Planning of experiments for a nonautonomous ornstein-uhlenbeck process

Lacko, Vladimír

doi:10.2478/v10127-012-0011-2

Cited by 16 publications

(3 citation statements)

References 11 publications

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“…Figure 2 presents how a variable Y changes as a function of its cause X for a number of different values of θ XY . We assume t of 100 ms (i.e., between t and t + 1) and that ω and σ remain constant, although these assumptions can be loosened (see Lacko, 2012).…”

Section: The Single Cause Casementioning

confidence: 99%

Causal Structure Learning in Continuous Systems

2020

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Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e., those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss-Markov ("Ornstein-Uhlenbeck") processes and show how such OU networks can express complex dynamic phenomena, such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world.

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Section: The Single Cause Casementioning

confidence: 99%

Causal Structure Learning in Continuous Systems

2020

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“…Analogously, the value of the corresponding information function attains a finite value as well. The idea to measure the relative efficiency of a design with respect to information obtained by observation of the full trajectory, which we call "ultimate efficiency" as Harman (2011) suggested, was later adopted in the works of Harman andŠtulajter (2011) and Lacko (2012), and plays a crucial role also in this paper. Compared with the standard setup the parametrisation of the model (1) has, however, a different structure.…”

Section: Ultimate Efficiency Of Designsmentioning

confidence: 99%

“…Studies carried out by Kise ľák and Stehlík (2008) and later Zagoraiou and Antognini (2009) show that equidistant designs are optimal also for a stationary variant of equation ( 3), that is, for t → ∞. Further analysis of model (3) with θ 1 and X 0 in the position of parameters was provided by Lacko (2012), who demonstrated that under the assumption of a time-dependent volatility the optimal sampling times are more concentrated in areas with lower levels of the volatility function.…”

Section: Introductionmentioning

confidence: 98%