Concept Of Subjective Probability Research Articles

Специфіка застосування математико-статистичних методів в українських дослідженнях благополуччя особистості

Personal well-being has been actively studied over the past two decades regarding the social practice demands. However, it is an extremely complex multi-concept which is difficult to verify. The article analyzes the mathematical and statistical methods used in Ukrainian studies of the phenomenon of personal well-being over the past five years. Firstly, the study shows that in domestic publications (especially articles) the importance is not given to the mathematical and statistical methods. Secondly, typical tasks in the study of personal well-being are the description of primary data, the study of similarity (Student’s t-test, Mann-Whitney’s U-test, Kraskal-Wallace’s H-test, Wilcoxon’s T-test, ANOVA) and the study of dependencies (Pearson’s correlation coefficient, Spearman’s rank-order correlation coefficient). Thirdly, correlation analysis is still one of the main analysis statistical tools over the past five years according the study of the links between well-being and other psychological phenomena. Since well-being is a highly complex system characterized by the presence of recurrent relationships and nonlinearity, it is important to use the synergetic paradigm and modern mathematical and statistical means of data analysis (Data mining), which allow to characterize systems characterized by ambiguity and uncertainty. Fourthly, application of new modern statistical methods is not yet widespreaded. When studying the phenomenon of personal well-being, the practice of processing small databases within the framework of applied statistics continues. Structural modeling, which makes it possible to confirm multidimensional models of well-being, is not widespreaded. Application of Bayesian networks of trust is quite promising, which are based on the concept of subjective probability, thus it is focused not on the study of objective reality, but on clarifying the individual’s ideas about it. Key words: psychological well-being, mathematical and statistical analysis, subjective well-being, modeling, personal well-being.

Methods of forming an expert assessment of the criteria of an information system for managing projects and programs

The article presents a method for determining and ranking significance of the criteria of an information system for managing projects and programs (hereinafter, PMIS) based on the concept of subjective probability with the help of expert assessments. The method of expert assessments is implemented by processing the opinions of experienced specialists on the possible values of losses and (or) the probability of their occurrence. It is also used in non-formalizable problem situations, when the lack of a sufficient array of information or its unreliability does not allow the use of purely formal mathematical methods. When analyzing the PMIS choice, expert assessments can be used, firstly, to form a subjective assessment of one or another PMIS with the subsequent use of this information in order to quantify it using statistical methods. Secondly, for a qualitative assessment of the PMIS choice in terms of determining their rank significance, priority in an ordered list of PMIS criteria. As the main stages of the proposed methodology, the following are proposed: 1) development of a list of assessed PMIS criteria and formation of a list of experts; 2) conducting a survey of experts in order to obtain a set of individual expert assessments according to the PMIS criteria; 3) calculation of the average assessment criteria of the PMIS; 4) checking the consistency of expert opinions on the rank significance of the assessed PMIS criteria based on the Kendall coefficient of concordance; 5) summing up the results of expert assessment of the PMIS criteria. The practical aspects of the expert assessment are considered: calculation tables, the method of filling them, processing and analyzing the results. The method of expert assessment of the PMIS criteria was further developed, thanks to which a set of effective and functional criteria was determined, which will be taken into account when developing technical requirements for this system

J. M. Keynes (D. Ellsberg) versus Ramsey (L. J. Savage B. de Finetti): The Role of Interval Valued Probability and the Weight of the Evidence (Ambiguity)

