Abstract

Principles of chance deference say that you should align your credences with the objective chances. Roughly: so long as you don't have information about what happens after t, your credence in A, given that the time t chance of A is n%, should be n%. Principles like this face difficulties in cases in which you are uncertain of the truth-conditions of the thoughts in which you invest credence, as well as cases in which you've lost track of the time. For an illustration of the first problem (due to John Hawthorne and Maria Lasonen-Aarnio): suppose that there are 100 tickets in the lottery, and the winning ticket will be drawn tomorrow. Before it is drawn, we introduce the name "Lucky" to refer to whoever it is that actually holds the winning ticket. Then, you know for sure that today's chance of Lucky winning is 1%. (It's a fair lottery, so Lucky has the same chance of winning as everyone else.) But you also know for sure that Lucky will win---given the way the name "Lucky" was introduced, it is a priori knowable that Lucky wins. So this appears to be a case in which your credences should depart from the known chances. For an illustration of the second problem: suppose that, although today is Tuesday, you don't know whether today is Tuesday or Wednesday. But suppose you know for sure that today's chance of A is 75%. and yesterday's chance of A was 25%. Then, for all you know, the Tuesday chance of A is 25% (which is so iff today is Wednesday), and for all you know, the Tuesday chance of A is 75% (which is so iff today is Tuesday). Then, the principle of chance deference says that, conditional today being Tuesday, your credence in A should be 75%; whereas, conditional on today being Wednesday, your credence in A should be 25%. Since you're not sure whether today is Tuesday or Wednesday, the principle says that your credence in A should be somewhere between 25% and 75%. But you know for sure that the current chance of A is 75%. So it seems that your credence in A should be 75%. In response to these two troubles, I propose an amendment of the principle of chance deference. This amended principle has a surprising consequence for debates about Elga's Sleeping Beauty puzzle. According to this new principle of chance deference, the 'Halfer' does not defer to the chances, whereas the 'Thirder' does.

Abstract

Predictive algorithms are playing an increasing prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm's predictions and the actual outcomes, for instance, that the rate of false positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results show that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except an expectational calibration criterion, is a necessary condition for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness.

Abstract

This talk will discuss, at a relatively high level, several advantages of dealing with betting scores as the underlying instrument for statistical inference (or their measure-theoretic cousins: e-values and nonnegative supermartingales).

Topics include: causal inference, nonparametric estimation, universal inference and multiple testing.

Some relevant papers:

- False discovery rate control with e-values R. Wang, A. Ramdas
- Admissible anytime-valid sequential inference must rely on nonnegative martingales A. Ramdas, J. Ruf, M. Larsson, W. Koolen
- Universal inference L. Wasserman, A. Ramdas, S. Balakrishnan PNAS, 2020
- Time-uniform, nonparametric, nonasymptotic confidence sequences S. Howard, A. Ramdas, J. Sekhon, J. McAuliffe Annals of Stat., 2021
- Time-uniform Chernoff bounds via nonnegative supermartingales S. Howard, A. Ramdas, J. Sekhon, J. McAuliffe Prob. Surveys, 2020

Abstract

An important question in economics is how people choose when facing uncertainty in the timing of rewards. In this paper we study preferences over time lotteries, in which the payment amount is certain but the payment time is uncertain. In expected discounted utility (EDU) theory decision makers must be risk-seeking over time lotteries. Here we explore growth-optimality, a normative model consistent with standard axioms of choice, in which decision makers maximise the growth rate of their wealth. Growth-optimality is consistent with both risk-seeking and risk-neutral behaviour in time lotteries, depending on how growth rates are computed. We discuss two approaches to compute a growth rate: the ensemble approach and the time approach. Revisiting existing experimental evidence on risk preferences in time lotteries, we find that the time approach accords better with the evidence than the ensemble approach. Surprisingly, in contrast to the EDU prediction, the higher the ensemble-average growth rate of a time lottery is, the less attractive it becomes compared to a sure alternative. Decision makers thus may not consider the ensemble-average growth rate as a relevant criterion for their choices. Instead, the time-average growth rate may be a better criterion for decision-making.

Abstract

There are three principal versions of the card game baccarat.

1. Baccarat punto banco is a nonstrategic game that is (or was, before COVID) a 40 billion dollar industry in Macau.

2. Baccarat chemin de fer is a two-person zero-sum game that played a role in the development of game theory, and evolved, over a period of about 100 years, into baccarat punto banco.

3. Baccarat banque is a three-person zero-sum game depending on a continuous parameter for which the most natural solution concept is not the Nash equilibrium. It was a predecessor of baccarat chemin de fer.

In this talk we discuss all three games, their history, and their game-theoretic aspects.

Abstract

Suppose an analog spinner is spun. That the spinner should stop on a particular exact angle x has probability zero according to classical probability theory. But at the same time, intuitively, it seems that the probability that the spinner should stop at angle x is more likely than that the spinner should turn into a square circle, which also has probability zero. Three kinds of attempts have been made to depart from classical probability theory that allow one to make subtler comparison than classical probability allows: fundamental conditional probabilities (or Popper functions), hyperreal probabilities and qualitative probabilities. Unfortunately, it is known that in a number of prominent cases, some of these approaches are guaranteed to violate the symmetries of the situation. For instance, there is no rotationally invariant hyperreal probability on the circle that assigns non-zero probability to every possible outcome. This leads to the mathematically interesting question of exactly when these subtler probabilities can be assigned in ways that respect symmetries. On a strong (and I argue correct) understanding of "respecting symmetries", the literature is close to a complete answer for the conditional probability case. I fill out the remaining details of that case, and give complete characterizations in the hyperreal and qualitative probability cases. This leads to a philosophical question: Is there anything philosophically special about the cases where it is possible to respect symmetries? Unfortunately, I am at this point unable to find a positive answer.

