Search results for "Probability Theory"
showing 10 items of 269 documents
Conditional Random Quantities and Compounds of Conditionals
2013
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a conditional event $E|H$ is looked at as a three-valued quantity with values 1, or 0, or $p$, where $p$ is the probability of $E|H$. We introduce a notion of iterated conditional random quantity of the form $(X|H)|K$ defined as a suitable conditional random quantity, which coincides with $X|HK$ when $H \subseteq K$. Based on a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of cohere…
Generalized probabilistic modus ponens
2017
Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the re…
Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence
2013
We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH c , where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y|K coincide. We show that X|HK coincides with a suitable c.r.q. Y|K and we apply this representation to Bayesian updating of probabilities, by also deepening some aspects of Bayes’ formula. Then, we introduce a notion of iterated c.r.q. (X|H)|K, by analyzing its relationship with X|HK. Our notion of iterated conditiona…
On approximation of a class of stochastic integrals and interpolation
2004
Given a diffusion Y = (Y_{t})_{t \in [0,T]} we give different equivalent conditions so that a stochastic integral has an L 2-approximation rate of n −η, {\rm \eta \in (0,1/2],} if one approximates by integrals over piece-wise constant integrands where equidistant time nets of cardinality n + 1 are used. In particular, we obtain assertions in terms of smoothness properties of g(Y T ) in the sense of Malliavin calculus. After optimizing over non-equidistant time-nets of cardinality n + 1 in case {\rm \eta > 0} , it turns out that one always obtains a rate of n^{ - 1/2}, which is optimal. This applies to all functions g obtained in an appropriate way by the real interpolation method between th…
An empirically grounded agent based model for modeling directs, conflict detection and resolution operations in air traffic management
2017
We present an agent based model of the Air Traffic Management socio-technical complex system that aims at modeling the interactions between aircrafts and air traffic controllers at a tactical level. The core of the model is given by the conflict detection and resolution module and by the directs module. Directs are flight shortcuts that are given by air controllers to speed up the passage of an aircraft within a certain airspace and therefore to facilitate airline operations. Conflicts resolution between flight trajectories can arise during the en-route phase of each flight due to both not detailed flight trajectory planning or unforeseen events that perturb the planned flight plan. Our mod…
Testing the Martingale Property of Exchange Rates: A Replication
2010
In this paper, we test the martingale property of a set of U.S. exchange rates already analyzed in a recent paper by Yilmaz [J. of Buss. and Ec. Stat., 2003]. We claim that the tests used by Yilmaz are not the most convenient to test the martingale hypothesis (or the equivalent martingale difference of the returns); hence, we compute a recently proposed test by Kuan and Lee [Stud. in Nonlin. Dyn. and Econ., 2004] and compare our results to Yilmaz's. Striking differences arise, which can give a clue about the type of data generating process governing the evolution of exchange rates in each sub-period.
On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach
2011
In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.
Martingale Convergence Theorems and Their Applications
2020
We became familiar with martingales X=(X n ) n∈N0 as fair games and found that under certain transformations (optional stopping, discrete stochastic integral) martingales turn into martingales. In this chapter, we will see that under weak conditions (non-negativity or uniform integrability) martingales converge almost surely. Furthermore, the martingale structure implies L p -convergence under assumptions that are (formally) weaker than those of Chapter 7. The basic ideas of this chapter are Doob’s inequality (Theorem 11.4) and the upcrossing inequality (Lemma 11.3).
Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain
2018
Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The p…
Polar motion prediction using the combination of SSA and Copula-based analysis
2018
The real-time estimation of polar motion (PM) is needed for the navigation of Earth satellite and interplanetary spacecraft. However, it is impossible to have real-time information due to the complexity of the measurement model and data processing. Various prediction methods have been developed. However, the accuracy of PM prediction is still not satisfactory even for a few days in the future. Therefore, new techniques or a combination of the existing methods need to be investigated for improving the accuracy of the predicted PM. There is a well-introduced method called Copula, and we want to combine it with singular spectrum analysis (SSA) method for PM prediction. In this study, first, we…