It is mathematically impossible to integrate a concept like Keynes’s weight of the evidence variable, w, or Ellsberg’s rho, ρ, into a subjective theory of probability explicitly because of the definitions of probability given by de Finetti, Ramsey and Savage. The Ramsey –de Finetti–Savage definition of probability identifies the subjective estimate of probability itself to be the degree of confidence or doubt a decision maker has in the outcome. This directly conflicts with Keynes’s view that the degree of confidence can never have anything to do with the logical probability estimate, which is a degree of rational belief. The degree of confidence estimate that a decision maker has in his estimate of logical probability is entirely separate from the probability estimate. They are completely independent from each other as explicitly stated by Keynes in chapter 6 of the A Treatise on Probability. The exact same type of analysis holds in the General Theory. The entire Liquidity Preference theory of the rate of interest erected by Keynes in the General Theory in chapters 13-17 is based on the definition of Liquidity Preference. Liquidity Preference is defined as a function of uncertainty. Uncertainty is then defined as a function of the weight of the evidence. Liquidity Preference is not a function of probability. Therefore, the confidence one has in one’s expectations of future outcomes, when the expectations are based on the estimated probabilities, is a conclusion that makes no sense in the subjective theories of Ramsey, de Finetti, Savage and of de Finetti and Savage. It is impossible to talk about the confidence one has in one’s probability estimate because the subjective probability estimate IS the decision maker’s degree of confidence. Ellsberg’s attempt to convince Savage to change his mind about the nature of and concept of subjective probability, as defined by Savage, was thus doomed to failure from the very beginning. A new definition of subjective probability from Savage (de Finetti or Ramsey) would have been required in order to deal with Ellsberg’s concerns. Savage (de Finetti or Ramsey) would have been forced to abandon their own definition of what subjective probability meant. It was impossible for Savage, de Finetti, Ramsey, or any advocate of the subjective theory of probability, to accept Ellsberg’s rho or Keynes’s w, as a measure of the confidence a decision maker has in his estimate of a probability, without completely changing their definition of what subjective probability means.

Probabilities for decision analysis in agriculture and rural resource economics: The need for a paradigm change

The notion that we can rationalize risky choice in terms of expected utility appears to be widely if not universally accepted in the agricultural and resource economics profession. While there have been many attempts to assess the risk preferences of farmers, there are few studies of their beliefs about uncertain events encoded as probabilities. We may attribute this neglect to scepticism in the profession about the concept of subjective probability. The general unwillingness to embrace this theory and its associated methods has all too often caused researchers to focus on problems for which frequency data are available, rather than on problems that are more important where data are generally sparse or lacking. In response, we provide a brief reminder of the merits of the subjectivist approach and extract some priorities for future research should there be a change of heart among at least some of the profession.

Assessing Strategic Risk

In recent decades, the concept of subjective probability has been increasingly applied to an adversary's choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction, and provide an axiomatic foundation for it.

A Probabilistic Approach to Approximate Reasoning

We propose an alternative approach to approximate reasoning which is totally different from the one developed by Zadeh. The present approach is independent of the choice of the translating rule of any implication operators. We use the concept of subjective probability instead of fuzzy membership function which has a strong resemblance to subjective probability.

Probabilistic Modeling in Design

A general procedure is proposed for evolving the form of a density function that is consistent with the concept of subjective probability. The procedure directly applies new data information to the updating of the form of a density function without imposing on it any theoretical distribution that could restrict its shape, and permits the direct use of judgment arising from real world experience. It is based on the simple concept that sample size is a measure of confidence in the shape of a density function. Two possible algorithms are given, and the concept is extended for simple “true” or “false” events. The importance of probability in artificial intelligence is also dicusssed, and its essentially subjective nature is described. Procedures are briefly suggested.

The use of subjective probability assessments to predict forest fire occurrence

This paper addresses the problem of predicting forest fire occurrence. A simple methodology is developed to elicit information, from experienced fire managers, for deriving subjective probability assessments concerning the number of fires that will be reported in their districts each day. The approach is based upon the assumption that such individuals can identify and classify similar fire environments with satisfactory consistency. Using the concept of subjective probability, a methodology is developed for combining classified experience with a decision maker's initial assessment concerning assessor behavior. A scoring rule is used to measure the accuracy of the assessments. The results of an experiment which was conducted in northern Ontario during the 1973 fire season are presented.

Logical foundations and measurement of subjective probability

This paper discusses some important foundations of subjective probability, which is considered to be the only meaningful interpretation of the word ‘probability’. After some preliminary warnings regarding the specification of an uncertain situation, the concept of subjective probability as a degree of belief is briefly discussed. It is shown that degrees of belief can be translated into prices which one is willing to pay for being allowed to bet on the outcome of an uncertain event. Several measuring devices for an operational definition of subjective probability are considered. It is argued that the rules of consistency form sufficient conditions for the existence of formally admissible subjective probabilities, although other, logical or empirical, reasons may induce to further restrictions. The usefulness of probabilistic thinking and behavior is emphasized and several recommendations are made for the further development of this area, including use of scoring rules and the evaluation of probability assessors. Finally, the problem of whether subjective probabilities reflect ‘true’ characteristics of the environment (like actual relative frequencies) is discussed, and recourse to a concept of ‘objective probability’ is rejected.