as replicability, which then needs to be defined in the particular case. Theodore Porter develops this as being the path pursued when trust has evaporated, being replaced with criteria. * Ethics associated with epistemology and

medical Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care practic ...

applications arise from potential abuse of statistics, such as selection of method or transformations of the data to arrive at different probability conclusions for the same data set. For example, the meaning of applications of a

statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properti ...

to a single person, such as one single cancer patient, when there is no frequentist interpretation for that patient to adopt. * Campaigns for statistical literacy must wrestle with the problem that most interesting questions around individual risk are very difficult to determine or interpret, even with the computer power currently available.

Topics of interest

Notes

Further reading