[PoSt] Philsophy of Statistics


Dark Knight
Probably I would be the wrong person to start a discussion like philosophy of statistics. Understanding models, programming, and bit of problem solving were my main interest to learn statistics. I never cared about details of the inference or philosophy aspect. I realized that it would be time consuming if I started to understand all statistical models, exploring all aspect of certain programming languages, technological updates ... etc. I would say we can't avoid those. It is possible that introducing a new model or acquire specific skill define a career path.
I consider the best way is by knowing about the abstract or philosophy side. Because this makes perfection on any of our attempts.

I recently read two articles on philosophy side. Technologist to Philosopher and A Socratic dialogue on mathematics. I found it interesting and motivating(second one mainly).

I would like to have discussion on PoSt. I actually believe that there is no difference in PoSt and PoS(philosophy of science). We could follow classic articles/books/personal experience to start our discussion.
I am not sure which is the best medium to discuss philosophy related questions. I feel group -Philosophy of statistics would be a nice choice. Already bugman and I are posted one question in the group.

Please post your suggestions.
I spent years studying ontology and epistimology (which is what you are discussing I think). Mine can be boiled down to, if I want to eat I need to run this model correctly. Not as interesting as say logical positivism, but it works as you get older.

There are actually two major elements of this dispute traditionally. Positivism versus post-positivism (which deals primarily with the nature of knowledge, but commonly how you achieve it) and how science changes, notably Kuhn's paradigm.

Good luck on this one :p
I'm a philosopher who dabbles in statistics, and I'm very interested in this discussion. FWIW, I think Kuhn is the most over-represented, misinterpreted voice in the Philosophy of Science in the past half-century. But we can talk about that later ;)

As far as suggestions go, I am intrigued by the book you suggest. You may also want to consider Ian Hacking's (2006) The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference (2nd Ed.).
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Dark Knight
Thanks noetsi, Smooth john. I am relatively new to this subject. I heard about kuhn and poppers work on philosophy of science. I will try to read that now.

I guess I get the Ian hacking's book from our library. It is nice that Amazon also started preview of the book.
Kuhn was not dealing with statistics per se (not sure he ever worked in that area). He was talking about how knowledge is achieved or perhaps better about how basic understandings of reality, basic paradigms changed particularly in science. The ongoing dispute in that area (well one as there are many) is whether knowledge is acquired incrementally or in dramatic revolutions. To me Kuhn comes down squarely in both camps arguing essentially that understanding of reality slowly changes and then at a certain point there is a dramatic change, one tied however to this build up. In my area of research, public management, this is called punctuated equilibrium. Note however, that is my interpretation of him and I don't come from a camp that stresses theoretical or philisophical approaches.

We want to make the trains run on time and aren't all that confident of in depth understanding of reality, of basic framework that ungirds research. I think statistics in the broad range of academic discourse tends to that as well. Broad theories of statistical reality appear to me (as a non-statistician) to be of limited importance. The focus is more on creating methods that achieve some limited purpose - philosophy is less emphasized.

I think the hard sciences, which I put statistics into, has been less influenced by the attack on positivism that has dominated academics since the sixties. But a lot of that I think is limited interest in such philisophical issues among statisticians. Dason will probably tell me I am crazy :p


Probably A Mammal
vinux, are you on the TS dropbox share yet? I have something there you might like to read.

Anyway, people talk about PoS they usually spit out positivism, Popper, and Kuhn. I agree that Kuhn is highly misinterpreted. I think he had a brilliant perspective on PoS, but his work was largely best exemplified by the historical synopses he did. People who criticize him tend to focus on wacky ideas like incommensurability (to which Feyerabend seemed to focus more on, to me). Kuhn's real contribution as I see it is identifying the historical role of institutional changes in the scientific culture like the inclusion of measurement and quantification in experimental design. Lakatos sort of did the same thing from a more abstract view in the development of theoretical ideas (especially in mathematics).

In any case, the issues with positivism, etc., aren't really important in modern philosophy of science. The idea that we could rigorously lay out science in some formal terms is clearly ridiculous. The more interesting subject is trying to identify the place of subjectivism in science--what role does interpretation play in the conclusions we draw from scientific experiments?

