SIST

Final part of B. Haig’s ‘What can psych stat reformers learn from the error-stat perspective?’ (Bayesian stats)

.

Here’s the final part of Brian Haig’s recent paper ‘What can psychology’s statistics reformers learn from the error-statistical perspective?’ in Methods in Psychology 2 (Nov. 2020). The full article, which is open access, is here. I will make some remarks in the comments.

5. The error-statistical perspective and the nature of science

Haig

As noted at the outset, the error-statistical perspective has made significant contributions to our philosophical understanding of the nature of science. These are achieved, in good part, by employing insights about the nature and place of statistical inference in experimental science. The achievements include deliberations on important philosophical topics, such as the demarcation of science from non-science, the underdetermination of theories by evidence, the nature of scientific progress, and the perplexities of inductive inference. In this article, I restrict my attention to two such topics: The process of falsification and the structure of modeling.

5.1. Falsificationism

The best known account of scientific method is the so-called hypothetico-deductive method. According to its most popular description, the scientist takes an existing hypothesis or theory and tests indirectly by deriving one or more observational predictions that are subjected to direct empirical test. Successful predictions are taken to provide inductive confirmation of the theory; failed predictions are said to provide disconfirming evidence for the theory. In psychology, NHST is often embedded within such a hypothetico-deductive structure and contributes to weak tests of theories.

Also well known is Karl Popper’s falsificationist construal of the hypothetico-deductive method, which is understood as a general strategy of conjecture and refutation. Although it has been roundly criticised by philosophers of science, it is frequently cited with approval by scientists, including psychologists, even though they do not, indeed could not, employ it in testing their theories. The major reason for this is that Popper does not provide them with sufficient methodological resources to do so.

One of the most important features of the error-statistical philosophy is its presentation of a falsificationist view of scientific inquiry, with error statistics serving an indispensable role in testing. From a sympathetic, but critical, reading of Popper, Mayo endorses his strategy of developing scientific knowledge by identifying and correcting errors through strong tests of scientific claims. Making good on Popper’s lack of knowledge of statistics, Mayo shows how one can properly employ a range of, often familiar, error-statistical methods to implement her all-important severity requirement. Stated minimally, and informally, this requirement says, “A claim is severely tested to the extent that it has been subjected to and passes a test that probably would have found flaws, were they present.” (Mayo, 2018, p. xii) Further, in marked contrast with Popper, who deemed deductive inference to be the only legitimate form of inference, Mayo’s conception of falsification stresses the importance of inductive, or content-increasing, inference in science. We have here, then, a viable account of falsification, which goes well beyond Popper’s account with its lack of operational detail about how to construct strong tests. It is worth noting that the error-statistical stance offers a constructive interpretation of Fisher’s oft-cited remark that the null hypothesis is never proved, only possibly disproved.

5.2. A hierarchy of models

In the past, philosophers of science tended to characterize scientific inquiry by focusing on the general relationship between evidence and theory. Similarly, scientists, even today, commonly speak in general terms of the relationship between data and theory. However, due in good part to the labors of experimentally-oriented philosophers of science, we now know that this coarse-grained depiction is a poor portrayal of science. The error-statistical perspective is one such philosophy that offers a more fine-grained parsing of the scientific process.

Building on Patrick Suppes’ (1962) important insight that science employs a hierarchy of models that ranges from experimental experience to theory, Mayo’s (1996) error-statistical philosophy initially adopted a framework in which three different types of models are interconnected and serve to structure error-statistical inquiry: Primary models, experimental models, and data models. Primary models, which are at the top of the hierarchy, break down a research problem, or question, into a set of local hypotheses that can be investigated using reliable methods. Experimental models take the mid-positon on the hierarchy and structure the particular models at hand. They serve to link primary models to data models. And, data models, which are at the bottom of the hierarchy, generate and model raw data, put them in canonical form, and check whether the data satisfy the assumptions of the experimental models. It should be mentioned that the error-statistical approach has been extended to primary models and theories of a more global nature (Mayo and Spanos, 2010) and, now, also includes a consideration of experimental design and the analysis and generation of data (Mayo, 2018).

This hierarchy of models facilitates the achievement of a number of goals that are important to the error-statistician. These include piecemeal strong testing of local hypotheses rather than broad theories, and employing the model hierarchy as a structuring device to knowingly move back and forth between statistical and scientific hypotheses. The error-statistical perspective insists on maintaining a clear distinction between statistical and scientific hypotheses, pointing out that psychologists often mistakenly take tests of significance to have direct implications for substantive hypotheses and theories.

6. The philosophy of statistics

A heartening attitude that comes through in the error-statistical corpus is the firm belief that the philosophy of statistics is an important part of statistical thinking. This emphasis on the conceptual foundations of the subject contrasts markedly with much of statistical theory, and most of statistical practice. It is encouraging, therefore, that Mayo’s philosophical work has influenced a number of prominent statisticians, who have contributed to the foundations of their discipline. Gelman’s error-statistical philosophy canvassed earlier is a prominent case in point. Through both precept and practice, Mayo’s work makes clear that philosophy can have a direct impact on statistical practice. Given that statisticians operate with an implicit philosophy, whether they know it or not, it is better that they avail themselves of an explicitly thought-out philosophy that serves their thinking and practice in useful ways. More particularly, statistical reformers recommend methods and strategies that have underlying philosophical commitments. It is important that they are identified, described, and evaluated.

The tools used by the philosopher of statistics in order to improve our understanding and use of statistical methods are considerable (Mayo, 2011). They include clarifying disputed concepts, evaluating arguments employed in statistical debates, including the core commitments of rival schools of thought, and probing the deep structure of statistical methods themselves. In doing this work, the philosopher of statistics, as philosopher, ascends to a meta-level to get purchase on their objects of study. This second-order inquiry is a proper part of scientific methodology.

It is important to appreciate that the error-statistical outlook is a scientific methodology in the proper sense of the term. Briefly stated, methodology is the interdisciplinary field that draws from disciplines that include statistics, philosophy of science, history of science, as well as indigenous contributions from the various substantive disciplines. As such, it is the key to a proper understanding of statistical and scientific methods. Mayo’s focus on the role of error statistics in science is deeply informed about the philosophy, history, and theory of statistics, as well as statistical practice. It is for this reason that the error-statistical perspective is strategically positioned to help the reader to go beyond the statistics wars.