Abstract

During the first decades of the 20th century, several mathematicians throughout Europe tackled the problem of defining axioms for probability calculus. However Borel, Fréchet and Lévy, the three most prominent probabilists in France in the 1920s and 1930s, adopted mixed attitudes towards those attempts : indifferent or hostile but always attentive. Although the three of them seem not to agree, we argue that their attitude is the result of the unfavorable context for the mathematical development of probability calculus in France in the beginning of the 20th century and a common outlook on both the foundation of probability and the role played by mathematics in scientific knowledge.

Abstract

A major goal of twentieth-century philosophy of science was to show how science could make progress toward the truth even if, at any moment, our best theories are false. To that end, Popper and others tried to develop a theory of truthlikeness, hoping to prove that theories get closer to the truth over time. That program encountered several notable setbacks. I propose the following: a method for answering an empirical question is progressive if the chance of outputting the true answer is strictly increasing with sample size. Surprisingly, many standard statistical methods are not even approximately progressive. What's worse, many problems do not admit strictly progressive solutions. However, I prove that it is often possible to approximate progressiveness arbitrarily well. Furthermore, every approximately progressive method must obey a version of Ockham’s razor. So it turns out that addressing the problem of progress uncovers a solution to another perennial problem: how can we give a non-circular argument for preferring simple theories when the truth may well be complex?

Abstract

A great deal of theorising about the proper place of statistical reasoning in the courtroom revolves around several canonical thought experiments that invoke toy statistical models of the situation in question. I will argue that all of these canonical thought experiments are flawed in various (albeit interesting) ways. In some cases the flaws involve subtle underspecification that leads to ambiguity about the intuitive judgement; in other cases the flaw is that the thought experiment stipulates that we forgo freely-available and relevant evidence. The upshot is that these thought experiments do not succeed in undermining the use of statistical evidence in the courtroom.

Abstract

An epistemology of induction should have all of the following features: 1. (The Evidentialist Theme) This epistemology should allow us to assess competing hypotheses in terms evidential support---in terms of how those hypotheses are each supported by the available evidence. 2. (The Reliabilist Theme) This epistemology should allow us to evaluate competing inductive methods in terms of reliability---in terms of how reliable those methods are for finding the true hypothesis. 3. (Continuity with Data Science) This epistemology should not only accommodate some intuitively justified inferences in science, but also join data scientists in solving some inference problems that exist in science. I will sketch how it is possible to develop such an epistemology of induction with all those three features. I will do that by walking you through a case study on inferring causation from statistical data.

Abstract

In this paper, we ask: how should an agent who has incoherent credences update when they learn new evidence? The standard Bayesian answer for coherent agents is that they should conditionalize; however, this updating rule is not defined for incoherent starting credences. We show how one of the main arguments for conditionalization, the Dutch strategy argument, can be extended to devise a target property for updating plans that can apply to them regardless of whether the agent starts out with coherent or incoherent credences. The main idea behind this extension is that the agent should avoid updating plans that increase the possible sure loss from Dutch strategies. This happens to be equivalent to avoiding updating plans that increase incoherence according to a distance-based incoherence measure.

Abstract

Abstract

Two common ways to forecast political outcomes are (i) prediction markets (Markets) and (ii) statistical models (Models). Which is more reliable?

Over the past several U.S. elections, the Models and Markets have disagreed substantially on their assessment of the mode likely outcome. In 2020, for example, the leading forecasters and poll aggregators forecasted a Joe Biden win with probability 90-95%, while almost all betting markets assessed Biden's chances in the 60-70% range.

An argument in favor of betting markets is that they are better able to aggregate information than forecasters, who predominantly rely on polling data. In addition, the fact that bettors risk their own money gives a concrete disincentive against betting for a candidate based purely on sentiment. Despite this, many insist that the discrepancy between the Models and Markets, in both 2020 and in previous election cycles, reflects an irrationality among market participants.

Proponents of models, such as FiveThirtyEight and the Economist, insist that their forecasts are consistently more accurate than the betting markets. Is this true?

I'll provide an overview of the claims on both sides and show the results of my analysis of the 2020 election based on a proposed market-based scoring metric, which evaluates the performance of probabilistic forecasts based on their would-be performance in the betting markets.

In addition to the analysis presented here, a running tally of results from the above analysis was updated and reported throughout the 2020 campaign at https://pivs538.herokuapp.com/.

Abstract

In this talk I will defend two theses about the relation between chances and credences. The first is that chances should be identified with the judgements or partial beliefs of a (hypothetical) unbounded and fully informed perfect inductive reasoner and not with any of the possible grounds for her judgements, such as frequencies or propensities. The second is a conditional version of the Principal Principle, which says that that rational conditional belief given the evidence should go by the expectation of conditional chance given this evidence. The two theses are mutually supporting and make better sense (I shall claim) of the role that chance plays in our reasoning about what to believe and do than rival accounts.

Location: Miller Hall

Abstract

It follows from plausible claims about the laws of physics and the narrowness of the most relevant reference class that the positive chances between 0.0 and 1.0 that lotteries yield are almost certainly merely epistemic rather than objective. It is, for example, merely a matter of our ignorance that a given fair coin toss will confer a 0.5 chance of landing heads. In actual objective fact, the chances that it will land heads are almost certainly either 0.0 or 1.0. I argue that, even if all chances between 0.0 and 1.0 are merely epistemic rather than objective, the provision by lottery of such merely epistemically equal positive chances of an indivisible, life-saving resource to those with equal claims renders things fairer by providing the equal distribution of something that it is rational to value equally, which makes a material difference to the goods people end up receiving.

Location: Miller Hall

Abstract

In March, over 800 statisticians endorsed an editorial in Nature entitled “Retire statistical significance”. Can we really blame current abuses on the word “significance”? The existence of the same abuses in the 19th century suggests not. See Working Paper 55.

