Higher-order Uncertainty Research Articles

Interval Type-2 enhanced possibilistic fuzzy C-means noisy image segmentation algorithm amalgamating weighted local information

The fuzzy clustering algorithms based on interval type-2 are effective methods for data clustering and image segmentation with some potential advantages in dealing with higher-order uncertainty. However, the fuzzy clustering algorithms based on interval type-2 have limited accuracy in noisy image segmentation. Therefore, we propose a new noisy image segmentation algorithm based on weighted local information for interval type-2 enhanced possibilistic fuzzy C-means clustering. Firstly, a new possibilistic fuzzy weighted local information factor, which amalgamates the mutually guided image filtering, is devised to control the relationship between mutually guided image filtering and the original image utilizing the absolute difference image between the original image and mutually guided image filtering. Additionally, two weighted sum functions are also introduced into the new possibilistic fuzzy weighted local information factor to calculate the grayscale differences between the current pixel and its neighborhood pixels. Secondly, the distance of the objective function is corrected using mutually guided image filtering to obtain the local features and global information of the image. Finally, this paper introduces the new possibilistic fuzzy weighted local information factor into the interval type-2 possibilistic fuzzy C-means and proposes a new interval type-2 enhanced possibilistic fuzzy C-means clustering algorithm with local information and mutually guided image filtering constraints to improve noisy image segmentation results. Through extensive experiments on noisy synthetic images and noisy real images, the proposed algorithm can achieve higher performance and more accurate segmentation results compared with several existing algorithms.

Signalling with Private Monitoring

Abstract We study dynamic signalling when the sender does not see the signals that her actions generate. The sender then uses her past play to forecast what a receiver believes, in turn forcing the receiver to forecast the previous forecast, and so forth. We identify a class of linear-quadratic-Gaussian games where this endogenous higher-order uncertainty can be handled. The sender’s second-order belief is key: it is a private state that she controls, and it creates a new channel for information transmission. We examine the role of higher-order uncertainty and this new signalling channel in applications to macroeconomics, reputation, and trading: inflationary biases under discretion can be larger; career-concerned agents may benefit from not knowing their reputations; and informed trades can carry more price impact. We also introduce an existence method for boundary value problems that can be used in other dynamic games.

Panics and prices

Rumors of a shortage may create higher-order uncertainty and cause panic buying even when there is no real shortage and most consumers are aware of this fact. We study the role of prices in alleviating, or even preventing, panic buying caused by such rumors. Under some circumstances, flexible prices fail to do so and panic buying is the unique equilibrium outcome. In our model consumers do not know their future tastes perfectly and panic buying reduces welfare because consumers now buy with only imperfect information about tastes. In these circumstances, a minimum support price—a price floor—prevents panic buying and leads to higher consumer surplus. Producer surplus may be higher as well.

A Subdomain uncertainty-guided Kriging method with optimized feasibility metric for time-dependent reliability analysis

Active learning strategy combined with single-loop Kriging method has attracted much attention for Time-dependent Reliability Analysis (TRA). Large sample pool across all time instants is required to comprehensively cover the failure surface. Identifying training samples with most existing methods requires assessing the response of the entire sample pool, leading to high time costs. Similarly, to assist in identifying critical sampling regions, evaluating failure probability with a large sample pool in each iteration is also time-consuming. Additionally, higher-order uncertainty information is typically ignored, impairing the sampling efficiency. To address these issues, a Subdomain Uncertainty-guided Kriging (SUK) Method is proposed. Stochastic processes are first equivalently converted to random variables. By simultaneously sampling random variables and time parameter, an equivalent sample pool with significantly reduced size is generated for adaptive sampling. With a concise subdomain uncertainty assessment function, critical sampling region, i.e. sensitive subdomain, is distinguished efficiently. By comprehensively considering both the expectation and standard deviation of feasibility function, a novel Optimized Feasibility Metric (OFM) is then proposed for active learning. The proportion of misclassified samples is analytically deduced as stopping criterion. Finally, comparison results on four examples demonstrate the good performances of the proposed subdomain uncertainty-guided Kriging method.

The inclusion of theory errors in PDF fits

We present ongoing work towards incorporating the missing higher-order uncertainty (MHOU) determined through scale variations in the assessment of parton distribution functions (PDFs). Our PDFs fitting employs the NNPDF4.0 methodology and our theory covariance matrix framework to account for theory errors. This approach relies on the integration of MHOUs and their correlations via a theory covariance matrix. We validate our estimation and assess the impact of theory errors on the PDFs and on LHC phenomenology.

Evaluating and selecting arguments in the context of higher order uncertainty.