7. Conclusion

The error-statistical outlook provides researchers, methodologists, and statisticians with a distinctive and illuminating perspective on statistical inference. Its Popper-inspired emphasis on strong tests is a welcome antidote to the widespread practice of weak statistical hypothesis testing that still pervades psychological research. More generally, the error-statistical standpoint affords psychologists an informative perspective on the nature of good statistical practice in science that will help them understand and transcend the statistics wars into which they have been drawn. Importantly, psychologists should know about the error-statistical perspective as a genuine alternative to the new statistics and Bayesian statistics. The new statisticians, Bayesians statisticians, and those with other preferences should address the challenges to their outlooks on statistics that the error-statistical viewpoint provides. Taking these challenges seriously would enrich psychology’s methodological landscape.

*This article is based on an invited commentary on Deborah Mayo’s book, Statistical inference as severe testing: How to get beyond the statistics wars (Cambridge University Press, 2018), which appeared at https://statmodeling.stat.colombia.edu/2019/04/12 It is adapted with permission. I thank Mayo for helpful feedback on an earlier draft.

Refer to the paper for the references. I invite your comments and questions.

 

Categories: Brian Haig, SIST | 3 Comments

Part 2 of B. Haig’s ‘What can psych stat reformers learn from the error-stat perspective?’ (Bayesian stats)

.

Here’s a picture of ripping open the first box of (rush) copies of Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars*, and here’s a continuation of Brian Haig’s recent paper ‘What can psychology’s statistics reformers learn from the error-statistical perspective?’ in Methods in Psychology 2 (Nov. 2020). Haig contrasts error statistics, the “new statistics”, and Bayesian statistics from the perspective of the statistics wars in psychology. The full article, which is open access, is here. I will make several points in the comments.

Haig

4. Bayesian statistics

Despite its early presence, and prominence, in the history of statistics, the Bayesian outlook has taken an age to assert itself in psychology. However, a cadre of methodologists has recently advocated the use of Bayesian statistical methods as a superior alternative to the messy frequentist practice that dominates psychology’s research landscape (e.g., Dienes, 2011; Kruschke and Liddell, 2018; Wagenmakers, 2007). These Bayesians criticize NHST, often advocate the use of Bayes factors for hypothesis testing, and rehearse a number of other well-known Bayesian objections to frequentist statistical practice.

Of course, there are challenges for Bayesians from the error-statistical perspective, just as there are for the new statisticians. For example, the frequently made claim that p values exaggerate the evidence against the null hypothesis, but Bayes factors do not, is shown by Mayo not to be the case. She also makes the important point that Bayes factors, as they are currently used, do not have the ability to probe errors and, thus, violate the requirement for severe tests. Bayesians, therefore need to rethink whether Bayes factors can be deployed in some way to provide strong tests of hypotheses through error control. As with the new statisticians, Bayesians also need to reckon with the coherent hybrid NHST afforded by the error-statistical perspective, and argue against it, rather than the common inchoate hybrids, if they want to justify abandoning NHST. Finally, I note in passing that Bayesians should consider, among other challenges, Mayo’s critique of the controversial Likelihood Principle, a principle which ignores the post-data consideration of sampling plans.

4.1. Contrasts between the Bayesian and error-statistical perspectives

One of the major achievements of the philosophy of error-statistics is that it provides a comprehensive critical evaluation of the major variants of Bayesian statistical thinking, including the classical subjectivist, “default”, pragmatist, and eclectic options within the Bayesian corpus. Whether the adoption of Bayesian methods in psychology will overcome the disorders of current frequentist practice remains to be seen. What is clear from reading the error-statistical literature, however, is that the foundational options for Bayesians are numerous, convoluted, and potentially bewildering. It would be a worthwhile exercise to chart how these foundational options are distributed across the prominent Bayesian statisticians in psychology. For example, the increasing use of Bayes factors for hypothesis testing purposes is accompanied by disorderliness at the foundational level, just as it is in the Bayesian literature more generally. Alongside the fact that some Bayesians are sceptical of the worth of Bayes factors, we find disagreement about the comparative merits of the subjectivist and default Bayesianism outlooks on Bayes factors in psychology (Wagenmakers et al., 2018).

The philosophy of error-statistics contains many challenges for Bayesians to consider. Here, I want to draw attention to three basic features of Bayesian thinking, which are rejected by the error-statistical approach. First, the error-statistical approach rejects the Bayesian insistence on characterizing the evidential relation between hypothesis and evidence in a universal and logical manner in terms of Bayes’ theorem. Instead, it formulates the relation in terms of the substantive and specific nature of the hypothesis and the evidence with regards to their origin, modeling, and analysis. This is a consequence of a strong commitment to a piecemeal, contextual approach to testing, using the most appropriate frequentist methods available for the task at hand. This contextual attitude to testing is taken up in Section 5.2, where one finds a discussion of the role different models play in structuring and decomposing inquiry.

Second, the error-statistical philosophy also rejects the classical Bayesian commitment to the subjective nature of prior probabilities, which the agent is free to choose, in favour of the more objective process of establishing error probabilities understood in frequentist terms. It also finds unsatisfactory the turn to the more popular objective, or “default”, Bayesian option, in which the agent’s appropriate degrees of belief are constrained by relevant empirical evidence. The error-statistician rejects this default option because it fails in its attempts to unify Bayesian and frequentist ways of determining probabilities.

And, third, the error-statistical outlook employs probabilities to measure how effectively methods facilitate the detection of error, and how those methods enable us to choose between alternative hypotheses. By contrast, orthodox Bayesians use probabilities to measure belief in hypotheses or degrees of confirmation. As noted earlier, most Bayesians are not concerned with error probabilities at all. It is for this reason that error-statisticians will say about Bayesian methods that, without supplementation with error probabilities, they are not capable of providing stringent tests of hypotheses.

4.2. The Bayesian remove from scientific practice

Two additional features of the Bayesian focus on beliefs, which have been noted by philosophers of science and statistics, draw attention to their outlook on science. First, Kevin Kelly and Clark Glymour worry that “Bayesian methods assign numbers to answers instead of producing answers outright.” (2004, p. 112) Their concern is that the focus on the scientist’s beliefs “screens off” the scientist’s direct engagement with the empirical and theoretical activities that are involved in the phenomenology of science. Mayo agrees that we should focus on the scientific phenomena of interest, not the associated epiphenomena of degrees of belief. This preference stems directly from the error-statistician’s conviction that probabilities properly quantify the performance of methods, not the scientist’s degrees of belief.

