Decision-theoretic Perspective Research Articles

Goodness-of-fit tests for multinomial models with inverse sampling

This article proposes goodness-of-fit tests for multinomial models using an inverse sampling scheme. From the multiple decision-theoretic perspective, we devise a test statistic and stopping rule that satisfy a prespecified probability level P* and obtain corresponding optimal sample sizes. Incomplete Dirichlet type II distribution functions are used to develop the procedure and to express the probability of correct decisions for various cell configurations for multinomial models. For empirical studies, Monte Carlo experiments are conducted, and for illustrations, various cell configurations of a wheel of fortune are demonstrated.

A sample size-dependent prior strategy for bridging the Bayesian-frequentist gap in point null hypothesis testing

Bayes factor, as a measure of the evidence provided by the data in favor of one hypothesis against its alternative, can be highly sensitive to the prior distributions of parameters involved in the hypotheses as well as to the sample size. This may cause a noticeable difference between the Bayesian and classical (frequentist) hypothesis testing results. In the worst-case scenario, the two results are in conflict, which is termed the Jeffreys-Lindley paradox. In this article, we propose a sample size-dependent prior strategy to bridge the Bayesian-frequentist gap from a decision-theoretical perspective. The central idea behind the proposed strategy is to adaptively adjust prior distributions for the parameters in line with the sample size to manage the risk of type I error in Bayesian hypothesis testing at the same level as that prespecified in frequentist hypothesis testing. The proposed strategy is inspired by the work of Maurice Stevenson Bartlett (M.S. Bartlett, A comment on D. V. Lindley’s statistical paradox, Biometrika, 44, 533–534, 1957), who suggested a sample size-dependent prior to make the Bayes factor independent of the sample size. In contrast to his work, we propose a strategy that leverages the use of sample size-dependent priors in Bayesian hypothesis testing and risk management when deciding the two hypotheses. To demonstrate the effectiveness of the proposed strategy, normal mean tests in the cases that (i) the variance is known (z-test) and (ii) the variance is unknown (t-test) are examined. It turns out that the Bayesian testing results coming out from the proposed strategy become consistent with their frequentist counterparts and the Jeffreys-Lindley paradox disappears.

The Stein effect for Fréchet means

The Fréchet mean is a useful description of location for a probability distribution on a metric space that is not necessarily a vector space. This article considers simultaneous estimation of multiple Fréchet means from a decision-theoretic perspective, and in particular, the extent to which the unbiased estimator of a Fréchet mean can be dominated by a generalization of the James–Stein shrinkage estimator. It is shown that if the metric space satisfies a nonpositive curvature condition, then this generalized James–Stein estimator asymptotically dominates the unbiased estimator as the dimension of the space grows. These results hold for a large class of distributions on a variety of spaces, including Hilbert spaces and, therefore, partially extend known results on the applicability of the James–Stein estimator to nonnormal distributions on Euclidean spaces. Simulation studies on phylogenetic trees and symmetric positive definite matrices are presented, numerically demonstrating the efficacy of this generalized James–Stein estimator.

Beyond Markov Decision Process with Scalar Markovian Rewards

Real-world decision problems often involve multiple competing objectives or a complex reward structure that violate Markov assumption. However, the existing research on sequential decision making under uncertainty primarily focused on Markov Decision Processes (MDPs) with scalar Markovian reward signals. My thesis considers settings where scalar Markovian rewards are not sufficient to produce desired behaviors. The first part of my thesis develops algorithms to optimize lexicographically ordered objectives. The second part considers autonomous agents which incorporate the perspective of their observer. As the perspective of the observer can depend on how the agents behaved so far, rewards in this setting can depend on histories (non-Markovian). In the final part of my thesis, I hope to characterize when rewards beyond scalar Markovian signals are needed from the decision theoretic perspective

Skilled Mutual Fund Selection: False Discovery Control Under Dependence

Selecting skilled mutual funds through the multiple testing framework has received increasing attention from finance researchers and statisticians. The intercept α of Carhart four-factor model is commonly used to measure the true performance of mutual funds, and positive α’s are considered as skilled. We observe that the standardized ordinary least-square estimates of α’s across the funds possess strong dependence and nonnormality structures, indicating that the conventional multiple testing methods are inadequate for selecting the skilled funds. We start from a decision theoretical perspective, and propose an optimal multiple testing procedure to minimize a combination of false discovery rate and false nondiscovery rate. Our proposed testing procedure is constructed based on the probability of each fund not being skilled conditional on the information across all of the funds in our study. To model the distribution of the information used for the testing procedure, we consider a mixture model under dependence and propose a new method called “approximate empirical Bayes” to fit the parameters. Empirical studies show that our selected skilled funds have superior long-term and short-term performance, for example, our selection strongly outperforms the S&P 500 index during the same period.