Human and artificial reasoning has to deal with uncertain environments. Ideally, probabilistic information is available. However, sometimes probabilistic information may not be precise or it is missing entirely. In such cases we reason with higher-order uncertainty. Formal argumentation is one of the leading formal methods to model defeasible reasoning in artificial intelligence, in particular in the tradition of Dung's abstract argumentation. Also from the perspective of cognition, reasoning has been considered as argumentative and social in nature, for instance by Mercier and Sperber. In this paper we use formal argumentation to provide a framework for reasoning with higher-order uncertainty. Our approach builds strongly on Haenni's system of probabilistic argumentation, but enhances it in several ways. First, we integrate it with deductive argumentation, both in terms of the representation of arguments and attacks, and in terms of utilizing abstract argumentation semantics for selecting some out of a set of possibly conflicting arguments. We show how our system can be adjusted to perform well under the so-called rationality postulates of formal argumentation. Second, we provide several notions of argument strength which are studied both meta-theoretically and empirically. In this way the paper contributes a formal model of reasoning with higher-order uncertainty with possible applications in artificial intelligence and human cognition.

Axiomatic framework of entropy measure for type-2 fuzzy sets with new representation method and its application to product ranking through online reviews

Type-2 fuzzy sets (T2FSs) have the advantage of representing higher-order uncertainty, they have demonstrated superior performance in several applications. In order to fully measure the uncertainty for T2FSs. In this study, several distribution characteristics of uncertainties within T2FSs are analyzed through type-1 fuzzy sets (T1FSs), and the axiomatic framework of fuzzy entropy and overall entropy of T2FSs is established as well. First, a new representation method for T2FSs is given. On this basis, the axiomatic definitions of fuzzy entropy for T1FSs and T2FSs are constructed by analyzing the distribution characteristics of fuzziness, and the construction theorems and basic properties of fuzzy entropy are studied. Further, the overall entropy of T2FSs is given, on this basis, a novel type-2 fuzzy entropy-based decision-making method is proposed, and applied to the selection of cold medicine through online reviews on AliHealth.cn. Finally, the feasibility and effectiveness of the developed definitions and methods are demonstrated by three comparative analyses.

Finite-sample corrected inference for two-step GMM in time series

This paper develops a finite-sample corrected inference for the efficient generalized method of moments (GMM) in time series. To capture a higher-order uncertainty embodied in estimating the time series GMM weight matrix, we extend the finite-sample corrected variance formula of Windmeijer (2005) to heteroskedasticity autocorrelated robust (HAR) inference. Using fixed-smoothing asymptotics, we show that our finite-sample corrected test statistics lead to standard asymptotic t or F critical values and suffer from less over-rejection of the null hypothesis than existing GMM procedures on finite-samples, including continuously updating GMM. Not only does our finite-sample corrected variance formula correct for the bias arising from the plugged-in long-run variance estimation, but it is also not exposed to a potential side effect of Windmeijer’s formula, which can introduce an additional source of over-rejection after the correction.

Rationalizability, Observability, and Common Knowledge

Abstract We study the strategic impact of players’ higher-order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which captures the behavioural implications of Rationality and Common Belief in Rationality (RCBR), where “rationality” is understood as sequential whenever the game is dynamic. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance, (1) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes (eductive coordination); (2) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg profiles (Stackelberg selection); (3) if it is commonly known that player $2$’s action is not observable (e.g. because $1$ is commonly known to move earlier, etc.), in a class of games which includes all of the above RCBR generically selects the equilibrium of the static game most favourable to player $1$ (pervasiveness of first-mover advantage).

Higher-order uncertainty bounds for mixed states

Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the Hilbert-space setup the measure of uncertainty is given by the skew information of the second kind, while the uncertainty lower bound is given by the Wigner–Yanase skew information associated with the conjugate observable. Higher-order corrections to the uncertainty lower bound are determined by higher-order quantum skew moments; expressions for these moments are worked out in closed form.

Proceed with Caution

AbstractIt is becoming more common that the decision-makers in private and public institutions are predictive algorithmic systems, not humans. This article argues that relying on algorithmic systems is procedurally unjust in contexts involving background conditions of structural injustice. Under such nonideal conditions, algorithmic systems, if left to their own devices, cannot meet a necessary condition of procedural justice, because they fail to provide a sufficiently nuanced model of which cases count as relevantly similar. Resolving this problem requires deliberative capacities uniquely available to human agents. After exploring the limitations of existing formal algorithmic fairness strategies, the article argues that procedural justice requires that human agents relying wholly or in part on algorithmic systems proceed with caution: by avoiding doxastic negligence about algorithmic outputs, by exercising deliberative capacities when making similarity judgments, and by suspending belief and gathering additional information in light of higher-order uncertainty.

Panics and Prices

Rumors of a shortage may create higher-order uncertainty and cause panic buying even when there is no real shortage and most consumers are aware of this fact. We study the role of prices in alleviating, or even preventing, panic buying caused by such rumors. Under some circumstances, flexible prices fail to do so and panic buying is the unique equilibrium outcome. In these circumstances, fixed prices prevent panic buying and lead to higher consumer surplus despite the possibility of rationing. Producer surplus may be higher as well.