Second, Henry Kyburg is puzzled by the Bayesian’s desire to “replace the fabric of science… with a vastly more complicated representation in which each statement of science is accompanied by its probability, for each of us.” (1992, p.149) Kyburg’s puzzlement prompts the question, ‘Why should we be interested in each other’s probabilities?’ This is a question raised by David Cox about prior probabilities, and noted by Mayo (2018).

This Bayesian remove from science contrasts with the willingness of the error-statistical perspective to engage more directly with science. Mayo is a philosopher of science as well as statistics, and has a keen eye for scientific practice. Given that contemporary philosophers of science tend to take scientific practice seriously, it comes as no surprise that she brings it to the fore when dealing with statistical concepts and issues. Indeed, her error-statistical philosophy should be seen as a significant contribution to the so-called new experimentalism, with its strong focus, not just on experimental practice in science, but also on the role of statistics in such practice. Her discussion of the place of frequentist statistics in the discovery of the Higgs boson in particle physics is an instructive case in point.

Taken together, these just-mentioned points of difference between the Bayesian and error-statistical philosophies constitute a major challenge to Bayesian thinking that methodologists, statisticians, and researchers in psychology need to confront.

4.3. Bayesian statistics with error-statistical foundations

One important modern variant of Bayesian thinking, which now receives attention within the error-statistical framework, is the falsificationist Bayesianism of Andrew Gelman, which received its major formulation in Gelman and Shalizi (2013). Interestingly, Gelman regards his Bayesian philosophy as essentially error-statistical in nature – an intriguing claim, given the anti-Bayesian preferences of both Mayo and Gelman’s co-author, Cosma Shalizi. Gelman’s philosophy of Bayesian statistics is also significantly influenced by Popper’s view that scientific propositions are to be submitted to repeated criticism in the form of strong empirical tests. For Gelman, best Bayesian statistical practice involves formulating models using Bayesian statistical methods, and then checking them through hypothetico-deductive attempts to falsify and modify those models.

Both the error-statistical and neo-Popperian Bayesian philosophies of statistics extend and modify Popper’s conception of the hypotheticodeductive method, while at the same time offering alternatives to received views of statistical inference. The error-statistical philosophy injects into the hypothetico-deductive method an account of statistical induction that employs a panoply of frequentist statistical methods to detect and control for errors. For its part, Gelman’s Bayesian alternative involves formulating models using Bayesian statistical methods, and then checking them through attempts to falsify and modify those models. This clearly differs from the received philosophy of Bayesian statistical modeling, which is regarded as a formal inductive process.

From the wide-ranging error-statistical evaluation of the major varieties of Bayesian statistical thought on offer, Mayo concludes that Bayesian statistics needs new foundations: In short, those provided by her error-statistical perspective. Gelman acknowledges that his falsificationist Bayesian philosophy is underdeveloped, so it will be interesting to learn how its further development relates to Mayo’s error-statistical perspective. It will also be interesting to see if Bayesian thinkers in psychology engage with Gelman’s brand of Bayesian thinking. Despite the appearance of his work in a prominent psychology journal, they have yet to do so. However, Borsboom and Haig (2013) and Haig (2018) provide sympathetic critical evaluations of Gelman’s philosophy of statistics.

It is notable that in her treatment of Gelman’s philosophy, Mayo emphasizes that she is willing to allow a decoupling of statistical outlooks and their traditional philosophical foundations in favour of different foundations, which are judged more appropriate. It is an important achievement of Mayo’s work that she has been able to consider the current statistics wars without taking a particular side in the debates. She achieves this by examining methods, both Bayesian and frequentist, in terms of whether they violate her minimal severity requirement of “bad evidence, no test”.

I invite your comments and questions.

*This picture was taken by Diana Gillooly, Senior Editor for Mathematical Sciences, Cambridge University Press, at the book display for the Sept. 2018 meeting of the Royal Statistical Society in Cardiff. She also had the honor of doing the ripping. A blogpost on the session I was in is here.

Categories: Brian Haig, SIST | 6 Comments

SIST: All Excerpts and Mementos: May 2018-July 2019 (updated)

Introduction & Overview

The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars* 05/19/18

Blurbs of 16 Tours: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST) 03/05/19

Statistical Inference as Severe Testing: Preface

Excursion 1

EXCERPTS

Tour I Ex1 TI (full proofs)

Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1) 09/08/18

Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2) 09/11/18

Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3) 09/15/18

Tour II Ex1 TII (full proofs)

Excursion 1 Tour II: Error Probing Tools versus Logics of Evidence-Excerpt 04/04/19

Souvenir C: A Severe Tester’s Translation Guide (Excursion 1 Tour II) 11/08/18

MEMENTOS

Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars) 10/29/18

 

Excursion 2

EXCERPTS

Tour I

Excursion 2: Taboos of Induction and Falsification: Tour I (first stop) 09/29/18

“It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based” (Keepsake by Fisher, 2.1) 10/05/18

Tour II

Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3) 10/10/18

MEMENTOS

Tour Guide Mementos and Quiz 2.1 (Excursion 2 Tour I Induction and Confirmation) 11/14/18

Mementos for Excursion 2 Tour II Falsification, Pseudoscience, Induction 11/17/18

 

Excursion 3

EXCERPTS

Tour I Ex3 TI (full proofs)

Where are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3 11/30/18

Neyman-Pearson Tests: An Episode in Anglo-Polish Collaboration: Excerpt from Excursion 3 (3.2) 12/01/18

First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3] 12/04/18

Tour II Ex3 TII (full proofs)

It’s the Methods, Stupid: Excerpt from Excursion 3 Tour II (Mayo 2018, CUP) 12/11/18

60 Years of Cox’s (1958) Chestnut: Excerpt from Excursion 3 tour II. 12/29/18

Tour III Ex3 Tour III(full proofs)

Capability and Severity: Deeper Concepts: Excerpts From Excursion 3 Tour III 12/20/18

MEMENTOS

Memento & Quiz (on SEV): Excursion 3, Tour I 12/08/18

Mementos for “It’s the Methods, Stupid!” Excursion 3 Tour II (3.4-3.6) 12/13/18

Tour Guide Mementos From Excursion 3 Tour III: Capability and Severity: Deeper Concepts 12/26/18