Location: Hill Center

Abstract

The paper argues that the current discussions on replicability and the abuse of significance testing do not do justice to the real problem: the untrustworthiness of published empirical evidence. When viewed from the error-statistical perspective the p-hacking, multiple testing, cherry-picking and low power studies are only symptoms of a much broader problem relating to the recipe-like implementation of statistical methods that contributes in many different ways to the untrustworthy evidence problem, including: (i) statistical misspecification, (ii) inadequate understanding and the poor implementation of inference procedures, and (iii) unwarranted evidential interpretations of frequentist inferential results. Indeed, a case is made that the same recipe-like implementation of statistical methods could easily render untrustworthy evidence replicable, when equally uninformed practitioners follow the same questionable implementation. It is also argued that alternative methods to replace significance testing, including using observed confidence intervals and estimation-based effects sizes, as well as lowering rejection thresholds, do not address the untrustworthy evidence problem since they are equally vulnerable to (i)-(iii). The paper also discusses the question of what replication could mean for observational data, as opposed to experimental data.

Abstract

Frequentism has a long and troubled history as an interpretation of probability. Recently, many have pursued the metaphysical project of accounting for single-case objective chance within Humean strictures. While these subjects might seem related only in their connection to probability broadly construed, I argue that the biggest problems for Humean chance are direct analogs of serious problems for frequentism and vice versa. I then attempt to diagnose the common origins of these difficulties with a view toward the prospects for Humean theories of chance in particular.

Abstract

Advantage play is the act of legally exploiting procedural or structural weaknesses in casino games, marketing or operations in a way that generates an edge over the casino. The most well-known advantage play is blackjack card counting, as first expounded by Edward Thorp in 1962. Over fifty-five years later, the range of opportunities has expanded.

Modern advantage players legally beat table games, side bets, slot machines, video poker, sports betting, casino promotions and anything else they find that is sufficiently profitable. They analyze shuffling algorithms used by automatic shufflers. They exploit bias in devices such as roulette wheels. They pounce on poorly conceived casino marketing campaigns. Today’s top players are limited only by their creativity and diligence.

In this talk we will give an overview of some of the most profitable methods used by today’s top players. These methods include hole-carding, ace tracking, information sharing, edge sorting, loss rebates and more. We will present case studies that cover some of the mathematical and strategic ideas behind these methods, including Phil Ivey’s edge sorting at Crockford’s Casino in London and Don Johnson’s exploitation of loss rebates in Atlantic City. In particular, we will present three “Loss Rebate Theorems,” based on an application of a well-known theorem on Brownian motion with drift, and show their applicability to a wide variety of highly profitable opportunities.

Speaker Bio:

Eliot Jacobson received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot was Associate Professor of Mathematics at Ohio University and Visiting Associate Professor and Lecturer of Computer Science at U.C. Santa Barbara. Eliot retired from academia in 2009.

After a decade as an advantage player, Eliot founded Jacobson Gaming, LLC in 2006. His company specialized in casino table game design, advantage play analysis, game development, and mathematical certification. Eliot's most recent book, "Advanced Advantage Play," (2015, Blue Point Books) is an industry best-seller on the topic of legally beating casino table games, side bets and promotions.

Eliot fully retired in 2017.

Abstract

Algorithms are increasingly used by public and private sector entities to streamline decisions about health care, welfare benefits, child abuse, public housing, policing, bail and sentencing. Although algorithms can render decisions more efficient, they can also exacerbate existing inequities and structural biases in society. This paper focuses on the debate about the fairness of algorithms in criminal justice. In this context, fairness is understood in at least two different ways, as predictive parity and classification parity. The received view in the literature, following a number of impossibility results, is that since no algorithm can concurrently satisfy both conceptions of fairness, there are tradeoffs in pursuing one or the other conception. I believe that this framing of the debate is erroneous. Both classification parity and predictive parity can be concurrently achieved provided the algorithm is sufficiently accurate. I demonstrate this claim by simulating a decision algorithm for binary classification, showing that departures from classification and predictive parity become smaller as algorithmic accuracy increases.

Abstract

David Lewis (and others) have famously argued against Adams's Thesis (that the probability of a conditional is the conditional probability of its consequent, given it antecedent) by proving various "triviality results." In this paper, I argue for two theses -- one negative and one positive. The negative thesis is that the "triviality results" do not support the rejection of Adams's Thesis, because Lewisian "triviality based" arguments against Adams's Thesis rest on an implausibly strong understanding of what it takes for some credal constraint to be a rational requirement (an understanding which Lewis himself later abandoned in other contexts). The positive thesis is that there is a simple (and plausible) way of modeling the epistemic probabilities of conditionals, which (a) obeys Adams's Thesis, and (b) avoids all of the existing triviality results.

Abstract

The box is either empty or contains $1 million (you can't see which). You will either receive (1) just the contents of the box, or (2) the contents of the box plus an extra $1,000. You get to choose (1) or (2). The catch is that a reliable predictor put the $1 million in the box if and only if he predicted you would refuse the extra $1,000. Should you take the $1,000?

This is Newcomb's Problem, which has divided philosophers since it was described by Nozick (1969). Those who favor taking the $1,000 are called "two-boxers" and are typically moved by the sort of "causal dominance reasoning" exemplified by the following speech: "I have no present control over the contents of the box. Whether the box is empty or not, I prefer having an extra $1,000. So I should take the $1,000."

It is often thought that various so-called "causal decision theories" (such as theories described by Stalnaker, Lewis, Gibbard & Harper, Joyce, and others) vindicate causal dominance reasoning, and so are attractive theories for two-boxers. Adapting observations due to Ahmed, Dorr, and Joyce, I argue that those theories do not vindicate causal dominance reasoning in general. Indeed, for each such theory there are Newcomb problems in which the theory recommends *one-boxing*. So none of those theories deserve the name "causal decision theory". I conclude that a true causal decision theory does not exist---or at least, does not exist yet.

Attendees interested in a playful introduction to disputes about Newcomb's problem may optionally wish to look at "Newcomb University: A Play in One Act" (The talk will be self-contained and no advance reading will be presupposed.