The Role of Beliefs in Asset Prices: Evidence from Exchange Rates

A long-standing challenge in the asset pricing literature is to understand why asset prices sometimes underreact and sometimes overreact to news. We seek to address this challenge in the context of currency markets. We construct a model of exchange rate determination disciplined by survey data, where short-lived investors each (1) receive noisy private signals about the future path of interest rate differentials between the US and other countries and (2) overestimate the persistence of interest rate differentials. The model is able to qualitatively and quantitatively match patterns of underreaction and overreaction of exchange rates in response to news. The model also matches the failure of uncovered interest rate parity (UIP), capturing the return predictability of interest rate differentials for the returns to borrowing in USD and lending in foreign currency, as well as the fact that this return predictability is declining in the maturity of bonds used to borrow and lend. Finally, we use the model to help understand the reversal of the failure of UIP in recent years, the role of higher-order uncertainty, and the persistence of subjective beliefs. Our results highlight the important role that investors' beliefs may play in asset price behavior.

Macro disagreement and analyst forecast properties

In this study, I examine whether macro disagreement, a higher-order uncertainty, affects the accuracy and informativeness of analysts’ earnings forecasts. Using macroeconomic dispersion measures from the Survey of Professional Forecasters database as a proxy for macro disagreement, I find that macro disagreement reduces forecast accuracy. I further explore this association for firms that are high in cyclicality and for analysts who enjoy more brokerage resources. The negative relationship between macro disagreement and forecast accuracy is more pronounced for firms that are high in cyclicality. I also find that brokerage resources have a moderating effect on the negative association between macro disagreement and forecast accuracy. I further find that the analyst earnings forecast is less informative to investors when macro disagreement is high.

Learning from trading activity in laboratory security markets with higher-order uncertainty

This experiment examines forecasting behavior under varying information conditions to assess the extent to which traders in security markets incorporate information in trading activity to resolve fundamental uncertainty and to resolve higher-order uncertainty. Fundamental uncertainty refers to a trader's uncertainty about liquidation value of the asset while higher-order uncertainty refers to uncertainty about the beliefs of other traders about liquidation value of the asset. I find that in an experimental security market, subjects incorporate the information contained in trading activity to the extent of about 88% to resolve both fundamental uncertainty and higher-order uncertainty. When a piece of public information (the information content of which is comparable to the information contained in trading activity) is made available to the subjects, then also the incorporation of available information remains in about the same range as reported with the first set of experiments. The inability and / or refusal to incorporate 100% of the information contained in trading activity is almost entirely attributable to an inability and / or refusal to Bayesian update. The refusal to Bayesian update is consistent with several other theories and allows post-trading forecasts to be significantly correlated with pre-trading forecasts.

Does rationality demand higher-order certainty?

Should you always be certain about what you should believe? In other words, does rationality demand higher-order certainty? First answer: Yes! Higher-order uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higher-order certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higher-order evidence. Which answer wins out? The first, I argue. Once we get clearer about what higher-order certainty is, a view emerges on which higher-order certainty does not, in fact, license any kind of insensitivity to higher-order evidence. The view as I will describe it has plenty of intuitive appeal. But it is not without substantive commitments: it implies a strong form of internalism about epistemic rationality, and forces us to reconsider standard ways of thinking about the nature of evidential support. Yet, the view put forth promises a simple and elegant solution to a surprisingly difficult problem in our understanding of rational belief.

Higher-Order Uncertainty in Financial Markets: Evidence from a Consensus Pricing Service

We look at the informational content of consensus pricing in opaque over-the-counter markets. We show that the availability of price data informs participants mainly about other participants’ valuations, rather than about the value of a financial security.

Complex probability expressions & higher-order uncertainty: Compositional semantics, probabilistic pragmatics & experimental data

We present novel experimental data pertaining to the use and interpretation of simple probability expressions (such as possible or likely) and complex ones (such as possibly likely or certainly possible) in situations of higher-order uncertainty, i.e., where speakers may be uncertain about the probability of a chance event. The data is used to critically assess a probabilistic pragmatics model in the vein of Rational Speech Act approaches (e.g., Frank and Goodman, 2012; Franke and Jäger, 2016; Goodman and Frank, 2016). The model embeds a simple compositional threshold-semantics for probability expressions, following recent work in formal linguistics (Swanson, 2006; Yalcin, 2007, 2010; Lassiter, 2010, 2017; Moss, 2015).

Rational Bubbles and Middlemen

This paper develops a finite-period model of rational bubbles where trade of an asset takes place through a chain of middlemen. We show that there exists a unique equilibrium, and a bubble can occur due to higher-order uncertainty. Under reasonable assumptions, the equilibrium price is increasing and accelerating during bubbles although the fundamental value is constant over time. Bubbles may be detrimental to the economy; however, bubble-bursting policies affect agents’ beliefs and it turns out that they have no effect on welfare. We also demonstrate that the possibility that middlemen obtain more information leads to larger bubbles.

Alliance formation under higher order uncertainty: Embeddedness, fear, and gradualism

Companies face higher order uncertainty when they decide whether to form strategic alliances. We develop a model to examine the key role played by higher order uncertainty in affecting strategic calculation with respect to alliance formation. Our analysis shows that fear of opportunism could prevent the formation of a mutually beneficial alliance even when companies believe they cannot be better off behaving opportunistically (a situation different from the prisoner's dilemma). This coordination problem worsens as the potential loss from relationship opportunism increases. However, it can significantly ease when companies form common approximate beliefs, as often happens when they are familiar with each other.