 

Excursion 4

EXCERPTS

Tour I

Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP) 12/26/18
(Full Excursion 4 Tour I)

Tour II

Excerpt from Excursion 4 Tour II: 4.4 “Do P-Values Exaggerate the Evidence?” 01/10/19
(Full Excursion 4 Tour II)

Tour III
(Full proofs of Excursion 4 Tour III)

Tour IV

Excerpt from Excursion 4 Tour IV: More Auditing: Objectivity and Model Checking 01/27/19

MEMENTOS

Mementos from Excursion 4: Blurbs of Tours I-IV 01/13/19

 

Excursion 5

Tour I

(Full) Excerpt: Excursion 5 Tour I — Power: Pre-data and Post-data (from “SIST: How to Get Beyond the Stat Wars”) 04/27/19

Tour II

(Full) Excerpt. Excursion 5 Tour II: How Not to Corrupt Power (Power Taboos, Retro Power, and Shpower) 06/07/19

Tour III

Deconstructing the Fisher-Neyman conflict wearing Fiducial glasses + Excerpt 5.8 from SIST 02/23/19

 

Excursion 6

Tour I Ex6 TI What Ever Happened to Bayesian Foundations?

Tour II

Excerpts: Souvenir Z: Understanding Tribal Warfare +  6.7 Farewell Keepsake from SIST + List of Souvenirs 05/04/19 (full excerpt)

 

*Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo, CUP 2018).

Categories: SIST, Statistical Inference as Severe Testing | 9 Comments

SIST: All Excerpts and Mementos: May 2018-May 2019

view from a hot-air balloon

Introduction & Overview

The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars* 05/19/18

Blurbs of 16 Tours: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST) 03/05/19

 

Excursion 1

EXCERPTS

Tour I

Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1) 09/08/18

Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2) 09/11/18

Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3) 09/15/18

Tour II

Excursion 1 Tour II: Error Probing Tools versus Logics of Evidence-Excerpt 04/04/19

Souvenir C: A Severe Tester’s Translation Guide (Excursion 1 Tour II) 11/08/18

MEMENTOS

Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars) 10/29/18

 

Excursion 2

EXCERPTS

Tour I

Excursion 2: Taboos of Induction and Falsification: Tour I (first stop) 09/29/18

“It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based” (Keepsake by Fisher, 2.1) 10/05/18

Tour II

Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3) 10/10/18

MEMENTOS

Tour Guide Mementos and Quiz 2.1 (Excursion 2 Tour I Induction and Confirmation) 11/14/18

Mementos for Excursion 2 Tour II Falsification, Pseudoscience, Induction 11/17/18

 

Excursion 3

EXCERPTS

Tour I

Where are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3 11/30/18

Neyman-Pearson Tests: An Episode in Anglo-Polish Collaboration: Excerpt from Excursion 3 (3.2) 12/01/18

First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3] 12/04/18

Tour II

It’s the Methods, Stupid: Excerpt from Excursion 3 Tour II (Mayo 2018, CUP) 12/11/18

60 Years of Cox’s (1958) Chestnut: Excerpt from Excursion 3 tour II. 12/29/18

Tour III

Capability and Severity: Deeper Concepts: Excerpts From Excursion 3 Tour III 12/20/18

MEMENTOS

Memento & Quiz (on SEV): Excursion 3, Tour I 12/08/18

Mementos for “It’s the Methods, Stupid!” Excursion 3 Tour II (3.4-3.6) 12/13/18

Tour Guide Mementos From Excursion 3 Tour III: Capability and Severity: Deeper Concepts 12/26/18

 

Excursion 4

EXCERPTS

Tour I

Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP) 12/26/18

Tour II

Excerpt from Excursion 4 Tour II: 4.4 “Do P-Values Exaggerate the Evidence?” 01/10/19

Tour IV

Excerpt from Excursion 4 Tour IV: More Auditing: Objectivity and Model Checking 01/27/19

MEMENTOS

Mementos from Excursion 4: Blurbs of Tours I-IV 01/13/19

 

Excursion 5

Tour I

(full) Excerpt: Excursion 5 Tour I — Power: Pre-data and Post-data (from “SIST: How to Get Beyond the Stat Wars”) 04/27/19

Tour III

Deconstructing the Fisher-Neyman conflict wearing Fiducial glasses + Excerpt 5.8 from SIST 02/23/19

 

Excursion 6

Tour II

Excerpts: Souvenir Z: Understanding Tribal Warfare +  6.7 Farewell Keepsake from SIST + List of Souvenirs 05/04/19

*Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo, CUP 2018).

Categories: SIST, Statistical Inference as Severe Testing | Leave a comment

Excerpts: Final Souvenir Z, Farewell Keepsake & List of Souvenirs

.

We’ve reached our last Tour (of SIST)*: Pragmatic and Error Statistical Bayesians (Excursion 6), marking the end of our reading with Souvenir Z, the final Souvenir, as well as the Farewell Keepsake in 6.7. Our cruise ship Statinfasst, currently here at Thebes, will be back at dock for maintenance for our next launch at the Summer Seminar in Phil Stat (July 28-Aug 11). Although it’s not my preference that new readers begin with the Farewell Keepsake (it contains a few spoilers), I’m excerpting it together with Souvenir Z (and a list of all souvenirs A – Z) here, and invite all interested readers to peer in. There’s a check list on p. 437: If you’re in the market for a new statistical account, you’ll want to test if it satisfies the items on the list. Have fun!

Souvenir Z: Understanding Tribal Warfare

We began this tour asking: Is there an overarching philosophy that “matches contemporary attitudes”? More important is changing attitudes. Not to encourage a switch of tribes, or even a tribal truce, but something more modest and actually achievable: to understand and get beyond the tribal warfare. To understand them, at minimum, requires grasping how the goals of probabilism differ from those of probativeness. This leads to a way of changing contemporary attitudes that is bolder and more challenging. Snapshots from the error statistical lens let you see how frequentist methods supply tools for controlling and assessing how well or poorly warranted claims are. All of the links, from data generation to modeling, to statistical inference and from there to substantive research claims, fall into place within this statistical philosophy. If this is close to being a useful way to interpret a cluster of methods, then the change in contemporary attitudes is radical: it has never been explicitly unveiled. Our journey was restricted to simple examples because those are the ones fought over in decades of statistical battles. Much more work is needed. Those grappling with applied problems are best suited to develop these ideas, and see where they may lead. I never promised,when you bought your ticket for this passage, to go beyond showing that viewing statistics as severe testing will let you get beyond the statistics wars.