Noetsi is right that knowledge is an important part of PoS. However, that sort of sweeps a grand amount of detail under the rug and dispatches the interplay between ontology and epistemology: e.g., does having a justifiable methodology that allows us to trust the conclusions of experiments as relaying knowledge about the phenomena under investigation also entail that we're making ontological assertions? Again, interpretation plays a big role here because both in terms of method, theory, and pragmatics, the results of any experiment can be interpreted in numerous ways and the very theoretical foundation that supports a methodology presumes certain things about the way the world is (we don't want to draw circular conclusions here!). The whole issue of paradigms and revolution is neither here nor there. Frankly, most philosophers in this area I've read agree that whatever dramatic shifts we've seen were in part due to large changes in scientific methodology. Of course you can talk about dramatic changes when you move from non-measurement to measurement scientific methods or you can talk about incommensurable interpretations when comparing Greek theorizing to modern scientific theories. But I'd rather stay away from getting into the details of that.

I don't know what would be considered a philosophy of statistics, largely because statistics is not necessarily a theoretical science. It is a methodology. It's theory is mathematical. It's practice can be taken as an art, in some regards. When we talk about the philosophy of biology or physics, we're talking squarely about the theories on which they are founded. Now, I am happy to jump on the philosophy of mathematics bandwagon. It's still something I'm interested in majoring in. But let's be clear, there are some distinct differences between philosophy of science as a study of the practice of science and the philosophy of statistics as a study of the practice of, say, data inquiry. I say data inquiry because if we look at statistics mathematically, we're really just going to sit here talking about mathematical/probability theory. That's not to say there aren't interesting questions, but I think there are distinct topics. I don't think that the topics that are of interest to the philosopher of science or of mathematics are really pertinent to those of statistics, because where PoSt comes in, we're really talking about PoS with statistical/inductive methodology. Difference.

With that said, the interests we have of statistics as a methodology with its relationship to the philosophy of science are squarely found in the philosophy of science. Already mentioned was the great Ian Hacking. He's done great work on inductive methods in science. Wesley Salmon has also explored methodology, but with an emphasis on causality (see Causality and Explanation). Then it goes without saying that Nancy Cartwright is especially lucid in explaining the way methods, especially statistical and econometric, play a role in science (take your pick, I haven't been let down by any of her books! But a good start is How the Laws of Physics Lie, and an advanced read is Hunting Causes and Using Them. We can also get pretty specific, like the philosopher of biology, Elliott Sober, does a good review of statistics role in interpreting facts in the first chapter of Evidence and Evolution. I also found Hausman's anthology on The Philosophy of Economics useful in exploring related topics with an economic emphasis.

The point of this listing is that if we're going to talk about PoSt, then we might want to do so in terms of methodology as has been the focus in all these areas of the philosophy of science. This doesn't diminish its importance or the interesting topics that can be covered, as the books above detail. We just have to respect what role statistics plays in scientific inquiry and how that can be explored in the philosophy of science. We can certain get abstract and talk about inductive reasoning (Hacking is good at this, among others both classic and contemporary) or we can get specific and focus on statistics as a mathematical inquiry. That realm of inquiry, though, should be made explicit when we talk about the various topics to follow, whatever those may be.

Addendum: There are a few particularly statistical questions that arise regarding statistical methodology and (inductive) inference. I'm reminded of this by Sober's work. The most important being the role of evidence in our inferences. But this isn't necessarily statistical, per se. It's brought up in pretty much every book I listed above. Where it's particularly statistical as in Sober's book is that evidence (data) plays a role through our methodology to give us a certain basis for drawing conclusions (e.g., confidence intervals). The more obvious one is the philosophical position we take regarding our interpretation of method, which in statistics is usually summed up as the frequentist vs Bayesian positions (I like Sober's focus on likelihoods). This doesn't deviate from my premise that PoSt is a look at method, but it does reveal there are important philosophical issues involving knowledge and interpretation about that method qua method. I don't think we can take these issues as philosophical questions of theory, per se, because there is no theoretical basis that the method is Bayes or about frequency. You can take one method, one conclusion, and simply interpret it from both positions sometimes. Neither position provide a theory that draws that interpretation for us. This, however, requires a bit of depth regarding what a theory means in a technical and philosophical sense.


Dark Knight
Bryan, I have shared two articles in the Dropbox. Thanks for the reference.

I am more interested in philosophy discussion in the statistical literature. It would definitely be about modelling approach or modelling explanation. I would love to see PoS problems we face in our workplace. I would reply to you all once I read the basics of PoS.


Probably A Mammal
So I noticed. Thanks! Comprehensive anthology there.

Anyway, it begs an important question that PoS problems arise in practice ('in the workplace'). That is, unless you work at the forefront of statistical methodology where you need to justify new ground! That is not to say we cannot do as you are interested in, discuss modeling approaches and their explanations. But running up against the various ways we can interpret our models and the larger body of philosophy involving the science we are in (for me that tends to be social and economic) are really 2 different issues, which is what I was driving at. There are concretely statistical issues to talk about (e.g., should we take a frequentist or Bayesian interpretation of our results? Should we use methods specific to those paradigms?) and then there are the broader PoS topics (e.g., does this model reveal something causal or about the truth of economic phenomena as seen in the world?) or we could go very abstract (can inductive reasoning actually provide new knowledge about the world?).