Abstract

There are two dominant paradigms in the theory of qualitative belief change. While belief revision theory attempts to describe the way in which rational agents revise their beliefs upon gaining new evidence about an essentially static world, the theory of belief update is concerned with describing how such agents change their qualitative beliefs upon learning that the world is changing in some way.

A similar distinction can be made when it comes to describing the way in which a rational agent changes their subjective probability assignments, or `credences', over time. On the one hand, we need a way to describe how these credences evolve when the agent learns something new about a static environment. On the other hand, we need a way to describe how they evolve when the agent learns that the world has changed.

According to orthodoxy, the correct answers to the questions of how an agent should revise their qualitative beliefs and numerical credences upon obtaining new information about a static world are given by the axiomatic AGM theory of belief revision and Bayesian conditionalisation, respectively. Now, under the influential Lockean theory of belief, an agent believes a proposition p if and only if their credence in p is sufficiently high (where what counts as `sufficiently high' is determined by some threshold value t 2 (1=2; 1]). Thus, assuming a Lockean theory of belief, Bayesian conditionalization de nes an alternative theory of qualitative belief revision, where p is in the revised belief set if and only if the agent's posterior credence in p is above the relevant threshold after conditionalising on the new evidence. Call this theory of belief revision `Lockean revision'. The relationship between Lockean revision and the AGM theory of belief revision was systematically described by Shear and Fitelson (forthcoming).

With regards to belief updating, the most widely accepted answers to the questions of how an agent should revise their qualitative beliefs and numerical credences upon obtaining new information about how the world is changing over time are given by Katsuno and Mendelzon's axiomatic theory of belief update (KM-update) and Lewis's technique of probabilistic imaging, respectively. In this sequel to our study of the relationship between Bayesian (viz., Lockean revision) and AGM revision, we investigate the relationships between Bayesian (viz., Lockean imaging) KM updating.

The latest draft can be downloaded: http://fitelson.org/tatbr.pdf

Abstract

Wagering on horse racing is an unforgiving arena in which the bettor’s probability estimates are tested against betting odds set by public consensus via the pari-mutuel system.

The underlying event, the horse race, is a complex real world phenomenon whose outcome is determined principally by the laws of physics and biology combined with a certain amount of random variation. Overlaid on this physical process is a complex milieu of jockeys, trainers and owners whose changing proclivities can also affect race outcomes. A race can be represented with a state-space model in which the race outcome is a stochastic function of the state parameters. Complicating the situation further, most of the parameters of interest (e.g. the fitness of a particular horse or the skill of a jockey) cannot be observed directly but must be inferred from past race results.

The large takeout (~17%) levied by the racetrack means that a would-be successful bettor needs to identify situations wherein the true probability of a bet winning is at least ~17% higher than that implied by the betting odds. Racetrack betting markets are largely efficient in the sense used to describe financial markets in that the betting odds are highly informative and largely unbiased estimators of the horses’ probabilities of winning. However in the speaker’s experience, probability lies in the eye of the beholder. A practical methodology will be described whereby superior probability estimates can be produced which result in long term betting profits.

Abstract

Typicality has been widely used in statistical mechanics in order to help explaining the approach to equilibrium of thermodynamic systems. I aim at showing that typicality reasoning qualifies for many situations beyond statistical mechanics. In particular, I show how regression to the mean rely on typicality and how probabilites arise from typicality.

Abstract

In his work on the inner world, Jakob von Uexkull describes how a creature like a tick, or a dog, or a child sees the world and how it moves inside its personal world. That world is called by him the umwelt of that creature. We adults also have our umwelts, but unlike a tick or a dog we enrich our umwelt by consulting the umwelts of other people and using science. A tick has its own, meager logic. A dog or a baby has a richer logic and we adults have a richer logic still. How do these logics work, especially since the first two logics are outside language? Can we still speak of the inferences made by a dog? An insect? Can we use our language to describe their inferences? Uexkull anticpiated many of the ideas current in Artificial Intelligence. The example of the Wumpus, popular in AI literature is anticipated by Uexkull with his example of a tick.

Abstract

We start by motivating as to how the notion of information arose, and how it evolved, via the idealistic scenario of a courtroom, and that of a hacker trying to break a computer's password. We then introduce the notion of Shannon entropy as a natural consequence of the basic Fisher-Hartley idea of self-information, and subsequently make the charge that Shannon took a giant leap of faith when he proposed his famous, and well lubricated, formula. A consequence is that Shannon's formula overestimates the inherent uncertainty in a random variable. We also question Shannon's strategy of taking expectations and suggest alternatives to it based on the Kolmogorov-Nagumo functions for the mean of a sequence of numbers. In the sequel, we put forward the case that the only way to justify Shannon's formula is to look at self-information as a utility in a decision theoretic context. This in turn enables an interpretation for the recently proposed notion of "extropy". We conclude our presentation with the assertion that a complete way to evaluate the efficacy of a predictive distribution (or a mathematical model) is by the tandem use of both entropy and extropy.

Abstract

In a standard Bayesian belief model, the prior is always common knowledge. This prevents such a model from representing agents’ probabilistic beliefs about the origins of their priors. By embedding such a standard model in a larger standard model, however, we can describe such beliefs using "pre-priors". When an agent’s prior and pre-prior are mutually consistent in a particular way, she must believe that her prior would only have been different in situations where relevant event chances were different, but that variations in other agents’ priors are otherwise completely unrelated to which events are how likely. Thus Bayesians who agree enough about the origins of their priors must have the same priors.

The paper can be found here: http://hanson.gmu.edu/prior.pdf

Abstract

I will discuss how ideas from the foundations of probability can be applied to resolve the current scientific replication crisis. I focus on two specific approaches:

1. Prediction Markets to incentivize more accurate assessments of the scientific community’s confidence that a result will replicate.
2. The Fundamental Principle of Probability to incentivize more accurate assessments of the author’s confidence that their own results will replicate.