6.7 Farewell Keepsake

Despite the eclecticism of statistical practice, conflicting views about the roles of probability and the nature of statistical inference – holdovers from long-standing frequentist–Bayesian battles – still simmer below the surface of today’s debates. Reluctance to reopen wounds from old battles has allowed them to fester. To assume all we need is an agreement on numbers – even if they’re measuring different things – leads to statistical schizophrenia. Rival conceptions of the nature of statistical inference show up unannounced in the problems of scientific integrity, irreproducibility, and questionable research practices, and in proposed methodological reforms. If you don’t understand the assumptions behind proposed reforms, their ramifications for statistical practice remain hidden from you.

Rival standards reflect a tension between using probability (a) to constrain the probability that a method avoids erroneously interpreting data in a series of applications (performance), and (b) to assign degrees of support, confirmation, or plausibility to hypotheses (probabilism). We set sail on our journey with an informal tool for telling what’s true about statistical inference: If little if anything has been done to rule out flaws in taking data as evidence for a claim, then that claim has not passed a severe test . From this minimal severe-testing requirement, we develop a statistical philosophy that goes beyond probabilism and performance. The goals of the severe tester (probativism) arise in contexts sufficiently different from those of probabilism that you are free to hold both, for distinct aims (Section 1.2). For statistical inference in science, it is severity we seek. A claim passes with severity only to the extent that it is subjected to, and passes, a test that it probably would have failed, if false. Viewing statistical inference as severe testing alters long-held conceptions of what’s required for an adequate account of statistical inference in science. In this view, a normative statistical epistemology –  an account of what’ s warranted to infer –  must be:

  directly altered by biasing selection effects
  able to falsify claims statistically
  able to test statistical model assumptions
  able to block inferences that violate minimal severity

These overlapping and interrelated requirements are disinterred over the course of our travels. This final keepsake collects a cluster of familiar criticisms of error statistical methods. They are not intended to replace the detailed arguments, pro and con, within; here we cut to the chase, generally keeping to the language of critics. Given our conception of evidence, we retain testing language even when the statistical inference is an estimation, prediction, or proposed answer to a question. The concept of severe testing is sufficiently general to apply to any of the methods now in use. It follows that a variety of statistical methods can serve to advance the severity goal, and that they can, in principle, find their foundations in an error statistical philosophy. However, each requires supplements and reformulations to be relevant to real-world learning. Good science does not turn on adopting any formal tool, and yet the statistics wars often focus on whether to use one type of test (or estimation, or model selection) or another. Meta-researchers charged with instigating reforms do not agree, but the foundational basis for the disagreement is left unattended. It is no wonder some see the statistics wars as proxy wars between competing tribe leaders, each keen to advance one or another tool, rather than about how to do better science. Leading minds are drawn into inconsequential battles, e.g., whether to use a prespecified cut-off  of 0.025 or 0.0025 –  when in fact good inference is not about cut-offs altogether but about a series of small-scale steps in collecting, modeling and analyzing data that work together to find things out. Still, we need to get beyond the statistics wars in their present form. By viewing a contentious battle in terms of a difference in goals –  finding highly probable versus highly well probed hypotheses – readers can see why leaders of rival tribes often talk past each other. To be clear, the standpoints underlying the following criticisms are open to debate; we’re far from claiming to do away with them. What should be done away with is rehearsing the same criticisms ad nauseum. Only then can we hear the voices of those calling for an honest standpoint about responsible science.

1. NHST Licenses Abuses. First, there’s the cluster of criticisms directed at an abusive NHST animal: NHSTs infer from a single P-value below an arbitrary cut-off to evidence for a research claim, and they encourage P-hacking, fishing, and other selection effects. The reply: this ignores crucial requirements set by Fisher and other founders: isolated significant results are poor evidence of a genuine effect and statistical significance doesn’t warrant substantive, (e.g., causal) inferences. Moreover, selective reporting invalidates error probabilities. Some argue significance tests are un-Popperian because the higher the sample size, the easier to infer one’s research hypothesis. It’s true that with a sufficiently high sample size any discrepancy from a null hypothesis has a high probability of being detected, but statistical significance does not license inferring a research claim H. Unless H’s errors have been well probed by merely finding a small P-value, H passes an extremely insevere test. No mountains out of molehills (Sections 4.3 and 5.1). Enlightened users of statistical tests have rejected the cookbook, dichotomous NHST, long lampooned: such criticisms are behind the times. When well-intentioned aims of replication research are linked to these retreads, it only hurts the cause. One doesn’t need a sharp dichotomy to identify rather lousy tests – a main goal for a severe tester. Granted, policy-making contexts may require cut-offs, as do behavioristic setups. But in those contexts, a test’s error probabilities measure overall error control, and are not generally used to assess well-testedness. Even there, users need not fall into the NHST traps (Section 2.5). While attention to banning terms is the least productive aspect of the statistics wars, since NHST is not used by Fisher or N-P, let’s give the caricature its due and drop the NHST acronym; “statistical tests” or “error statistical tests” will do. Simple significance tests are a small part of a conglomeration of error statistical methods.

To continue reading: Excerpt Souvenir Z, Farewell Keepsake & List of Souvenirs can be found here.

*We are reading Statistical Inference as Severe Testing: How to Get beyond the Statistics Wars (2018, CUP)

***

 

Where YOU are in the journey.

 


Categories: SIST, Statistical Inference as Severe Testing | Leave a comment

(Full) Excerpt of Excursion 4 Tour I: The Myth of “The Myth of Objectivity”

A month ago, I excerpted just the very start of Excursion 4 Tour I* on The Myth of the “Myth of Objectivity”. It’s a short Tour, and this continues the earlier post.