Elucidating the Common Basis for Task-Dependent Differential Manifestations of Category Advantage: A Decision Theoretic Approach.

Cross-category hues are differentiated easier than otherwise equidistant hues that belong to the same linguistic category. This effect is typically manifested through both accuracy and response time gains in tasks with a memory component, whereas only response times are affected when there is no memory component. This raises the question of whether there is a common generative process underlying the differential behavioral manifestations of category advantage in color perception. For instance, within the framework of noisy evidence accumulation models, changes in accuracy can be readily attributed to an increase in the efficacy of perceptual evidence integration (after controlling for threshold setting), whereas changes in response time can also be attributed to shorter nondecisional delays (e.g., due to facilitated signal detection). To address the latent decision processes underlying category advantage across different behavioral demands, we introduce a decision-theoretic perspective (i.e., diffusion decision model) to categorical color perception in three complementary experiments. In Experiment 1, we collected data from a binary color naming task (1) to determine the green-blue boundary in our sample and (2) to trace how parameter estimates of interest in the model output change as a function of color typicality. In Experiments 2 and 3, we used same-different task paradigms (with and without a memory component, respectively) and traced the category advantage in color discrimination in two parameters of the diffusion decision model: nondecision time and drift rate. An increase in drift rate predominantly characterized the category advantage in both tasks. Our results show that improved efficiency in perceptual evidence integration is a common driving force behind different manifestations of category advantage.

Multilabel Classification with Partial Abstention: Bayes-Optimal Prediction under Label Independence

In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the form of a subset of all labels. In this paper, we study an extension of the setting of MLC, in which the learner is allowed to partially abstain from a prediction, that is, to deliver predictions on some but not necessarily all class labels. This option is useful in cases of uncertainty, where the learner does not feel confident enough on the entire label set. Adopting a decision-theoretic perspective, we propose a formal framework of MLC with partial abstention, which builds on two main building blocks: First, the extension of underlying MLC loss functions so as to accommodate abstention in a proper way, and second the problem of optimal prediction, that is, finding the Bayes-optimal prediction minimizing this generalized loss in expectation. It is well known that different (generalized) loss functions may have different risk-minimizing predictions, and finding the Bayes predictor typically comes down to solving a computationally complexity optimization problem. In the most general case, given a prediction of the (conditional) joint distribution of possible labelings, the minimizer of the expected loss needs to be found over a number of candidates which is exponential in the number of class labels. We elaborate on properties of risk minimizers for several commonly used (generalized) MLC loss functions, show them to have a specific structure, and leverage this structure to devise efficient methods for computing Bayes predictors. Experimentally, we show MLC with partial abstention to be effective in the sense of reducing loss when being allowed to abstain.

Explaining gaps in the logical lexicon of natural languages: A decision-theoretic perspective on the square of Aristotle

Across languages, certain logically natural concepts are not lexicalized, even though they can be expressed by complex expressions. This is for instance the case for the quantifier not all. In this paper, we propose an explanation for this fact based on the following idea: the logical lexicon of languages is partly shaped by a tradeoff between informativity and cost, and the inventory of logical expressions tends to maximize average informativity and minimize average cost. The account we propose is based on a decision-theoretic model of how speakers choose their messages in various situations (a version of the Rational Speech Act model). EARLY ACCESS

A Memoir on Model Selection Criterion between Two Nested and Non-Nested Stochastic Linear Regression Models

The main purpose of this paper is to discuss some applications of internally studentized residuals 9n the model selection criterion between two nested and non-nested stochastic linear regression models. Joseph et.al [1] formulated various proposals from a Bayesian decision-theoretic perspective regarding model selection Criterion. Oliver Francois et.al [2] proposed novel approaches to model selection based on predictive distributions and approximations of the deviance. Jerzy szroeter [3] in his paper depicted the development of statistical methods to test non-nested models including regressions, simultaneous equations. In particular new criteria for a model selection between two nested/ non-nested stochastic linear regression models have been suggested here.

