Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Error parameters are inevitable in systems. In formal verification, previous reasoning methods seldom considered the probability information of errors. In this article, errors are described as symmetric truncated normal intervals consisting of the intervals and symmetric truncated normal probability density. Furthermore, we also rigorously prove lemmas and a theorem to partially simplify the calculation process of truncated normal intervals and independently verify the formulas of variance and expectation of symmetric truncated interval given by some scholars. The mathematical derivation process or verification codes are provided for most of the key formulas in this article. Hence, we propose a new reasoning method that combines the probability information of errors with the previous statistical reasoning methods. Finally, an engineering example of the reasoning verification of train acceleration is provided. After simulating the large-scale cases, it is shown that the simulation results are consistent with the theoretical reasoning results. This method needs more calculation, while it is more effective in detecting non-error’s fault factors than other error reasoning methods.

The optimal emergency decision-making method with incomplete probabilistic information

Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc. These emergencies can bring huge disasters to people, even worse, the time left for people to make critical decisions is usually very limited. When an emergency occurs, the most important thing for people is to make reasonable decisions as soon as possible to deal with the current problems, otherwise, the situation may deteriorate further. The paper proposes an emergency decision-making algorithm under the constraints of the limited time and incomplete information, the research is mainly carried out from the following aspects, firstly, we use the data structure of the hesitant fuzzy probabilistic linguistic set to collect the basic data after careful comparison, which has three advantages, (1) considering the hesitation in the decision-making process, each evaluation information is allowed to contain multiple values instead of just one value; (2) each evaluation value is followed by a probability value, which further describes the details of the evaluation information; (3) the data structure allows some probability information to be unknown, which effectively expands the application scope of the algorithm. Secondly, the maximization gap model is proposed to calculate unknown parameters, the model can distinguish alternatives with small differences. Thirdly, all the evaluation information will be aggregated by the dynamic hesitant probability fuzzy weighted arithmetic operator. Subsequently, an instance is given to illustrate the effectiveness and the accuracy of the algorithm proposed in the paper. Finally, the advantages of the proposed algorithm are further demonstrated by comparing it with other outstanding algorithms. The main contribution of the paper is that we propose the maximization gap model to obtain the unknown parameters, which can effectively and accurately distinguish alternatives with small differences.

READING KEYNES’S POLICY PAPERS THROUGH THE PRISM OF HIS TREATISE ON PROBABILITY: INFORMATION, EXPECTATIONS, AND REVISION OF PROBABILITIES IN ECONOMIC POLICY

When scholars investigate the legacy of John Maynard Keynes’s Treatise on Probability (1921) for the development of Keynes’s thinking, the attention usually focuses on the connections among Keynes’s probability theory, his conception of decision-making under uncertainty, and the theory of the functioning of the macroeconomic system that derives from it—through the marginal efficiency of capital, the preference for liquidity, and the self-referential functioning of financial markets. By contrast, this paper aims to investigate the connections between Keynes’s probability theory, on the one hand, and his economic policy recommendations, on the other. It concentrates on the policy recommendations defended by Keynes during the Great Depression but also after the General Theory. Keynes’s economic policy can be understood as a framework for decision-making in situations of uncertainty: fiscal policy aims to induce private agents to change their “rational” probability statements, while monetary policy aims to allow more weight to these statements.

Communicating Probability Information in Hurricane Forecasts: Assessing Statements that Forecasters Use on Social Media and Implications for Public Assessments of Reliability

Forecasters are responsible for predicting the weather and communicating risk with stakeholders and members of the public. This study investigates the statements that forecasters use to communicate probability information in hurricane forecasts and the impact these statements may have on how members of the public evaluate forecast reliability. We use messages on Twitter to descriptively analyze probability statements in forecasts leading up to Hurricanes Harvey, Irma, Maria, and Florence from forecasters in three different groups: the National Hurricane Center, local Weather Forecast Offices, and in the television broadcast community. We then use data from a representative survey of United States adults to assess how members of the public wish to receive probability information and the impact of information format on assessments of forecast reliability. Results from the descriptive analysis indicate forecasters overwhelmingly use words and phrases in place of numbers to communicate probability information. In addition, the words and phrases forecasters use are generally vague in nature -- they seldom include rank adjectives (e.g., “low” or “high”) to qualify blanket expressions of uncertainty (e.g., “there is a chance of flooding”). Results from the survey show members of the public generally prefer both words/phrases and numbers when receiving forecast information. They also show information format affects public judgments of forecast reliability; on average, people believe forecasts are more reliable when they include numeric probability information.

Selective outcome reinstatement during evaluation drives heuristics in risky choice

A ubiquitous feature of human decision making under risk is that individuals differ from each other, as well as from normativity, in how they incorporate reward and probability information. One possible explanation for these deviations is a desire to reduce the number of potential outcomes considered during choice evaluation. Although multiple behavioral models can be invoked involving selective consideration of choice outcomes, whether differences in these tendencies underlie behavioral differences in sensitivity to reward and probability information is unknown. Here we consider neural evidence where we exploit magnetoencephalography (MEG) to decode the actual choice outcomes participants consider when they decide between a gamble and a safe outcome. We show that variability in tendencies of individual participants to reinstate neural outcome representations, based on either their probability or reward, explains variability in the extent to which their choices reflect consideration of probability and reward information. In keeping with this we also show that participants who are higher in behavioral impulsivity fail to preferentially reinstate outcomes with higher probability. Our results suggest that neural differences in the degree to which outcomes are considered shape risk taking strategy, both in decision making tasks, as well as in real life.

Background Uncertainty Can Increase Risk Aversion in Decision Making

Here, we aim to investigate the effect of background uncertainty on decision making systematically. After reviewing the existing empirical studies, we argue that two types of uncertainty should be distinguished: a) ambiguity, i.e., uncertain outcomes without probability information, and b) risk, i.e., uncertainties involving probabilities regarding a negative outcome. We test the hypothesis that the type of uncertainty moderates the effect of background uncertainty on risk preferences. To test our hypothesis, we conducted four experimental studies. In this project we host all analyses scripts, data and linked preregistration of Study 3 and Study 4.

Reading Keynes’s policy papers through the prism of his Treatise on Probability: information, expectations and revision of probabilities in economic policy

When scholars investigate the legacy of Keynes’s Treatise on Probability (1921) for the development of Keynes’s thinking, the attention usually focuses on the connections between Keynes’s probability theory, his conception of decision-making under uncertainty and the theory of the functioning of the macroeconomic system that derives from it - through the marginal efficiency of capital, the preference for liquidity and the self-referential functioning of financial markets. By contrast, the paper aims to investigate the connections between Keynes’s probability theory on the one hand, and his economic policy recommendations on the other. It concentrates on the policy recommendations defended by Keynes during the Great Depression but also after the General Theory. Keynes’s economic policy can be understood as a framework for decision-making in situations of uncertainty: fiscal policy aims to induce private agents to change their “rational” probability statements, while monetary policy aims to allow more weight to these statements.