4.1    Dirty Hands: Statistical Inference Is Sullied with Discretionary Choices

If all flesh is grass, kings and cardinals are surely grass, but so is everyone else and we have not learned much about kings as opposed to peasants. (Hacking 1965, p.211)

Trivial platitudes can appear as convincingly strong arguments that everything is subjective. Take this one: No human learning is pure so anyone who demands objective scrutiny is being unrealistic and demanding immaculate inference. This is an instance of Hacking’s “all flesh is grass.” In fact, Hacking is alluding to the subjective Bayesian de Finetti (who “denies the very existence of the physical property [of] chance” (ibid.)). My one-time colleague, I. J. Good, used to poke fun at the frequentist as “denying he uses any judgments!” Let’s admit right up front that every sentence can be prefaced with “agent x judges that,” and not sweep it under the carpet (SUTC) as Good (1976) alleges. Since that can be done for any statement, it cannot be relevant for making the distinctions in which we are interested, and we know can be made, between warranted or well-tested claims and those so poorly probed as to be BENT. You’d be surprised how far into the thicket you can cut your way by brandishing this blade alone. Continue reading

Categories: objectivity, SIST | Leave a comment

Mementos from Excursion 4: Objectivity & Auditing: Blurbs of Tours I – IV

Excursion 4: Objectivity and Auditing (blurbs of Tours I – IV)

 

.

Excursion 4 Tour I: The Myth of “The Myth of Objectivity”

Blanket slogans such as “all methods are equally objective and subjective” trivialize into oblivion the problem of objectivity. Such cavalier attitudes are at odds with the moves to take back science The goal of this tour is to identify what there is in objectivity that we won’t give up, and shouldn’t. While knowledge gaps leave room for biases and wishful thinking, we regularly come up against data that thwart our expectations and disagree with predictions we try to foist upon the world. This pushback supplies objective constraints on which our critical capacity is built. Supposing an objective method is to supply formal, mechanical, rules to process data is a holdover of a discredited logical positivist philosophy.Discretion in data generation and modeling does not warrant concluding: statistical inference is a matter of subjective belief. It is one thing to talk of our models as objects of belief and quite another to maintain that our task is to model beliefs. For a severe tester, a statistical method’s objectivity requires the ability to audit an inference: check assumptions, pinpoint blame for anomalies, falsify, and directly register how biasing selection effects–hunting, multiple testing and cherry-picking–alter its error probing capacities.

Keywords

objective vs. subjective, objectivity requirements, auditing, dirty hands argument, phenomena vs. epiphenomena, logical positivism, verificationism, loss and cost functions, default Bayesians, equipoise assignments, (Bayesian) wash-out theorems, degenerating program, transparency, epistemology: internal/external distinction

 

Excursion 4 Tour II: Rejection Fallacies: Whose Exaggerating What?

We begin with the Mountains out of Molehills Fallacy (large n problem): The fallacy of taking a (P-level) rejection of H0 with larger sample size as indicating greater discrepancy from H0 than with a smaller sample size. (4.3). The Jeffreys-Lindley paradox shows with large enough n, a .05 significant result can correspond to assigning H0 a high probability .95. There are family feuds as to whether this is a problem for Bayesians or frequentists! The severe tester takes account of sample size in interpreting the discrepancy indicated. A modification of confidence intervals (CIs) is required.

It is commonly charged that significance levels overstate the evidence against the null hypothesis (4.4, 4.5). What’s meant? One answer considered here, is that the P-value can be smaller than a posterior probability to the null hypothesis, based on a lump prior (often .5) to a point null hypothesis. There are battles between and within tribes of Bayesians and frequentists. Some argue for lowering the P-value to bring it into line with a particular posterior. Others argue the supposed exaggeration results from an unwarranted lump prior to a wrongly formulated null.We consider how to evaluate reforms based on bayes factor standards (4.5). Rather than dismiss criticisms of error statistical methods that assume a standard from a rival account, we give them a generous reading. Only once the minimal principle for severity is violated do we reject them. Souvenir R summarizes the severe tester’s interpretation of a rejection in a statistical significance test. At least 2 benchmarks are needed: reports of discrepancies (from a test hypothesis) that are, and those that are not, well indicated by the observed difference.

Keywords

significance test controversy, mountains out of molehills fallacy, large n problem, confidence intervals, P-values exaggerate evidence, Jeffreys-Lindley paradox, Bayes/Fisher disagreement, uninformative (diffuse) priors, Bayes factors, spiked priors, spike and slab, equivocating terms, severity interpretation of rejection (SIR)

 

Excursion 4 Tour III: Auditing: Biasing Selection Effects & Randomization

Tour III takes up Peirce’s “two rules of inductive inference”: predesignation (4.6) and randomization (4.7). The Tour opens on a court case transpiring: the CEO of a drug company is being charged with giving shareholders an overly rosy report based on post-data dredging for nominally significant benefits. Auditing a result includes checking for (i) selection effects, (ii) violations of model assumptions, and (iii) obstacles to moving from statistical to substantive claims. We hear it’s too easy to obtain small P-values, yet replication attempts find it difficult to get small P-values with preregistered results. I call this the paradox of replication. The problem isn’t P-values but failing to adjust them for cherry picking and other biasing selection effects. Adjustments by Bonferroni and false discovery rates are considered. There is a tension between popular calls for preregistering data analysis, and accounts that downplay error probabilities. Worse, in the interest of promoting a methodology that rejects error probabilities, researchers who most deserve lambasting are thrown a handy line of defense. However, data dependent searching need not be pejorative. In some cases, it can improve severity. (4.6)

Big Data cannot ignore experimental design principles. Unless we take account of the sampling distribution, it becomes difficult to justify resampling and randomization. We consider RCTs in development economics (RCT4D) and genomics. Failing to randomize microarrays is thought to have resulted in a decade lost in genomics. Granted the rejection of error probabilities is often tied to presupposing their relevance is limited to long-run behavioristic goals, which we reject. They are essential for an epistemic goal: controlling and assessing how well or poorly tested claims are. (4.7)

Keywords

error probabilities and severity, predesignation, biasing selection effects, paradox of replication, capitalizing on chance, bayes factors, batch effects, preregistration, randomization: Bayes-frequentist rationale, bonferroni adjustment, false discovery rates, RCT4D, genome-wide association studies (GWAS)

 

Excursion 4 Tour IV: More Auditing: Objectivity and Model Checking

While all models are false, it’s also the case that no useful models are true. Were a model so complex as to represent data realistically, it wouldn’t be useful for finding things out. A statistical model is useful by being adequate for a problem, meaning it enables controlling and assessing if purported solutions are well or poorly probed and to what degree. We give a way to define severity in terms of solving a problem.(4.8) When it comes to testing model assumptions, many Bayesians agree with George Box (1983) that “it requires frequentist theory of significance tests” (p. 57). Tests of model assumptions, also called misspecification (M-S) tests, are thus a promising area for Bayes-frequentist collaboration. (4.9) When the model is in doubt, the likelihood principle is inapplicable or violated. We illustrate a non-parametric bootstrap resampling. It works without relying on a theoretical  probability distribution, but it still has assumptions. (4.10). We turn to the M-S testing approach of econometrician Aris Spanos.(4.11) I present the high points for unearthing spurious correlations, and assumptions of linear regression, employing 7 figures. M-S tests differ importantly from model selection–the latter uses a criterion for choosing among models, but does not test their statistical assumptions. They test fit rather than whether a model has captured the systematic information in the data.