Analysing and exemplifying forensic conclusion criteria in terms of Bayesian decision theory

There is ongoing discussion in forensic science and the law about the nature of the conclusions reached based on scientific evidence, and on how such conclusions – and conclusion criteria – may be justified by rational argument. Examples, among others, are encountered in fields such as fingermarks (e.g., ‘this fingermark comes from Mr. A's left thumb’), handwriting examinations (e.g., ‘the questioned signature is that of Mr. A’), kinship analyses (e.g., ‘Mr. A is the father of child C’) or anthropology (e.g., ‘these are human remains'). Considerable developments using formal methods of reasoning based on, for example (Bayesian) decision theory, are available in literature, but currently such reference principles are not explicitly used in operational forensic reporting and ensuing decision-making. Moreover, applied examples, illustrating the principles, are scarce. A potential consequence of this in practical proceedings, and hence a cause of concern, is that underlying ingredients of decision criteria (such as losses quantifying the undesirability of adverse decision consequences), are not properly dealt with. There is merit, thus, in pursuing the study and discussion of practical examples, demonstrating that formal decision-theoretic principles are not merely conceptual considerations. Actually, these principles can be shown to underpin practical decision-making procedures and existing legal decision criteria, though often not explicitly apparent as such. In this paper, we will present such examples and discuss their properties from a Bayesian decision-theoretic perspective. We will argue that these are essential concepts for an informed discourse on decision-making across forensic disciplines and the development of a coherent view on this topic. We will also emphasize that these principles are of normative nature in the sense that they provide standards against which actual judgment and decision-making may be compared. Most importantly, these standards are justified independently of peoples' observable decision behaviour, and of whether or not one endorses these formal methods of reasoning.

The Logical Consistency of Simultaneous Agnostic Hypothesis Tests

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided.

Decision theory, motor planning, and visual memory: deciding where to reach when memory errors are costly.

Limitations in visual working memory (VWM) have been extensively studied in psychophysical tasks, but not well understood in terms of how these memory limits translate to performance in more natural domains. For example, in reaching to grasp an object based on a spatial memory representation, overshooting the intended target may be more costly than undershooting, such as when reaching for a cup of hot coffee. The current body of literature lacks a detailed account of how the costs or consequences of memory error influence what we encode in visual memory and how we act on the basis of remembered information. Here, we study how externally imposed monetary costs influence behavior in a motor decision task that involves reach planning based on recalled information from VWM. We approach this from a decision theoretic perspective, viewing decisions of where to aim in relation to the utility of their outcomes given the uncertainty of memory representations. Our results indicate that subjects accounted for the uncertainty in their visual memory, showing a significant difference in their reach planning when monetary costs were imposed for memory errors. However, our findings indicate that subjects memory representations per se were not biased by the imposed costs, but rather subjects adopted a near-optimal post-mnemonic decision strategy in their motor planning.

Losses and use efficiencies along the phosphorus cycle – Part 2: Understanding the concept of efficiency

Part 1 of this paper showed that losses and efficiencies are highly similar concepts used to valuate the quality of a production process from an input–output economics perspective. Both concepts are useful in methods that aim to reduce the amount of input (money, material, labor, etc.) needed to get a certain desired output. Yet, from a decision-theoretic perspective, both concepts are secondary. They are subordinate to the desired goal, product, or service, i.e., the efficacy, and the overall impacts on a tangible system, i.e., effectiveness (which we consider as an overall utility) and are of superior importance to an action or a decision.Part 2 provides an in-depth discussion of efficiency. We show that we need an overall objective (a kind of total utility), such as effectiveness or resilience, as a target variable for sustainable resource use. Efficiency is a valuation function that assesses how much we have to invest in order to receive a certain quantity and/or quality of a desired outcome or product. We conceive of effectiveness as the capability of an action, decision, or technology to attain a meaningful and satisfying overall result (with respect to a specific perspective/interest or overall objective). We further shed light on several misperceived relationships between efficacy and efficiency. Both material/technical and economic efficiency can be defined as a fraction of two variables, i.e., the ratio between input and output. Here, the nominator (i.e., the output) is usually what we consider as efficacy. For the agro-use of P (and many organismic systems), the material-biophysical output is not linearly related to the input, but we are facing the Law of Marginal Diminishing Returns (which contrasts with the Tayloristic idea that increasing throughput increases efficiency). Thus, unrealistic expectations and misperceptions may emerge. We exemplarily discuss and substantiate by theoretical and data-based arguments why the objective to “increase global P nutrient use efficiency by 30% and the outcome of yield by 30%” is not possible in the next decades as the antagonistic relationship between efficacy and efficiency and the diverging options in different countries and world regions are ignored. Finally, we briefly illuminate in what way the evaluation of phosphorus management may be considered sustainable and what rebound effects may be mastered. This is done by discussing system boundaries, evaluation perspectives, and the factors discussed in the context of efficacy, efficiency, and effectiveness.