So when you say "in our workplace," what do you have in mind? The more practical issues we face regarding our models or the broader issues behind the assumptions of our scientific enterprise and methods?


Dark Knight
I do research in a management institution. So I get chance to meet scholars in humanities, public policy, economics,..., etc. I attend some of their conferences and sometime I feel silly about their experiment and analysis. May be I am not good at qualitative analysis. Anyway I used to get chance to involve in debates. I have posted one question in the group. I am a novice in the area of PoS. I am not sure those has anything to do with philosophy.


Probably A Mammal
I like the article you put in there. It takes a look at statistics abstracted from where its methods are applied (e.g., science or law) and focuses on the ways in which our assumptions and interpretations can influence the method as method (and ties it together at the end). For instance, he talks about the construction of a probability model, and many philosophers from Carnap to Hacking have lots to say on this fact alone. Is probability subjective? What about physical probability (there's only absolute outcomes--either it happened or it didn't: 0 or 1)? I think he begs a question in the abstract in saying "Inference is only of value if it can be used." What does he mean by "used" here? It's sophistry if it means the inference plays a role thereafter (e.g., in supporting a theory), and it seems wrong if we're just going to say an inference is only valuable when it's pragmatic. Nevertheless, it looks to be a good bit of research. I agree that statistics (theoretically) relies nearly entirely on probability, which is largely (as far as I'm concerned) mathematical. Nevertheless, even in mathematics the connection to "uncertainty of what" has to be asked, and that's where we see these philosophical paradigms arise. Uncertainty in a (mathematical) vacuum is moot. But do those probability models apply everywhere? Do they apply to subjective situations (subjective priors?) or physical (absolute outcomes) reality? These questions, I argue, require the broader PoS that I alluded to earlier. This is why I see statistics and any PoSt to be focused on methodology qua method, not as theory. Where that arises, we move immediately into non-statistical realms about how we interpret information or assumptions we make about the world, but I digress.
Bryan, I think there is some sense to beginning with apparently naive questions.

1. When we "do" statistics, what are we doing?

2. Do statistics tell us something about the world, or something about our way of dealing with the world? Is there a difference?

3. Do statistics place different ethical demands on us than do other types of information?

These are very basic, but nontrivial questions.
I don't know what would be considered a philosophy of statistics, largely because statistics is not necessarily a theoretical science. It is a methodology. It's theory is mathematical. It's practice can be taken as an art, in some regards.
That somes things up pretty well. But statistics is unusual in that, while arguably a branch of mathematics, many are involved in it who are not mathematicians. Therefore, unusually for an academic arena, the theory of statistics gets less emphasis I think even among many academicians - something rare in my observation. Statistics deals with how things occur primarily, not why nor is there a grand underlying meta theory behind it - at least one that gets discussed much. But again I am not a statistician and only rarely read pure statistical journals. So I may be entirely off base :p


Probably A Mammal
Bryan, I think there is some sense to beginning with apparently naive questions.

1. When we "do" statistics, what are we doing?

2. Do statistics tell us something about the world, or something about our way of dealing with the world? Is there a difference?

3. Do statistics place different ethical demands on us than do other types of information?

These are very basic, but nontrivial questions.
I agree, they are nontrivial, but to my point, these are distinctly statistical questions as opposed to PoS questions. I mean, you could naively ask those of any activity: When we "do" art, what are we doing? (Philosophy of aesthetics). I find questions like those to be distinctly about the practice of the subject matter, like one can study computer ethics without really delving into any sort of computability theory or talk about bioethics without the philosophy of biology. I think some of these questions can be quite interesting, but those you listed are not :p

To note, I am biased in that my primary interest in the philosophy of science involves methodology and the way interpretation influences our theories (or is coextensive with them from a structuralist perspective). This area of statistics is pretty much entirely subsumed under the philosophy of mathematics (see structuralism in mathematics). Where statistics is concerned, I think I am most interested in its place as an applied mathematics and the way inductive methods can lead to new information.
I think statistics, like business, suffers from conflict between those who simply want to use it as a tool and theoriest. The former (I am certainly one) don't care why it works as long as it works. We have limited interest in broader theory or the essential assumptions behind statistics as a whole (we do care for obvious reasons if assumptions that influence results are violated, but that tends to be a narrowly technical definition of such violations). At heart I believe most who use statistics are positivist, they believe the results are reality (that is you can use statistics to generate reality ignoring the problems that post-positivist raise in that). I believe this is generally true of the hard sciences to which I think statistics generally belongs.