Keywords

adequacy for a problem, severity (in terms of problem solving), model testing/misspecification (M-S) tests, likelihood principle conflicts, bootstrap, resampling, Bayesian p-value, central limit theorem, nonsense regression, significance tests in model checking, probabilistic reduction, respecification

 

Where you are in the Journey 

Categories: SIST, Statistical Inference as Severe Testing | 2 Comments

Excerpt from Excursion 4 Tour II: 4.4 “Do P-Values Exaggerate the Evidence?”

getting beyond…

Excerpt from Excursion 4 Tour II*

 

4.4 Do P-Values Exaggerate the Evidence?

“Significance levels overstate the evidence against the null hypothesis,” is a line you may often hear. Your first question is:

What do you mean by overstating the evidence against a hypothesis?

Several (honest) answers are possible. Here is one possibility:

What I mean is that when I put a lump of prior weight π0 of 1/2 on a point null H0 (or a very small interval around it), the P-value is smaller than my Bayesian posterior probability on H0.

More generally, the “P-values exaggerate” criticism typically boils down to showing that if inference is appraised via one of the probabilisms – Bayesian posteriors, Bayes factors, or likelihood ratios – the evidence against the null (or against the null and in favor of some alternative) isn’t as big as 1 − P. Continue reading

Categories: SIST, Statistical Inference as Severe Testing | 1 Comment

January Invites: Ask me questions (about SIST), Write Discussion Analyses (U-Phils)

.

ASK ME. Some readers say they’re not sure where to ask a question of comprehension on Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP)–SIST– so here’s a special post to park your questions of comprehension (to be placed in the comments) on a little over the first half of the book. That goes up to and includes Excursion 4 Tour I on “The Myth of ‘The Myth of Objectivity'”. However,I will soon post on Tour II: Rejection Fallacies: Who’s Exaggerating What? So feel free to ask questions of comprehension as far as p.259.

All of the SIST BlogPost (Excerpts and Mementos) so far are here.

.

WRITE A DISCUSSION NOTE: Beginning January 16, anyone who wishes to write a discussion note (on some aspect or issue up to p. 259 are invited to do so (<750 words, longer if you wish). Send them to my error email.  I will post as many as possible on this blog.

We initially called such notes “U-Phils” as in “You do a Philosophical analysis”, which really only means it’s an analytic excercize that strives to first give the most generous interpretation to positions, and then examines them. See the general definition of  a U-Phil.

Some Examples:

Mayo, Senn, and Wasserman on Gelman’s RMM** Contribution

U-Phil: A Further Comment on Gelman by Christian Hennig.

For a whole group of reader contributions, including Jim Berger on Jim Berger, see: Earlier U-Phils and Deconstructions

If you’re writing a note on objectivity, you might wish to compare and contrast Excursion 4 Tour I with a paper by Gelman and Hennig (2017): “Beyond subjective and objective in Statistics”.

These invites extend through January.

Categories: SIST, Statistical Inference as Severe Testing | Leave a comment

SIST* Blog Posts: Excerpts & Mementos (to Dec 31 2018)

Surveying SIST Blog Posts So Far

Excerpts

  • 05/19: The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars
  • 09/08: Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1)
  • 09/11: Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2)
  • 09/15: Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3)
  • 09/29: Excursion 2: Taboos of Induction and Falsification: Tour I (first stop)
  • 10/10: Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3)
  • 11/30: Where are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3
  • 12/01: Neyman-Pearson Tests: An Episode in Anglo-Polish Collaboration: Excerpt from Excursion 3 (3.2)
  • 12/04: First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3]
  • 12/11: It’s the Methods, Stupid: Excerpt from Excursion 3 Tour II  (Mayo 2018, CUP)
  • 12/20: Capability and Severity: Deeper Concepts: Excerpts From Excursion 3 Tour III
  • 12/26: Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP)
  • 12/29: 60 Years of Cox’s (1958) Chestnut: Excerpt from Excursion 3 tour II.

Mementos, Keepsakes and Souvenirs

  • 10/29: Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars)
  • 11/8:   Souvenir C: A Severe Tester’s Translation Guide (Excursion 1 Tour II)
  • 10/5:  “It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based” (Keepsake by Fisher, 2.1)
  • 11/14: Tour Guide Mementos and Quiz 2.1 (Excursion 2 Tour I Induction and Confirmation)
  • 11/17: Mementos for Excursion 2 Tour II Falsification, Pseudoscience, Induction
  • 12/08: Memento & Quiz (on SEV): Excursion 3, Tour I
  • 12/13: Mementos for “It’s the Methods, Stupid!” Excursion 3 Tour II (3.4-3.6)
  • 12/26: Tour Guide Mementos From Excursion 3 Tour III: Capability and Severity: Deeper Concepts

*Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo, CUP 2018).

Categories: SIST, Statistical Inference as Severe Testing | Leave a comment

Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP)

.