Abstract

Uncertainty in real life takes many forms. An analyst can hesitate to specify a prior for a Bayesian model, or be ignorant of the mechanism that gave rise to the missing data. Such kinds of uncertainty cannot be faithfully captured by a single probability, but can be by a set of probabilities, and in special cases by a capacity function or a belief function.

In this talk, I motivate sets of probabilities as an attractive modeling strategy, which encodes low-resolution information in both the data and the model with little need to concoct unwarranted assumptions. I present a prior-free belief function model for multinomial data, which delivers posterior inference as a class of random convex polytopes. I discuss challenges that arise with the employment of belief and capacity functions. Specifically, how the choice of conditioning rules reconciles among a trio of unsettling posterior phenomena: dilation, contraction and sure loss. These findings underscores the invaluable role of judicious judgment in handling low-resolution probabilistic information.

Abstract

In 1987, historian of science Lorraine Daston wrote about the impact of mathematics on the nascent insurance industry in England.

"Despite the efforts of mathematicians to apply probability theory and mortality statistics to problems in insurance and annuities in the late seventeenth and early eighteenth centuries, the influence of this mathematical literature on the voluminous trade in annuities and insurance was negligible until the end of the eighteenth century."

Abstract

There are two sources of randomness in our fundamental physical theories: quantum mechanical probabilities and statistical mechanical probabilities. The former are crucial for understanding quantum effects such as the interference patterns. The latter are important for understanding thermodynamic phenomena such as the arrow of time. It is standard to postulate the two kinds of probabilities independently and to take both of them seriously. In this talk, I will introduce a new framework for thinking about quantum mechanics in a time-asymmetric universe, for which the two kinds of probabilities can be reduced to just one. We will then consider what that means for the Mentaculus Vision (Loewer 2016) and the phenomena that I call “nomic vagueness.” Time permitting, we will also briefly compare and contrast my theory with some other proposals in the literature by Albert (2000), Wallace (2012), and Wallace (2016).

We will not assume detailed knowledge of physics, and we will introduce the necessary concepts in the first half of the talk. For optional reading, please see: https://arxiv.org/abs/1712.01666

Abstract

Probability theory started on the right foot with Cardano, Fermat and Pascal when it restricted itself to finite sample spaces, and was reduced to counting finite sets. Then it got ruined by attempts to come to grips with that fictional (and completely superfluous) 'notion' they called 'infinity'.

A lot of probability theory can be done by keeping everything finite, and whatever can't be done that way, is not worth doing. We live in a finite world, and any talk of 'infinite' sample spaces is not even wrong, it is utterly meaningless. The only change needed, when talking about an 'infinite' sequence of sample spaces, say of n coin tosses, {H,T}^n, for 'any' n, tacitly implying that you have an 'infinite' supply of such n, is to replace it by the phrase 'symbolic n'.

This new approach is inspired by the philosophy and ideology behind symbolic computation. Symbolic computation can also redo, ab initio, without any human help, large parts of classical probability theory.

Abstract

Choice functions constitute a very general and simple mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules to imprecise-probabilistic uncertainty models. Choice functions can be given a clear behavioural interpretation in terms of attitudes towards gambling.

I will introduce choice functions as a tool to model uncertainty, and connect them with sets of desirable gambles, a very popular but less general imprecise-probabilistic uncertainty model. Once this connection is in place, I will focus on two important devices for both models. First, I will discuss about performing conservative inferences with both models. Second, I will discuss how both models can cope with assessments of symmetry and indifference.

Abstract

High-profile failures of replication in the social and biological sciences underwrites a minimal requirement of evidence: If little or nothing has been done to rule out flaws in inferring a claim, then it has not passed a severe test. A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. This minimal severe-testing requirement leads to reformulating significance tests (and related methods) to avoid familiar criticisms and abuses. Viewing statistical inference as severe testing–whether or not you accept it–offers a key to understand and get beyond the statistics wars.

Bio: Deborah G. Mayo is Professor Emerita in the Department of Philosophy at Virginia Tech and is a visiting professor at the London School of Economics and Political Science, Centre for the Philosophy of Natural and Social Science. She is the author of Error and the Growth of Experimental Knowledge (Chicago, 1996), which won the 1998 Lakatos Prize awarded to the most outstanding contribution to the philosophy of science during the previous six years. She co-edited Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science (CUP, 2010) with Aris Spanos, and has published widely in the philosophy of science, statistics, and experimental inference. She will co-direct a summer seminar on Philosophy of Statistics, intended for philosophy and social science faculty and post docs, July 28-August, 2019.

Link to the proofs of the first Tour of Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo 2018, CUP)

Abstract

There will be no seminar today.

Abstract

1) Confusion at the level of the payoff functions (convexity matters), 2) Confusion concerning the Law of Large Numbers, 3) Misuse of the notion of probability. http://www.fooledbyrandomness.com/FatTails.html for more details and papers.

Abstract

Why is there an apparent arrow of time? The standard answer, due to Ludwig Boltzmann and developed by the contemporary Boltzmannians, attributes its origin in a special boundary condition on the physical space-time, now known as the “Past Hypothesis.” In essence, it says that the “initial” state of the universe was in a very orderly (low-entropy) state. In this talk, I would like to consider an alternative theory, motivated by the (in)famous Principle of Indifference. I will argue that the two theories, at least in some cosmological models, are in fact empirically on a par when we consider their de se (self-locating) content about where we are in time. As we shall see, our comparative study leads to an unexpected skeptical conclusion about our knowledge of the past. We will then think about what this means for the general issue in philosophy of science about theory choice and pragmatic considerations.

Abstract

One common reason given for thinking that there are non-trivial objective probabilities—or chances—in worlds where the fundamental laws are deterministic is that such probabilities play an important explanatory role. I examine this argument in detail and show that insofar as it is successful it places significant constraints on the further metaphysical theory that we give of deterministic chance.

