# Reading for philosophy of statistics / statistical inference

Had a quick look around and although there are some questions on statistics there is not one that asks this specific question.

I am about to return to university to study a masters in a statistical discipline (statistics methods in ecology).

Who/what can I read that will help me answer the following questions:

• How does statistical inference differ from other types of scientific knowledge?
• What are the philosophical positions that underpin a justified belief in the results of statistical analysis?
• Are there any philosophical differences between 'weak' statistical inference and 'strong' inference.

By weak inference I mean the kind of result that often appears in the field of ecology or the social sciences. By strong inference I mean large hadron collider experiment proves existence of higgs boson beyond reasonable doubt type of result. Is there a philosophical difference or is it simply a matter of degree?

I am not looking for the answers to these questions here, just where I can do some reading on the topic.

It is a brand new area for me so if my questions are not well formulated for a sensible answer then please let me know and I'll edit the question as best I can.

• Meillassoux and Ayache may be relevant here... – Joseph Weissman Aug 24 '16 at 17:15
• Good question; I don't know anything that could help, but I would suspect that its more than a difference of degree. – Mozibur Ullah Aug 24 '16 at 19:12
• All empirical knowledge is believed to come from hypothetico-deductive inference, statistical inference is a quantified version of that. The main philosophical interpretations are frequentism, propensitivism and Bayesianism en.wikipedia.org/wiki/Probability_interpretations On weak vs strong tests see Mayo's Severe Tests and Methodological Underdetermination phil.vt.edu/dmayo/personal_website/EGEK_6.pdf – Conifold Aug 24 '16 at 23:29
• Try googling "fuzzy logic in statistical reasoning", or "fuzzy logic degrees of truth", e.g., en.wikipedia.org/wiki/Degree_of_truth , or just "fuzzy logic", e.g., en.wikipedia.org/wiki/Fuzzy_logic Instead of true/false, statistics corresponds to many-valued logics with truth values between 0 and 1, which is more-or-less what's modelled by fuzzy logic. – John Forkosh Aug 25 '16 at 6:54

One topic at the intersection of statistics and philosophy of science is causation, and specifically, how to establish causal claims based on probability and statistics, both experimentally and observationally.

Researchers in this area include Judea Pearl, Clark Glymour, Richard Scheines and Peter Spirtes.

You might find this article on the SEP on the philosophy of statistics useful in tackling some of the questions; however I think the wider questions lie outside this area:

The evaluation of models touches on deep issues in the philosophy of science, because the statistical model often determines how the data-generating system under investigation is conceptualized and approached (Kieseppa 2001). Model choice thus resembles the choice of a theory, a conceptual scheme, or even of a whole paradigm, and thereby might seem to transcend the formal frameworks for studying theoretical rationality (cf. Carnap 1950, Jeffrey 1980).

The remark attributed to Carnap/Jeffrey seems to suggest and perhaps corroborate that the difference between 'weak' & 'strong' inference is more than a matter of degree; the articles touched on are mentioned in the bibliography and may be useful to look at.

Ian Hacking is a philosopher who has written a lot about stats. More recently Nancy Cartwright (a philosopher) has written some very interesting stuff against Randomized Controlled Trials as the Gold Standard for research.

• Can you please add a reference for the randomized controlled trials paper? That is interesting – Simon Dirmeier Sep 4 '16 at 10:26