Tour I The Myth of “The Myth of Objectivity”*

 

Objectivity in statistics, as in science more generally, is a matter of both aims and methods. Objective science, in our view, aims to find out what is the case as regards aspects of the world [that hold] independently of our beliefs, biases and interests; thus objective methods aim for the critical control of inferences and hypotheses, constraining them by evidence and checks of error. (Cox and Mayo 2010, p. 276)

Whenever you come up against blanket slogans such as “no methods are objective” or “all methods are equally objective and subjective” it is a good guess that the problem is being trivialized into oblivion. Yes, there are judgments, disagreements, and values in any human activity, which alone makes it too trivial an observation to distinguish among very different ways that threats of bias and unwarranted inferences may be controlled. Is the objectivity–subjectivity distinction really toothless, as many will have you believe? I say no. I know it’s a meme promulgated by statistical high priests, but you agreed, did you not, to use a bit of chutzpah on this excursion? Besides, cavalier attitudes toward objectivity are at odds with even more widely endorsed grass roots movements to promote replication, reproducibility, and to come clean on a number of sources behind illicit results: multiple testing, cherry picking, failed assumptions, researcher latitude, publication bias and so on. The moves to take back science are rooted in the supposition that we can more objectively scrutinize results – even if it’s only to point out those that are BENT. The fact that these terms are used equivocally should not be taken as grounds to oust them but rather to engage in the difficult work of identifying what there is in “objectivity” that we won’t give up, and shouldn’t. Continue reading

Categories: Error Statistics, SIST, Statistical Inference as Severe Testing | 4 Comments

Where Are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3

Excursion 3 Statistical Tests and Scientific Inference

Tour I Ingenious and Severe Tests

[T]he impressive thing about [the 1919 tests of Einstein’s theory of gravity] is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted.The theory is incompatible with certain possible results of observation – in fact with results which everybody before Einstein would have expected. This is quite different from the situation I have previously described, [where] . . . it was practically impossible to describe any human behavior that might not be claimed to be a verification of these [psychological] theories. (Popper 1962, p. 36)

Mayo 2018, CUP

The 1919 eclipse experiments opened Popper’ s eyes to what made Einstein’ s theory so different from other revolutionary theories of the day: Einstein was prepared to subject his theory to risky tests.[1] Einstein was eager to galvanize scientists to test his theory of gravity, knowing the solar eclipse was coming up on May 29, 1919. Leading the expedition to test GTR was a perfect opportunity for Sir Arthur Eddington, a devout follower of Einstein as well as a devout Quaker and conscientious objector. Fearing “ a scandal if one of its young stars went to jail as a conscientious objector,” officials at Cambridge argued that Eddington couldn’ t very well be allowed to go off to war when the country needed him to prepare the journey to test Einstein’ s predicted light deflection (Kaku 2005, p. 113). Continue reading

Categories: SIST, Statistical Inference as Severe Testing | 1 Comment

SIST* Posts: Excerpts & Mementos (to Nov 30, 2018)

Surveying SIST Posts so far

SIST* BLOG POSTS (up to Nov 30, 2018)

Excerpts

  • 05/19: The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars
  • 09/08: Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1)
  • 09/11: Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2)
  • 09/15: Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3)
  • 09/29: Excursion 2: Taboos of Induction and Falsification: Tour I (first stop)
  • 10/10: Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3)
  • 11/30: Where are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3

Mementos, Keepsakes and Souvenirs

  • 10/29: Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars)
  • 11/8:   Souvenir C: A Severe Tester’s Translation Guide (Excursion 1 Tour II)
  • 10/5:  “It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based” (Keepsake by Fisher, 2.1)
  • 11/14: Tour Guide Mementos and Quiz 2.1 (Excursion 2 Tour I Induction and Confirmation)
  • 11/17: Mementos for Excursion 2 Tour II Falsification, Pseudoscience, Induction

*Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo, CUP 2018)

Categories: SIST, Statistical Inference as Severe Testing | 3 Comments

Tour Guide Mementos and QUIZ 2.1 (Excursion 2 Tour I: Induction and Confirmation)

.

Excursion 2 Tour I: Induction and Confirmation (Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars)

Tour Blurb. The roots of rival statistical accounts go back to the logical Problem of Induction. (2.1) The logical problem of induction is a matter of finding an argument to justify a type of argument (enumerative induction), so it is important to be clear on arguments, their soundness versus their validity. These are key concepts of fundamental importance to our journey. Given that any attempt to solve the logical problem of induction leads to circularity, philosophers turned instead to building logics that seemed to capture our intuitions about induction. This led to confirmation theory and some projects in today’s formal epistemology. There’s an analogy between contrasting views in philosophy and statistics: Carnapian confirmation is to Bayesian statistics, as Popperian falsification is to frequentist error statistics. Logics of confirmation take the form of probabilisms, either in the form of raising the probability of a hypothesis, or arriving at a posterior probability. (2.2) The contrast between these types of probabilisms, and the problems each is found to have in confirmation theory are directly relevant to the types of probabilisms in statistics. Notably, Harold Jeffreys’ non-subjective Bayesianism, and current spin-offs, share features with Carnapian inductive logics. We examine the problem of irrelevant conjunctions: that if x confirms H, it confirms (H & J) for any J. This also leads to what’s called the tacking paradox.

Quiz on 2.1 Soundness vs Validity in Deductive Logic. Let ~C be the denial of claim C. For each of the following argument, indicate whether it is valid and sound, valid but unsound, invalid. Continue reading

Categories: induction, SIST, Statistical Inference as Severe Testing, Statistics | 10 Comments

Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars)

Stat Museum

Excursion 1 Tour II: Error Probing Tools vs. Logics of Evidence 

Blurb. Core battles revolve around the relevance of a method’s error probabilities. What’s distinctive about the severe testing account is that it uses error probabilities evidentially: to assess how severely a claim has passed a test. Error control is necessary but not sufficient for severity. Logics of induction focus on the relationships between given data and hypotheses–so outcomes other than the one observed drop out. This is captured in the Likelihood Principle (LP). Tour II takes us to the crux of central wars in relation to the Law of Likelihood (LL) and Bayesian probabilism. (1.4) Hypotheses deliberately designed to accord with the data can result in minimal severity. The likelihoodist wishes to oust them via degrees of belief captured in prior probabilities. To the severe tester, such gambits directly alter the evidence by leading to inseverity. (1.5) Stopping rules: If a tester tries and tries again until significance is reached–optional stopping–significance will be attained erroneously with high probability. According to the LP, the stopping rule doesn’t alter evidence. The irrelevance of optional stopping is an asset for holders of the LP, it’s the opposite for a severe tester. The warring sides talk past each other. Continue reading

Categories: SIST, Statistical Inference as Severe Testing | 1 Comment

The Physical Reality of My New Book! Here at the RSS Meeting

.

Categories: SIST | 3 Comments

Blog at WordPress.com.