Although the mathematical bases of risk are not entirely derived from the probability theory, the two have a delicate and unique relationship. At the origin of the science of risk, insurance companies flourished in the 17^th and 18^th centuries, where the calculation of insurance premium was based on probabilistic concepts, especially those developed by Pascal. Distinguished mathematicians such as Huygens, Bernoulli, and Bayes all belonged to this era. The probability theory was often used for risk analysis with relatively simple structures such as chemicals and toxicology, and this tendency is still dominant today. However, as risk targets expanded to include complex and non-linear phenomena such as environmental and social risks, the conventional, simple probability theory proved inadequate. In particular, probabilistic tools cannot be used to assess the complex mechanisms of low-level radiation risk. Moreover, huge earthquakes and nuclear power plant meltdown incidents that have a low frequency of occurrence but devastating repercussions cannot be approached with the probability theory. The appropriate mathematical model for such risks has not yet been developed.

The authors suggest three problems for social decision by minimum risk principle, those are how to distribute risk to different stakeholders, how to transform objective probabilities of risk events into the subjective probabilities and how to ignore rare risk events purposively for our daily life. In order to solve the problems the authors suppose cooperative researches among welfare economics, statistical decision theory and fuzzy mathematics etc.

The chain of catastrophic events (the 2011 disaster) raised a number of critical questions associated with the methodological issues of “risk analysis” in managing the emergent characteristics of low-frequency and high-consequence risks. In this paper, salient methodological issues in responding to such a surprise and complex risk event are explored in terms of “limit of scientific risk assessment”, “deficit in risk governance” and “insufficient risk communication” taking account of the lessons learned from the 2011 disaster.

Health effects of radiation exposure is not easy for laymen/laywomen to understand because of numerous and complicated technical terms. First, basic notions on radiation including deterministic effects and stochastic effects are introduced. Second, the long-term cohort study on radiation effects to the atomic bomb survivors' health is introduced. Third, evaluation of health effects of radiation exposure is discussed with an illustration of misuse of linear non-threshold model. Finally, we touch briefly the fundamental issues in statistics regarding the interpretation of probability, with an introduction of the journal which recently declared to ban p-value.

The four articles in this special issue were reviewed from the perspective of a “flexible” Bayesian approach. This approach, while accepting the Bayesian axiomatic system, seeks to make it flexible enough to take psychological factors into consideration when faced with real social problem solving. The comments are given in terms of four viewpoints, namely, (1) assessment of uncertainty by subjective probability, (2) assessment of damage by loss function, (3) integration of uncertainty and loss, and (4) risk communication.

The purpose of this research is to reveal how the marketing mix strategy in the department store influences the customer's shopping trip behavior to the department store. The model represents the mechanism of frequency of coming to the stores with framework of an hierarchical Bayes Poisson regression model. The model includes three explanatory variables: “Store loyalty”, “Direct mail”, and “Events”. These variables are also modeled by functional form with parameters. As a result, we could confirm that direct mail is one of the marketing mix variables that have the most effect on frequency of coming to the store.

The purpose of this research is to offer the point which utilizes the brand association network for brand management. For this purpose, the consumer survey was performed four times from the same respondents in order to collect brand association networks.

The following three points became clear from result of this survey

● The brand association network change with time

● The change is not only an addition and disappearance of the association in a network, but also combination of a link, and cutting.

● The relations among associations are not stable, and changes with time. This means that a certain association meaning has also changes with time.

Advertising investment risk has become high due to the explosive information increase and the commoditization evolution. In order to reduce such risk, it is important to understand the relation between advertising elements and consumer responses, and apply the knowledge to decision making process of advertising production. There have been lots of efforts to develop a set of scales to measure the advertising perceptions and relate it to the consumer responses. However, that is not adequate when we assume to support the actual practices of the advertising production. Although the advertising perceptions are helpful to understand the reasons of the consumer responses, they don't directly lead the way to the advertising production.

In this study, we analyze the effects of 28 elements of TV advertisements on the advertising perceptions and the consumer responses. The elements adopted in this study are controllable by advertisers so that they can apply the research findings to the advertising production. Empirical analyses using a dataset of the advertising perceptions and the consumer responses to more than 800 TV advertisements clarified not only the important advertising elements which had high impacts on the consumer responses but also how and why they affect consumer responses. Simultaneously, simulation of the consumer responses using random forests was found to be helpful to explore the effective combination of the advertising elements.