Bayesian decision theory,subjective and objective probabilities,and acceptance of empirical hypotheses

It is argued that we need a richer version of Bayesian decision theory, admitting both subjective and objective probabilities and providing rational criteria for choice of our prior probabilities. We also need a theory of tentative acceptance of empirical hypotheses. There is a discussion of subjective and of objective probabilities and of the relationship between them, as well as a discussion of the criteria used in choosing our prior probabilities, such as the principles of indifference and of maximum entropy, and the simplicity ranking of alternative hypotheses.     

Probabilistic models in human sensorimotor control

Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control. Bayesian decision theory (BDT) has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty. BDT has two components: Bayesian statistics and decision theory. Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body. Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics. We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates, can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman filter-based processes to estimate time-varying states. Finally, we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and select optimal actions. We review results that suggest we plan movements based on statistics of our actions that result from signal-dependent noise on our motor outputs. Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty.     

Causal decision theory

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of indeterminacy nor a type of ignorance. Rather, it is sui generis.     

Conditionals in causal decision theory

This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87)      

Against causal decision theory

Proponents of causal decision theories argue that classical Bayesian decision theory (BDT) gives the wrong advice in certain types of cases, of which the clearest and commonest are the medical Newcomb problems. I defend BDT, invoking a familiar principle of statistical inference to show that in such cases a free agent cannot take the contemplated action to be probabilistically relevant to its causes (so that BDT gives the right answer). I argue that my defence does better than those of Ellery Eells and Richard Jeffrey; and that it applies, where necessary, to other types of Newcomb problem.     

Temporal control of movements in sensorimotor synchronization.

Under conditions in which the temporal structure of events (e.g., a sequence of tones) is predictable, performing movements in synchrony with this sequence of events (e.g., dancing) is an easy task. A rather simplified version of this task is studied in the sensorimotor synchronization paradigm. Participants are instructed to synchronize their finger taps with an isochronous sequence of signals (e.g., clicks). Although this is an easy task, a systematic error is observed: Taps usually precede clicks by several tens of milliseconds. Different models have been proposed to account for this effect ("negative asynchrony" or "synchronization error"). One group of explanations is based on the idea that synchrony is established at the level of central representations (and not at the level of external events), and that the timing of an action is determined by the (anticipated) action effect. These assumptions are tested by manipulating the amount of sensory feedback available from the tap as well as its temporal characteristics. This article presents an overview of these representational models and the empirical evidence supporting them. It also discusses other accounts briefly in the light of further evidence.     

The Bayesian reader: explaining word recognition as an optimal Bayesian decision process

This article presents a theory of visual word recognition that assumes that, in the tasks of word identification, lexical decision, and semantic categorization, human readers behave as optimal Bayesian decision makers. This leads to the development of a computational model of word recognition, the Bayesian reader. The Bayesian reader successfully simulates some of the most significant data on human reading. The model accounts for the nature of the function relating word frequency to reaction time and identification threshold, the effects of neighborhood density and its interaction with frequency, and the variation in the pattern of neighborhood density effects seen in different experimental tasks. Both the general behavior of the model and the way the model predicts different patterns of results in different tasks follow entirely from the assumption that human readers approximate optimal Bayesian decision makers.     

Bayesian analysis of the piecewise diffusion decision model

Most past research on sequential sampling models of decision-making have assumed a time homogeneous process (i.e., parameters such as drift rates and boundaries are constant and do not change during the deliberation process). This has largely been due to the theoretical difficulty in testing and fitting more complex models. In recent years, the development of simulation-based modeling approaches matched with Bayesian fitting methodologies has opened the possibility of developing more complex models such as those with time-varying properties. In the present work, we discuss a piecewise variant of the well-studied diffusion decision model (termed pDDM) that allows evidence accumulation rates to change during the deliberation process. Given the complex, time-varying nature of this model, standard Bayesian parameter estimation methodologies cannot be used to fit the model. To overcome this, we apply a recently developed simulation-based, hierarchal Bayesian methodology called the probability density approximation (PDA) method. We provide an analysis of this methodology and present results of parameter recovery experiments to demonstrate the strengths and limitations of this approach. With those established, we fit pDDM to data from a perceptual experiment where information changes during the course of trials. This extensible modeling platform opens the possibility of applying sequential sampling models to a range of complex non-stationary decision tasks.     

Rule utilitarianism and decision theory

The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, not in hedonistic or in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments.After describing the difficulties of act utilitarianism, rule utilitarianism is discussed as a possibly superior alternative. Brandt and Lyons have tried to show that these two forms of utilitarianism are actually equivalent. To test Brandt's and Lyons's equivalence thesis, a decision-theoretical model for utilitarian theory is proposed. The model shows that the thesis is definitely false. The basic difference between the two theories results from the expectation effect and the incentive effect, which, surprisingly enough, have been almost completely neglected in the philosophical literature. The paper illustrates these two effects in connection with the moral duty of promise keeping.Yet, even if we do neglect the expectation and the incentive effects, and concentrate on the coordination effect, as most of the philosophical literature does, it can be shown that rule utilitarianism and act utilitarianism have very different practical implications. This is demonstrated by analysis of three voting situations. Hence, the equivalence thesis fails even under the assumptions most favorable to it.     

A sensorimotor theory of temporal tracking and beat induction

In this paper, we develop a theory of the neurobiological basis of temporal tracking and beat induction as a form of sensory-guided action. We propose three principal components for the neurological architecture of temporal tracking: (1) the central auditory system, which represents the temporal information in the input signal in the form of a modulation power spectrum; (2) the musculoskeletal system, which carries out the action and (3) a controller, in the form of a parieto-cerebellar-frontal loop, which carries out the synchronisation between input and output by means of an internal model of the musculoskeletal dynamics. The theory is implemented in the form of a computational algorithm which takes sound samples as input and synchronises a simple linear mass-spring-damper system to simulate audio-motor synchronisation. The model may be applied to both the tracking of isochronous click sequences and beat induction in rhythmic music or speech, and also accounts for the approximate Weberian property of timing.     

Regret and instability in causal decision theory

Andy Egan has recently produced a set of alleged counterexamples to causal decision theory (CDT) in which agents are forced to decide among causally unratifiable options, thereby making choices they know they will regret. I show that, far from being counterexamples, CDT gets Egan??s cases exactly right. Egan thinks otherwise because he has misapplied CDT by requiring agents to make binding choices before they have processed all available information about the causal consequences of their acts. I elucidate CDT in a way that makes it clear where Egan goes wrong, and which explains why his examples pose no threat to the theory. My approach has similarities to a modification of CDT proposed by Frank Arntzenius, but it differs in the significance that it assigns to potential regrets. I maintain, contrary to Arntzenius, that an agent facing Egan??s decisions can rationally choose actions that she knows she will later regret. All rationality demands of agents it that they maximize unconditional causal expected utility from an epistemic perspective that accurately reflects all the available evidence about what their acts are likely to cause. This yields correct answers even in outlandish cases in which one is sure to regret whatever one does.