Abstract

The last twenty years has seen an enormous rise in Bayesian models of cognitive phenomena, which posit that human mental function is approximately rational or optimal in nature. Contemporary theorizing has begun to settle on a “Common Wisdom”, in which human perception and cognition are seen as approximately optimal relative to the objective probabilities in the real world — “the statistics of the environment,” as it is often put. However traditional philosophy of probability in Bayesian theory generally assumes an epistemic or subjectivist conception of probability, which holds that probabilities are characteristics of observers’ states of knowledge, and do not have objective values — which implies, contrary to the Common Wisdom, that there is actually no such thing as an objective observer-independent “statistics of the environment.” In this talk I will discuss why exactly Bayesians have historically favored the subjectivist attitude towards probability, and why cognitive science should as well, highlighting some of the inconsistencies in current theoretical debate in cognitive science. My aim is partly to criticize the current state of the field, but mostly to point to what I see as a more productive way in which a subjective conception of probability can inform models of cognition.

Abstract

Objective chances are used to guide credences and in scientific explanations. Knowing there’s a high chance that the smoke in the room disperses, you can both infer that it will, and explain why it does. Defenders of ‘Best Systems’ and other Humean accounts (Lewis, Loewer, Hoefer) claim to be uniquely well placed to account for both features. These accounts reduce chance to non-modal features of reality. Chances are therefore objective and suitable for use in scientific explanations. Because Humean accounts reduce chance to patterns in actual events, they limit the possible divergence between relative frequencies and chances. Agents who align their credences with known chances are then guaranteed to do reasonably well when predicting events. So it seems Humean accounts can justify principles linking chance to credence such as Lewis’ Principal Principle. But there’s a problem. When used in scientific explanations, Humean chances and relative frequencies must be allowed to diverge to arbitrarily high degrees. So if we consider the scientific question of whether agents who align their credences to the (actual) Humean chances will do well, it is merely probable they will. The scientific use of chance undercuts the advantage Humeans claim over their rivals in showing how chance and credence principles are justified. By seeing how, we clarify the role of chance−credence principles in accounts of chance.

Abstract

Baseball has seemingly become a showcase for the triumph of statistical and probabilistic analysis over subjective, biased, traditional knowledge--the expertise of scorers replacing that of scouts. Little is known, however, about the way scorers and scouts actually make assessments of value. Over the twentieth century, scouts, no less than scorers, had to express their judgments numerically--the practices of scorers and scouts are far more similar than different. Through the history of judgments of value in baseball, we can come to a deeper understanding about the nature of expertise and numerical objectivity, as well as the rise of data analysis more broadly.

Abstract

In Willful Ignorance: The Mismeasure of Probability (Wiley, 2014) I traced the evolution of (additive) probability from its humble origins in games of chance to its current dominance in scientific and business activity. My main thesis was that mathematical probability is nothing more nor less than a way to quantify uncertainty by drawing an analogy with a “metaphorical lottery.” In some situations, this hypothetical lottery can be more complex than simply drawing a ball from an urn. In that case, the resulting probabilities are based on a protocol, essentially a set of procedures that define precisely how such a lottery is being performed. Absent an explicit protocol, there may be considerable ambiguity and confusion about what, if anything, the probability statement really means. I believe that many philosophical debates about foundational issues in statistics could be illuminated by thoughtful elucidation of implicit protocols. Attention to such protocols is increasingly important in the context of Big Data problems. I will conclude with a rather surprising application of these ideas to the analysis of individualized causal effects.

Abstract

Glenn Shafer interviews Daniel Kahneman.

Abstract

Causal decision theory (CDT) has serious difficulty handling asymmetric instability problems (Richter 1984, Weirich 1985, Egan 2007). I explore the idea that the key to solving these problems is Isaac Levi’s thesis that "deliberation crowds out prediction" i.e. that agents cannot assign determinate credences to their currently available options. I defend the view against recent arguments of Alan Hájek’s and sketch an imaging-based version of CDT with indeterminate credences and expected values. I suggest that imaging might be thought of as the hypothetical revision method appropriate to making true rather than learning true and argue that CDT should be seen not as a rival to orthodox decision theory, but simply as a more permissive account of the norms of rationality.

Abstract

When measured over decades in countries that have been relatively stable, returns from stocks have been substantially better than returns from bonds. This is often attributed to investors' risk aversion.

In the theory of finance based on game-theoretic probability, in contrast, time-rescaled Brownian motion and the equity premium both emerge from speculation. This explanation accounts for the magnitude of the premium better than risk aversion.

See Working Paper 47 at www.probabilityandfinance.com. Direct link is http://www.probabilityandfinance.com/articles/47.pdf.

Abstract

The main divide in the philosophical discussion of chances, is between Humean and anti-Humean views. Humeans think that statements about chance can be reduced to statements about patterns in the manifold of actual fact (the ‘Humean Mosaic’). Non-humeans deny that reduction is possible. If one goes back and looks at Lewis’ early papers on chance, there are actually two separable threads in the discussion: one that treats chances as recommended credences and one that identifies chances with patterns in the manifold of categorical fact. I will defend a half humean view that retains the first thread and rejects the second.

The suggestion wiill that what the Humean view can be thought of as presenting the patterns in the Humean mosaic as the basis for inductive judgments built into the content of probabilistic belief. This could be offered as a template for accounts of laws, capacities, dispositions, and causes – i.e., all of the modal outputs of Best System style theorizing. In each case, the suggestion will be, these are derivative quantities that encode inductive judgments based on patterns in the manifold of fact. They extract projectible regularities from the pattern of fact and give us belief-forming and decision-making policies that have a general, pragmatic justification.