Behavior in the centipede game: A decision-theoretical perspective

The centipede game is a two-player finite game of perfect information where a unique subgame perfect Nash equilibrium appears to be intuitively unappealing and descriptively inadequate. This paper analyzes behavior in the centipede game when a traditional game-theoretical assumption that players maximize expected utility is relaxed. We demonstrate the existence of a descriptively adequate subgame perfect equilibrium under two standard decision-theoretical assumptions. First, players choose under uncertainty in a probabilistic manner as captured by embedding a core deterministic decision theory in a model of probabilistic choice. Second, players adopt non-linear decision weights and overweight the likelihood of rare events as captured, for example, by rank-dependent utility or prospect theory.

Behavior in the Centipede Game: A Decision-Theoretical Perspective

The centipede game is a two-player finite game of perfect information where a unique subgame perfect Nash equilibrium appears to be intuitively unappealing and descriptively inadequate. This paper analyzes behavior in the centipede game when a traditional game-theoretical assumption that players maximize expected utility is relaxed. We demonstrate the existence of a descriptively adequate subgame perfect equilibrium under two standard decision-theoretical assumptions. First, players choose under uncertainty in a probabilistic manner as captured by embedding a core deterministic decision theory in a model of probabilistic choice. Second, players adopt non-linear decision weights and overweight the likelihood of rare events as captured, for example, by rank-dependent utility or prospect theory.

Statistical Causality from a Decision-Theoretic Perspective

We present an overview of the decision-theoretic framework of statistical causality, which is well suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and it is related to and contrasted with other current formulations, such as structural equation models and potential responses. Topics and applications covered include confounding, the effect of treatment on the treated, instrumental variables, and dynamic treatment strategies.

On the bayes-optimality of F-measure maximizers

The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems.

Using Priced Options to Solve the Exposure Problem in Sequential Auctions

We propose a priced options model for solving the exposure problem of bidders with valuation synergies participating in a sequence of online auctions. We consider a setting in which complementary-valued items are offered sequentially by different sellers, who have the choice of either selling their item directly or through a priced option. In our model, the seller fixes the exercise price for this option, and then sells it through a first-price auction. We analyze this model from a decision-theoretic perspective and we show, for a setting where the competition is formed by local bidders (which desire a single item), that using options can increase the expected profit for both sides. Furthermore, we derive the equations that provide minimum and maximum bounds between which the bids of the synergy buyer are expected to fall, in order for both sides of the market to have an incentive to use the options mechanism. Next, we perform an experimental analysis of a market in which multiple synergy buyers are active simultaneously. We show that, despite the extra competition, some synergy buyers may benefit, because sellers are forced to set their exercise prices for options at levels which encourage participation of all buyers.

Speeded Reaching Movements around Invisible Obstacles

We analyze the problem of obstacle avoidance from a Bayesian decision-theoretic perspective using an experimental task in which reaches around a virtual obstacle were made toward targets on an upright monitor. Subjects received monetary rewards for touching the target and incurred losses for accidentally touching the intervening obstacle. The locations of target-obstacle pairs within the workspace were varied from trial to trial. We compared human performance to that of a Bayesian ideal movement planner (who chooses motor strategies maximizing expected gain) using the Dominance Test employed in Hudson et al. (2007). The ideal movement planner suffers from the same sources of noise as the human, but selects movement plans that maximize expected gain in the presence of that noise. We find good agreement between the predictions of the model and actual performance in most but not all experimental conditions.

Personalised, predictive and preventive medicine: a decision-theoretic perspective

Background. The last decade has witnessed remarkable developments in medical treatment that is personalised, predictive and preventive. The advances made here have the potential to bring about radical change, not only in diagnostic tests and prescriptions, but also in more fundamental patterns in the provision of health care. Methods. The conceptual framework and principles of modern decision theory are applied to some of the ethical issues raised by recent advances in personalised, predictive and preventive medicine, including questions about limits of autonomy and the implications of justice and fairness in the distribution of health care services. Results. A new way of conceptualising and understanding the ethical issues raised by personalised, predictive and preventive medicine is sketched. Such medicine involves decisions under risk and decisions under uncertainty, depending on the extent to which current knowledge gaps can be filled. Conclusions. The various ways of conceptualising and understanding these problems need to be discussed before personalised, predictive and preventive medicine is implemented in practical health care.