I have not seen in statistics anything like the broader theories that seek to undergird other academic fields. It focuses on solving problems not meta assumptions or grand theory.

I have not seen, although admitedly I operate at a pretty low level in statistics, anything that challenges positivism in statistics or even something like the uncertainty principal in physics that suggest much is not knowable. Statisticians would likely agree that the state of the art does not allow definite conclusions in some areas, not that this is inherently impossible.
Just out of curiosity, what do you guys mean by "positivism"? I see it used as a whipping boy in lot's of social science discourse, but it is rarely made explicit enough for decent analysis.

Positivism was the dominant intellectual paradigm in most research areas until the late sixties (and arguably remains so in practice although rejected commonly in theory). Essentially it asserts that reality is defined by what is discoverable through scientific method. If knowledge is not discovered through scientific method than (depending on the author) it either does not exist or is not valid knowledge. Inherent in this, although not part of the philosophy per se, is what is called scientific method - essentially ways we conduct analysis. It includes rules such as letting the data not opinion decide what is correct, avoiding "subjective" analysis, the use of null hypothesis (which have philisophical not just practical elements to it) and so on.

The post-positivist critique is complex and varied. One element of it argues that it is impossible to avoid subjectivity in analysis, because human beings are inherently subjective. Similarly, it argues that it is impossible to let the data answer questions (critical to positivism's focus on objectivity) because even basic steps such as which data you gather and what questions you ask are subjective. Qualitative analysts argued that many of the rules such as random sampling were invalid for both methodological and philisophical reasons. In general this critique notes that largely hidden in positivism are central assumptions such as support for the existing state of knowledge that are not without challenge - certainly that were judgements as compared to being certain.

I barely touched on this topic, its incredibly complex. It reached its heights I think from the sixties through the eighties. Today I would guess that most researchers who pay attention to such are post-positivist in theory although commonly positivist in the way they do their research. Beyond the issues I have raised, their is the added related issue of the status in society of researchers and research.
Thanks noetsi. I have serious doubts that positivism was ever expressed so baldly or believed so naively by any philosopher. It seems at best a caricature of epistemological realism.
I was not trying to claim that it was believed quite that way (although my comments do reflect the views of many of its critics). :p Just sumarizing some of the central elements in a very general way as expressed by academics - few of whoom were philosophers. I lack the training in honesty in philosophy to express it precisely. Logical positivist, people like Herman Simon took truly extreme positions, most I am sure did not. You might look at (on opposite extremes) the statements of Herman Simon and (as a critic) Lincoln and Guba.

As is often the case in academics there were pratical elements at play here. Positivism had many useful aspects to the social sciences which felt itself slighted in the public mind (and in funding) relative to the hard sciences. It (many academics believed) increased the legitimacy of social science research if they were conducting "real" scientific research. And to do so, it was felt, they had to use scientific methods (notably statistical analysis) and apply what social scientists felt were the values and behaviors of hard scientists. Whether the hard sciences actually used those methods as rigerously as was perceived in the social sciences is questonable, but it was felt they were in the heyday of positivism which ran roughly from the late forties to mid sixties. This was not concidently an era with extreme confidence in the use of scientific method to address social issues and the beginning of the revolution in computers which made the analysis possible.

It has been argued, to me with some validity, that it is inherently in academics advantage to support positivism. If there is no objective way to do research, then researchers lack the ability to generate answers that are "better" (and thus more legitimate) in society relative to those that lack the specialized academic training. This of course reduces the validity of research, and particularly social science research, in the general public. By claiming they had a unique, more effective way to generate knowledge researchers were ablet to increase the possibility their research would be accepted and decrease the validity of non-academic commentators. Essentially they were claiming through positivism that they had the only legitimate way to discover reality. Then to empirical research is very hard to justify generally if you don't accept positivist tenets.

So even those who reject positivism, which is likely most academics today, in practice conduct research as if scientific method was correct.

You might look at the history of "behaviorialism" the form of positivism that applied to political science and related fields. It reflects well the difference between politics, practical issues, and philosophy in the academic community. A community that is loath to admit it conducts research in fundamentally subjective ways... :p

If you think about the assumptions on this board, it is pretty easy to see just how deeply positivism is held to even today. Largely of course without question. Do most here believe that statistical method is inherently objective, that accepting the status quo in theory until disproven is the proper way to do analysis, that statisticans understand reality better than non-statisticans, that rarefied objective facts exist seperate from the meaning attached to them in society? Without really questioning any of that? Probably.

I know I do, and I am not even a statistician.