Abstract

A recent proposal to "redefine statistical significance" (Benjamin, et al. Nature Human Behaviour, 2017) claims that false positive rates "would immediately improve" by factors greater than two and fall as low as 5%, and replication rates would double simply by changing the conventional cutoff for 'statistical significance' from P<0.05 to P<0.005. I will survey several criticisms of this proposal and also analyze the veracity of these major claims, focusing especially on how Benjamin, et al neglect the effects of P-hacking in assessing the impact of their proposal. My analysis shows that once P-hacking is accounted for the perceived benefits of the lower threshold all but disappear, prompting two main conclusions:

(i) The claimed improvements to false positive rate and replication rate in Benjamin, et al (2017) are exaggerated and misleading.

(ii) There are plausible scenarios under which the lower cutoff will make the replication crisis worse.

My full analysis can be downloaded here.

Abstract

Psychologists and behavioral economists agree that many of our preferences are constructed, rather than innate or pre-computed and stored. Little research, however, has explored the implications that established facts about human attention and memory have when people marshal evidence for their decisions. This talk provides an introduction to Query Theory, a psychological process model of preference construction that explains a broad range of phenomena in individual choice with important personal and social consequences, including our reluctance to change also known as status-quo-bias and our excessive impatience when asked to delay consumption.

Abstract

For nearly 100 years, researchers have persisted in using p-values in spite of fierce criticism. Both Bayesians and Neyman-Pearson purists contend that use of a p-value is cheating even in the simplest case, where the hypothesis to be tested and a test statistic are specified in advance. Bayesians point out that a small p-value often does not translate into a strong Bayes factor against the hypothesis. Neyman-Pearson purists insist that you should state a significance level in advance and stick with it, even if the p-value turns out to be much smaller than this significance level. But many applied statisticians persist in feeling that a p-value much smaller than the significance level is meaningful evidence. In the game-theoretic approach to probability (see my 2001 book with Vladimir Vovk, described at www.probabilityandfinance.com, you test a statistical hypothesis by using its probabilities to bet. You reject at a significance level of 0.01, say, if you succeed in multiplying the capital you risk by 100. In this picture, we can calibrate small p-values so as to measure their meaningfulness while absolving them of cheating. There are various ways to implement this calibration, but one of them leads to a very simple rule of thumb: take the square root of the p-value. Thus rejection at a significance level of 0.01 requires a p-value of one in 10,000.

Abstract

According to Pritchard's analysis of luck (PAL), an event is lucky just in case it fails to obtain in a sufficiently large class of sufficiently close possible worlds. Though there are several reasons to like the PAL, it faces at least two counterexamples. After reviewing those counterexamples, I introduce a new, statistical analysis of luck (SAL). The reasons to like the PAL are also reasons to like the SAL, but the SAL is not susceptible to the counterexamples.

Abstract

The sciences, especially fundamental physics, contain theories that posit objective probabilities. But what are objective probabilities?

Are they fundamental features of reality as mass or charge might be? or do more fundamental facts, for example frequencies, ground probabilities?

In my talk I will survey some views about what probabilities there are and what grounds them.

Abstract

Dynamic approaches to understanding the foundations of physical probability in the non-fundamental sciences (from statistical physics through evolutionary biology and beyond) turn on special properties of physical processes that are apt to produce "probabilistically patterned" outcomes. I will introduce one particular dynamic approach of especially wide scope.

Then a problem: dynamic properties on their own are never quite sufficient to produce the observed patterns; in addition, some sort of probabilistic assumption about initial conditions must be made. What grounds the initial condition assumption? I discuss some possible answers.

Abstract

Of R.A. Fisher's countless statistical innovations, fiducial probability is one of the very few that has found little favor among probabilists and statisticians. Fiducial probability is still misunderstood today and rarely mentioned in current textbooks. This presentation will attempt to offer a historical perspective on the topic, explaining Fisher's motivations and subsequent oppositions from his contemporaries. The talk is based on my newly released book "Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times."

Abstract

It is an old and familiar challenge to normative theories of personal probability that they do not make room for non-trivial uncertainties about (the non-controversial parts of) logic and mathematics. Savage (1967) gives a frank presentation of the problem, noting that his own (1954) classic theory of rational preference serves as a poster-child for the challenge.

Here is the outline of this presentation:
     First is a review of the challenge.
     Second, I comment on two approaches that try to solve the challenge by making surgical adjustments to the canonical theory of coherent personal probability. One approach relaxes the Total Evidence Condition: see Good (1971). The other relaxes the closure conditions on a measure space: see Gaifman (2004). Hacking (1967) incorporates both of these approaches.
     Third, I summarize an account of rates of incoherence, explain how to model uncertainties about logical and mathematical questions with rates of incoherence, and outline how to use this approach in order to guide the uncertain agent in the use of, e.g., familiar numerical Monte Carlo methods in order to improve her/his credal state about such questions (2012).

References:
Gaifman, H. (2004) Reasoning with Limited Resources and Assigning Probabilities to Arithmetic Statements. Synthese 140: 97-119.
Good, I.J. (1971) Twenty-seven Principles of Rationality. In Good Thinking, Minn. U. Press (1983): 15-19.
Hacking, I. (1967) Slightly More Realistic Personal Probability. Phil. Sci. 34: 311-325.
Savage, L.J. (1967) Difficulties in the Theory of Personal Probability. Phil. Sci. 34: 305-310.
Seidenfeld, T., Schervish, M.J., and Kadane, J.B. (2012) What kind of uncertainty is that? J.Phil. 109: 516-533.

Abstract

'Regularity' conditions provide bridges between possibility and probability. They have the form:

If X is possible, then the probability of X is positive (or equivalents). Especially interesting are the conditions we get when we understand 'possible' doxastically, and 'probability' subjectively. I characterize these senses of 'regularity' in terms of a certain internal harmony of an agent's probability space (omega, F, P). I distinguish three grades of probabilistic involvement. A set of possibilities may be recognized by such a probability space by being a subset of omega; by being an element of F; and by receiving positive probability from P. An agent's space is regular if these three grades collapse into one.

I review several arguments for regularity as a rationality norm. An agent could violate this norm in two ways: by assigning probability zero to some doxastic possibility, and by failing to assign probability altogether to some doxastic possibility. I argue for the rationality of each kind of violation.

