POSSIBILITIES OF MATHEMATICAL DEFINITION OF UNFAVOURABLE COURSE OF SUBARACHNOID HAEMORRHAGE IN THE ACUTE PERIOD

Subarachnoid haemorrhage (SAH) is associated with a 30-day mortality rate of 50% and is one of the most life-threatening cerebrovascular diseases. Objective. Toevaluatetheprognosticsignificance and informativeness of some clinical indicators, highlighting the most optimal and reliable potential factors in the development of a mathematical equation for calculating the personal probability of complications in patients with subarachnoid hemorrhage of atraumatic etiology. Materials and methods. A clinical experimental study involved 87 patients with SAH, 44 were men, 43 – women. On the first day after SAH, half of the patients were hospitalized – 46 people (52,87%). Results. The constructed model for calculating the probability of events such as secondary ischemia, hydrocephalus, or cerebral vasospasm over the next 14 days indicates the correctness and adequacy of the constructed model of logistic regression.The personal probability of a complication is calculated by the formula: p = 1 / (1 + e-z), where p is the % probability of a complication of SAH; z = –45,5 + 17,5* Copeptine –0.44 × Na + 0,06 × Age + 1,99 × Ball (Hunt-Hess). Conclusions. The prognostic model allows us to consider that secondary ischemia and cerebral vasospasm are not only predictors of poor prognosis and potential factors for the formation of complications, but also are indicators for the correct determination of individual cumulative risk in SAH. Keywords: notraumatic hemorrhage, C. S. Ogilvy, copeptin, SIADH syndrome, hyponatremia, prognosis, logistic regression.

Countable additivity, idealization, and conceptual realism

This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory – in particular, Savage’s theory of subjective expected utility and personal probability. I show that Savage’s reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealized assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage’s theory and explore some technical properties in relation to other axioms of the system.

Depression is related to an absence of optimistically biased belief updating about future life events

BackgroundWhen challenged with information about the future, healthy participants show an optimistically biased updating pattern, taking desirable information more into account than undesirable information. However, it is unknown how patients suffering from major depressive disorder (MDD), who express pervasive pessimistic beliefs, update their beliefs when receiving information about their future. Here we tested whether an optimistically biased information processing pattern found in healthy individuals is absent in MDD patients.MethodMDD patients (n = 18; 13 medicated; eight with co-morbid anxiety disorder) and healthy controls (n = 19) estimated their personal probability of experiencing 70 adverse life events. After each estimate participants were presented with the average probability of the event occurring to a person living in the same sociocultural environment. This information could be desirable (i.e. average probability better than expected) or undesirable (i.e. average probability worse than expected). To assess how desirable versus undesirable information influenced beliefs, participants estimated their personal probability of experiencing the 70 events a second time.ResultsHealthy controls showed an optimistic bias in updating, that is they changed their beliefs more toward desirable versus undesirable information. Overall, this optimistic bias was absent in MDD patients. Symptom severity correlated with biased updating: more severely depressed individuals showed a more pessimistic updating pattern. Furthermore, MDD patients estimated the probability of experiencing adverse life events as higher than healthy controls.ConclusionsOur findings raise the intriguing possibility that optimistically biased updating of expectations about one's personal future is associated with mental health.

Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation: The Annuity Benchmark

The present paper considers a retiree of a certain age who is endowed with a certain amount of wealth and is facing alternative investment opportunities. One possibility is to buy a single premium immediate (participating) annuity-contract. This insurance product pays a life-long pension payment of a certain amount, depending e.g. on the age of the retiree, the operating cost of the insurance company and the return the company is able to realize from its investments. The alternative possibility is to invest the single premium into a portfolio of mutual funds and to periodically withdraw a fixed amount that is assumed to be equivalent to the consumption stream generated by the annuity. The particular advantage of this self-annuitization strategy compared to the life annuity is its greater liquidity and the possibility of leaving money for heirs. However, the risk of self-annuitization is to outlive the assets before the uncertain date of death. The risk can thus be specified by considering the probability of running out of money before the uncertain date of death. The determination of this personal probability of consumption shortfall with respect to German insurance and capital market conditions is the objective of this paper.