A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

EXPRESS: Learning to Set Prices

The authors empirically examine how firms learn to set prices in a new market. The 2012 privatization of off-premise liquor sales in Washington State created a unique opportunity to observe retailers learn to set prices from the point at which their learning process began. Tracking this market as it evolved through time, the authors find that firms indeed learn to set more profitable prices, that these prices increasingly reflect demand fundamentals, and they ultimately converge to levels consistent with (static) profit maximization. The paper further demonstrates that initial pricing mistakes are largest for products whose demand conditions differ the most from those of previously privatized markets, that retailers with previous experience in the category are initially better-informed, and that learning is faster for products with more precise sales information. These findings indicate that firm behavior converges to rational models of firm conduct, but also reveal that such convergence takes time to unfold and play out differently for different firms. These patterns suggest important roles for both firm learning and heterogeneous firm capabilities.

Using Rational Models to Interpret the Results of Experiments on Accent Adaptation

Exposure to unfamiliar non-native speech tends to improve comprehension. One hypothesis holds that listeners adapt to non-native-accented speech through distributional learning—by inferring the statistics of the talker's phonetic cues. Models based on this hypothesis provide a good fit to incremental changes after exposure to atypical native speech. These models have, however, not previously been applied to non-native accents, which typically differ from native speech in many dimensions. Motivated by a seeming failure to replicate a well-replicated finding from accent adaptation, we use ideal observers to test whether our results can be understood solely based on the statistics of the relevant cue distributions in the native- and non-native-accented speech. The simple computational model we use for this purpose can be used predictively by other researchers working on similar questions. All code and data are shared.

Judgment and Decision-Making Processes

The field of judgment and decision making (JDM) arose in psychology to test the rational assumptions posed in other fields such as economics and statistics. This has led to three major contributions of the field. First, to the extent that people systematically deviate from rational models, their decisions are less than optimal. This has consequences for both business practice and for assumptions in many professional fields, such as finance, medicine, and law. Second, the deviation from rational models has led JDM researchers to identify categories of psychological processes that do guide decision making. These include associationistic memory processes, psychophysical processes, emotional processes, and learning. Third, building on the first two contributions, the field of JDM has merged rational and psychological perspectives to explore ways to improve decision making. These methods include a variety of interventions known as nudges, choice architecture, debiasing, and the use of external aids such as algorithms and the wisdom of crowds. The three contributions of JDM help researchers in a number of fields analyze problems and design helpful solutions. Workplace examples include designing better processes for hiring and evaluation, goal setting, and employee retirement savings planning.

Reconstructing the Einstellung effect

The Einstellung effect was first described by Abraham Luchins in his doctoral thesis published in 1942. The effect occurs when a repeated solution to old problems is applied to a new problem even though a more appropriate response is available. In Luchins' so-called water jar task, participants had to measure a specific amount of water using three jars of different capacities. Luchins found that subjects kept using methods they had applied in previous trials, even if a more efficient solution for the current trial was available: an Einstellung effect. Moreover, Luchins studied the different conditions that could possibly mediate this effect, including telling participants to pay more attention, changing the number of tasks, alternating between different types of tasks, as well as putting participants under time pressure. In the current work, we reconstruct and reanalyze the data of the various experimental conditions published in Luchins' thesis. We furthermore show that a model of resource-rational decision-making can explain all of the observed effects. This model assumes that people transform prior preferences into a posterior policy to maximize rewards under time constraints. Taken together, our reconstructive and modeling results put the Einstellung effect under the lens of modern-day psychology and show how resource-rational models can explain effects that have historically been seen as deficiencies of human problem-solving.

Episodes in Model-Theoretic Xenology: Rationals as Positive Integers in R#

Meyer and Mortensen’s Alien Intruder Theorem includes the extraor- dinary observation that the rationals can be extended to a model of the relevant arithmetic R♯, thereby serving as integers themselves. Al- though the mysteriousness of this observation is acknowledged, little is done to explain why such rationals-as-integers exist or how they operate. In this paper, we show that Meyer and Mortensen’s models can be identified with a class of ultraproducts of finite models of R♯, providing insights into some of the more mysterious phenomena of the rational models.