Philosophy and the practice of Bayesian statistics

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3: Further typo fixes. v4: Revised in response to referee

A canonical theory of dynamic decision-making

Decision-making behavior is studied in many very different fields, from medicine and eco- nomics to psychology and neuroscience, with major contributions from mathematics and statistics, computer science, AI, and other technical disciplines. However the conceptual- ization of what decision-making is and methods for studying it vary greatly and this has resulted in fragmentation of the field. A theory that can accommodate various perspectives may facilitate interdisciplinary working. We present such a theory in which decision-making is articulated as a set of canonical functions that are sufficiently general to accommodate diverse viewpoints, yet sufficiently precise that they can be instantiated in different ways for specific theoretical or practical purposes. The canons cover the whole decision cycle, from the framing of a decision based on the goals, beliefs, and background knowledge of the decision-maker to the formulation of decision options, establishing preferences over them, and making commitments. Commitments can lead to the initiation of new decisions and any step in the cycle can incorporate reasoning about previous decisions and the rationales for them, and lead to revising or abandoning existing commitments. The theory situates decision-making with respect to other high-level cognitive capabilities like problem solving, planning, and collaborative decision-making. The canonical approach is assessed in three domains: cognitive and neuropsychology, artificial intelligence, and decision engineering

An Instrumentalist Account of How to Weigh Epistemic and Practical Reasons for Belief

When one has both epistemic and practical reasons for or against some belief, how do these reasons combine into an all-things-considered reason for or against that belief? The question might seem to presuppose the existence of practical reasons for belief. But we can rid the question of this presupposition. Once we do, a highly general ‘Combinatorial Problem’ emerges. The problem has been thought to be intractable due to certain differences in the combinatorial properties of epistemic and practical reasons. Here we bring good news: if we accept an independently motivated version of epistemic instrumentalism—the view that epistemic reasons are a species of instrumental reasons—we can reduce The Combinatorial Problem to the relatively benign problem of how to weigh different instrumental reasons against each other. As an added benefit, the instrumentalist account can explain the apparent intractability of The Combinatorial Problem in terms of a common tendency to think and talk about epistemic reasons in an elliptical manner

Slim Epistemology with a Thick Skin

The distinction between “thick” and “thin” value concepts, and its importance to ethical theory, has been an active topic in recent meta-ethics. This paper defends three claims regarding the parallel issue about thick and thin epistemic concepts. (1) Analogy with ethics offers no straightforward way to establish a good, clear distinction between thick and thin epistemic concepts. (2) Assuming there is such a distinction, there are no semantic grounds for assigning thick epistemic concepts priority over the thin. (3) Nor does the structure of substantive epistemological theory establish that thick epistemic concepts enjoy systematic theoretical priority over the thin. In sum, a good case has yet to be made for any radical theoretical turn to thicker epistemology

Slim Epistemology with a Thick Skin

The distinction between ‘thick’ and ‘thin’ value concepts, and its importance to ethical theory, has been an active topic in recent meta-ethics. This paper defends three claims regarding the parallel issue about thick and thin epistemic concepts. (1) Analogy with ethics offers no straightforward way to establish a good, clear distinction between thick and thin epistemic concepts. (2) Assuming there is such a distinction, there are no semantic grounds for assigning thick epistemic concepts priority over the thin. (3) Nor does the structure of substantive epistemological theory establish that thick epistemic concepts enjoy systematic theoretical priority over the thin. In sum, a good case has yet to be made for any radical theoretical turn to thicker epistemology

Asset Pricing Theories, Models, and Tests

An important but still partially unanswered question in the investment field is why different assets earn substantially different returns on average. Financial economists have typically addressed this question in the context of theoretically or empirically motivated asset pricing models. Since many of the proposed “risk” theories are plausible, a common practice in the literature is to take the models to the data and perform “horse races” among competing asset pricing specifications. A “good” asset pricing model should produce small pricing (expected return) errors on a set of test assets and should deliver reasonable estimates of the underlying market and economic risk premia. This chapter provides an up-to-date review of the statistical methods that are typically used to estimate, evaluate, and compare competing asset pricing models. The analysis also highlights several pitfalls in the current econometric practice and offers suggestions for improving empirical tests

Reliable credence and the foundations of statistics

If the goal of statistical analysis is to form justified credences based on data, then an account of the foundations of statistics should explain what makes credences justified. I present a new account called statistical reliabilism (SR), on which credences resulting from a statistical analysis are justified (relative to alternatives) when they are in a sense closest, on average, to the corresponding objective probabilities. This places (SR) in the same vein as recent work on the reliabilist justification of credences generally [Dunn, 2015, Tang, 2016, Pettigrew, 2018], but it has the advantage of being action-guiding in that knowledge of objective probabilities is not required to identify the best-justified available credences. The price is that justification is relativized to a specific class of candidate objective probabilities, and to a particular choice of reliability measure. On the other hand, I show that (SR) has welcome implications for frequentist-Bayesian reconciliation, including a clarification of the use of priors; complemen- tarity between probabilist and fallibilist [Gelman and Shalizi, 2013, Mayo, 2018] approaches towards statistical foundations; and the justification of credences outside of formal statistical settings. Regarding the latter, I demonstrate how the insights of statistics may be used to amend other reliabilist accounts so as to render them action-guiding. I close by discussing new possible research directions for epistemologists and statisticians (and other applied users of probability) raised by the (SR) framework