Quantitative Precipitation Forecasting Using an Improved Probability-Matching Method and Its Application to a Typhoon Event

This present study aims to explore how forecasters can quickly make accurate predictions by using various high-resolution model forecasts. Based on three high temporal-spatial resolution (3 km, hourly) numerical weather prediction models (CMA-MESO, CMA-GD, CMA-SH3) from the China Meteorological Administration (CMA), the hourly precipitation characteristics of three model within 24 h from March to September 2020 are discussed and integrated into a single, hourly, deterministic quantitative precipitation forecast (QPF) by making use of an improved weighted moving average probability-matching method (WPM). The results are as follows: (1) In non-rainstorm forecasts, CMA-MESO and CMA-GD have similar forecast abilities. However, in rainstorm forecasts, CMA-MESO has a notable advantage over the other two models. Thus, CMA-MESO is selected as a critical factor when participating in sensitivity experiments. (2) Compared with the traditional equal-weight probability-matching method (PM), the WPM improves the different grade QPF because it can effectively reduce rainfall pattern bias by making use of the weighted moving average (WMA). Additionally, the WPM threat score in rainstorm forecast similarly improved from 0.051 to 0.056, with a 9.8% increase relative to the PM. (3) The sensitivity experiments show that an optimal rainfall intensity score (WPM-best) can further improve the QPF and overcome all single models in both rainstorm and non-rainstorm forecasts, and the WPM-best has a rainstorm threat score skill of 0.062, with an increase of 21.6% compared with the PM. The performance of the WPM-best will be better if the precipitation intensity is stronger and the valid forecast periods is longer. It should be noted that there is no need to select models before using the WPM-best method, because WPM-best can give a very low weight to the less-skillful model in a more objective way. (4) The improved WPM method is also applied to investigate the heavy-rainfall case induced by typhoon Mekkhala (2020), where the improved WPM technique significantly improves rainstorm forecasting ability compared with a single model.

To maximize or randomize? An experimental study of probability matching in financial decision making

Probability matching, also known as the “matching law” or Herrnstein’s Law, has long puzzled economists and psychologists because of its apparent inconsistency with basic self-interest. We conduct an experiment with real monetary payoffs in which each participant plays a computer game to guess the outcome of a binary lottery. In addition to finding strong evidence for probability matching, we document different tendencies towards randomization in different payoff environments—as predicted by models of the evolutionary origin of probability matching—after controlling for a wide range of demographic and socioeconomic variables. We also find several individual differences in the tendency to maximize or randomize, correlated with wealth and other socioeconomic factors. In particular, subjects who have taken probability and statistics classes and those who self-reported finding a pattern in the game are found to have randomized more, contrary to the common wisdom that those with better understanding of probabilistic reasoning are more likely to be rational economic maximizers. Our results provide experimental evidence that individuals—even those with experience in probability and investing—engage in randomized behavior and probability matching, underscoring the role of the environment as a driver of behavioral anomalies.

Rational After All: Changes in Probability Matching Behaviour Across Time in Humans and Monkeys

Probability matching—where subjects given probabilistic in-put respond in a way that is proportional to those input probabilities—has long been thought to be characteristic of primate performance in probability learning tasks in a variety of contexts, from decision making to the learning of linguistic variation in humans. However, such behaviour is puzzling because it is not optimal in a decision theoretic sense; the optimal strategy is to always select the alternative with the highest positive-outcome probability, known as maximising(in decision making) or regularising (in linguistic tasks). While the tendency to probability match seems to depend somewhat on the participants and the task (i.e., infants are less likely to probability match than adults, monkeys probability matchless than humans, and probability matching is less likely in linguistic tasks), existing studies suffer from a range of deficiencies which make it difficult to robustly assess these differences. In this project we present a series of experiments which systematically test the development of probability matching behaviour over time in simple decision making tasks, across species (humans and Guinea baboons), task complexity, and task domain (linguistic vs non-linguistic).

Honeybees solve a multi-comparison ranking task by probability matching

Honeybees forage on diverse flowers which vary in the amount and type of rewards they offer, and bees are challenged with maximizing the resources they gather for their colony. That bees are effective foragers is clear, but how bees solve this type of complex multi-choice task is unknown. Here, we set bees a five-comparison choice task in which five colours differed in their probability of offering reward and punishment. The colours were ranked such that high ranked colours were more likely to offer reward, and the ranking was unambiguous. Bees' choices in unrewarded tests matched their individual experiences of reward and punishment of each colour, indicating bees solved this test not by comparing or ranking colours but by basing their colour choices on their history of reinforcement for each colour. Computational modelling suggests a structure like the honeybee mushroom body with reinforcement-related plasticity at both input and output can be sufficient for this cognitive strategy. We discuss how probability matching enables effective choices to be made without a need to compare any stimuli directly, and the use and limitations of this simple cognitive strategy for foraging animals.

Behavioral Psychology’s Matching Law Describes the Allocation of Covert Attention: A Choice Rule for the Mind

The matching law describes the allocation of behavior over a wide range of settings, including laboratory experimental chambers, forest foraging patches, sports arenas, and board games. Interestingly, matching persists in settings in which economic analyses predict quite different distributions of behavior (and it also differs systematically from “probability matching”). We tested whether the matching law also describes the allocation of covert cognitive processes. Sixty-four participants viewed two, small, vertically arranged adjacent stimuli that projected an image that fit within the fovea. A trial-version of the reward contingencies used in matching law experiments determined which stimulus was the target. The amount of time the stimuli were available was tailored to each subject so that they were not able to make use of the information in both stimuli even though an eye-tracking experiment confirmed that they saw both. The implication of this restriction is that subjects had to decide which stimulus to attend to prior to each trial. The only available objective basis for this decision was the relative frequencies that a stimulus was the target. Although shifts in attention were covert, and the procedure did not provide explicit reinforcers, the matching law equation described the division of attention between two small, briefly presented stimuli as accurately as it describes the allocation of key pecking between two illuminated disks in hungry pigeons.

A Method for Probability Matching Based on the Ensemble Maximum for Quantitative Precipitation Forecasts

A probability matching (PM) product using the ensemble maximum (EnMax) as the basis for spatial reassignment was developed. This PM product was called the PM max and its localized version was called the local PM (LPM) max. Both products were generated from a 10-member ensemble with 3-km horizontal grid spacing and evaluated over 364 36-h forecasts in terms of the fractions skill score. Performances of the PM max and LPM max were compared to those of the traditional PM mean and LPM mean, which both used the ensemble mean (EnMean) as the basis for spatial reassignment. Compared to observations, the PM max typically outperformed the PM mean for precipitation rates ≥5 mm h−1; this improvement was related to the EnMax, which had better spatial placement than the EnMean for heavy precipitation. However, the PM mean produced better forecasts than the PM max for lighter precipitation. It appears that the global reassignment used to produce the PM max was responsible for its poorer performance relative to the PM mean at light precipitation rates, as the LPM max was more skillful than the LPM mean at all thresholds. These results suggest promise for PM products based on the EnMax, especially for rare events and ensembles with insufficient spread.