Conditional responses in rodents such as locomotion have been reported for drugs of abuse and similar to the placebo response in humans, may be associated with the expectation of reward. We examined several conditional opioid-like responses and the influence of drug expectation on conditioned place preference and concomitant conditional locomotion. Male C57BL/6J mice were conditioned with the s...

We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our sublinear expectation, we give a simple construction, in a quasi-sure sense, of the (linear) conditional expectations, and hence give a representation for the c...

A double forecasting model based on conditional expectation is proposed through probability distribution of port cargo throughput. A compound variable, being composed of the number of cargo ships arriving at the port and the operating efficiency of handling equipment, is constructed. The port cargo throughput is the sum of all compound variables which indicated the cargo throughput each time wh...

Given a probability space (Ω,F , P ), a F -measurable random variable X , and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L-predictor (also known as “the least mean square error” predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient conditions under which the conditional expecta...

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non-additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining the notion of independence of non-additive probabilities and Nash equilibrium. Journal of Economic Li...

2 Review of probability. 5 2.1 Properties of expectation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Convergence of random variables. . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Convergence in probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Informati...

Abstract Recently a regular (unconditional) decision process has been mathematically formulated from the multistage decision process in Bellman and Zadeh's paper "Decision-making in a fuzzy environment". According to the available information on total fuzziness, we propose two types of conditional decision process for regular decision process. One is an "a posteriori conditional decision proces...

We examine the relationship between the Cooper-Herskovitz score of a Bayesian network and the conditional entropies of the nodes of the networks conditioned on the probability distributions of their parents. We show that minimizing the conditional entropy of each node of the BNS conditioned on its set of parents amounts to maximization of the CH score. The main result is a lower bound on the si...