Both kinds of violations of regularity have serious consequences for traditional Bayesian epistemology. I consider their ramifications for:

- conditional probability

- conditionalization

- probabilistic independence

- decision theory

Abstract

This talk is devoted to a new paradigm of machine learning, in which Intelligent Teacher is involved. During training stage, Intelligent Teacher provides Student with information that contains, along with classification of each example, additional privileged information (for example, explanation) of this example. The talk describes two mechanisms that can be used for significantly accelerating the speed of Student's learning using privileged information: (1) correction of Student's concepts of similarity between examples, and (2) direct Teacher-Student knowledge transfer.

In this talk I also will discuss a general ideas in philosophical foundation of induction and generalization related to the Huber's concept of falsifiability and to holistic methods of inference.

Abstract

Bayesian decision theory assumes that its subjects are perfectly coherent: logically omniscient and able to perfectly access their information. Since imperfect coherence is both rationally permissible and widespread, it is desirable to extend decision theory to accommodate incoherent subjects. New 'no-go' proofs show that the rational dispositions of an incoherent subject cannot in general be represented by a single assignment of numerical magnitudes to sentences (whether or not those magnitudes satisfy the probability axioms). Instead, we should attribute to each incoherent subject a whole family of probability functions, indexed to choice conditions. If, in addition, we impose a "local coherence" condition, we can make good on the thought that rationality requires respecting easy logical entailments but not hard ones. The result is an extension of decision theory that applies to incoherent or fragmented subjects, assimilates into decision theory the distinction between knowledge-that and knowledge-how, and applies to cases of "in-between belief".

This is joint work with Agustin Rayo (MIT).

Abstract

This talk, which is drawn from Looking Forward: Prediction and Uncertainty in Modern America (forthcoming, University of Chicago Press), will examine weather forecasting and cotton forecasting as forms of knowledge production that initially sought to conquer unpredictability but ultimately accepted uncertainty in modern economic life. It will focus on contests between government and commercial forecasters over who had the authority to predict the future and the ensuing epistemological debates over the value and meaning of forecasting itself. Intellectual historians and historians of science have conceptualized the late nineteenth century in terms of “the taming of chance” in the shift from positivism to probabilism, but, as this talk will demonstrate, Americans also grappled with predictive uncertainties in daily life during a time when they increasingly came to believe in but also question the predictability of the weather, the harvest, and the future.

Abstract

In game-theoretic probability, Forecaster gives probabilities (or upper expectations) on each round of the game, and Skeptic tests these probabilities by betting, while Reality decides the outcomes. Can Forecaster pass Skeptic's tests?

As it turns out, Forecaster can defeat any particular strategy for Skeptic, provided only that each move prescribed by the strategy varies continuously with respect to Forecaster's previous move. Forecaster wants to defeat more than a single strategy for Skeptic; he wants to defeat simultaneously all the strategies Skeptic might use. But as we will see, Forecaster can often amalgamate the strategies he needs to defeat by averaging them, and then he can play against the average. This is called defensive forecasting. Defeating the average may be good enough, because when any one of the strategies rejects Forecaster's validity, the average will reject as well, albeit less strongly.

This result has implications for the meaning of probability. It reveals that the crucial step in placing an evidential question in a probabilistic framework is its placement in a sequence of questions. Once we have chosen the sequence, good sequential probabilities can be given, and the validation of these probabilities by experience signifies less than commonly thought.

References:
(1) Defensive forecasting, by Vladimir Vovk, Akimichi Takemura. and Glenn Shafer (Working Paper \#8 at http://www.probabilityandfinance.com/articles/08.pdf).
(2) Game-theoretic probability and its uses, especially defensive forecasting, by Glenn Shafer (Working Paper \#22 at http://www.probabilityandfinance.com/articles/22.pdf).

Abstract

Derivative valuation theory is based on the formalism of abstract probability theory and random variables. However, when it is made part of the pricing tool that the 'quant' (quantitative analyst) develops and that the option trader uses, it becomes a pricing technology. The latter exceeds the theory and the formalism. Indeed, the contingent payoff (defining the derivative) is no longer the unproblematic random variable that we used to synthesize by dynamic replication, or whose mathematical expectation we used merely to evaluate, but it becomes a contingent claim. By this distinction we mean that the contingent claim crucially becomes traded independently of its underlying asset, and that its price is no longer identified with the result of a valuation. On the contrary, it becomes a market given and will now be used as an input to the pricing models, inverting them (implied volatility and calibration). One must recognize a necessity, not an accident, in this breach of the formal framework, even read in it the definition of the market now including the derivative instrument. Indeed, the trading of derivatives is the primary purpose of their pricing technology, and not a subsidiary usage. The question then poses itself of a possible formalization of this augmented market, or more simply, of the market. To that purpose we introduce the key notion of writing.

Abstract

Higher-order evidence is evidence that you're handling information out of accord with epistemic norms. For instance, you may gain evidence that you're possibly drugged and can't think straight. A natural thought is that you respond by lowering your confidence that you got a complex calculation right. If so, HOE has a number of peculiar features. For instance, if you should take it into account, it leads to violations of Good's theorem and the norm to update by conditionalization. This motivates a number of philosophers to embrace the steadfast position: you shouldn't lower your confidence even though you have evidence you're drugged. I disagree. I argue that HOE is a kind of information-loss. This both explains its peculiar features and shows what's wrong with some recent steadfast arguments. Telling agents not to respond is like telling them never to forget anything.

Abstract

Kolmogorov's measure-theoretic axioms of probability formalize the Knightean notion of risk. Classical statistics adds a degree of Knightean uncertainty, since there is no probability distribution on the parameters, but uncertainty and risk are clearly separated. Game-theoretic probability formalizes the picture in which both risk and uncertainty interfere at every moment. The fruitfulness of this picture will be demonstrated by open theories in science and the emergence of stochasticity and probability in finance.