Browse By Author Name - Bermejo, Iñigo - e-spacio
http://e-spacio.uned.es/fez/
Universidad Nacional de Educación a DistanciaspFez 2.1 RC3http://blogs.law.harvard.edu/tech/rssEvaluation of Markov models with discontinuities
http://e-spacio.uned.es/fez/view/bibliuned:95-Jperez-003
Background. Several methods, such as the half-cycle correction and the life-table method, were developed to attenuate the error introduced in Markov models by the discretization of time. Elbasha and Chhatwal have proposed alternative “corrections” based on numerical integration techniques. They present an example whose results suggest that the trapezoidal rule, which is equivalent to the half-cycle correction, is not as accurate as Simpson’s 1/3 and 3/8 rules. However, they did not take into consideration the impact of discontinuities. Objective. To propose a method for evaluating Markov models with discontinuities. Design. Applying the trapezoidal rule, we derive a method that consists of adjusting the model by setting the cost at each point of discontinuity to the mean of the left and right limits of the cost function. We then take from the literature a model with a cycle length of 1 year and a discontinuity on the cost function and compare our method with other “corrections” using as the gold standard an equivalent model with a cycle length of 1 day. Results. As expected, for this model, the life-table method is more accurate than assuming that transitions occur at the beginning or the end of cycles. The application of numerical integration techniques without taking into account the discontinuity causes large errors. The model with averaged cost values yields very small errors, especially for the trapezoidal and the 1/3 Simpson rules. Conclusion. In the case of discontinuities, we recommend applying the trapezoidal rule on an averaged model because this method has a mathematical justification, and in our empirical evaluation, it was more accurate than the sophisticated 3/8 Simpson rule.2020-06-18T08:29:16Z
Pérez-Martín, Jorge
og Bermejo, Iñigo
og Díez, Francisco J.
Markov influence diagrams: a graphical tool for cost-effectiveness analysis
http://e-spacio.uned.es/fez/view/bibliuned:95-Jperez-002
Markov influence diagrams (MIDs) are a new type of probabilistic graphical models that extend influence diagrams in the same way as Markov decision trees extend decision trees. They have been designed to build state-transition models, mainly in medicine, and perform cost-effectiveness analysis. Using a causal graph that may contain several variables per cycle, MIDs can model various features of the patient without multiplying the number of states; in particular, they can represent the history of the patient without using tunnel states. OpenMarkov, an open-source tool, allows the decision analyst to build and evaluate MIDs—including cost-effectiveness analysis and several types of deterministic and probabilistic sensitivity analysis—with a graphical user interface, without writing any code. This way, MIDs can be used to easily build and evaluate complex models whose implementation as spreadsheets or decision trees would be cumbersome or unfeasible in practice. Furthermore, many problems that previously required discrete event simulation can be solved with MIDs, i.e., within the paradigm of state-transition models, in which many health economists feel more comfortable.2020-06-18T06:57:50Z
Díez, Francisco J.
og Yebra, Mar
og Bermejo, Iñigo
og Palacios-Alonso, Miguel Angel
og Arias Calleja, Manuel
og Luque, Manuel
og Pérez-Martín, Jorge
New types of probabilistic graphical models: applications to medicine
http://e-spacio.uned.es/fez/view/tesisuned:IngInf-Ibermejo
Probabilistic graphical models (PGMs) play a major role in much of the modern research in reasoning with uncertainty, decision analysis, planning, pattern recognition, and many other areas. Several types of PGMs have been proposed in the last two decades. However, there are some problems for which none of these types are appropriate. For example, none of the types of PGMs proposed has been widely adopted for representing and solving asymmetric decision problems. Decision analysis networks (DANs) have been recently proposed by our research group and they needed efficient evaluation algorithms in order to be applicable to real-world problems. In this thesis, I propose a new algorithm that evaluates DANs by recursively decomposing them into a set of symmetric DANs, which can then be evaluated with standard algorithms, such as variable elimination or arc reversal. The efficiency of this algorithm matches that of the algorithms proposed for other asymmetric representations. Similarly, existing types of PGMs were not apt as dynamic modeling methods for cost-effectiveness analysis (CEA). The existing dynamic PGMs are burdened by the complexity of their evaluation and can only solve unicriterion problems. Only Markov infuence diagrams (MIDs), a more restricted type of dynamic PGMs also proposed by our research group, are suitable to build complex dynamic models to perform CEA. I have developed new types of potentials and new sensitivity analysis algorithms, with which I have been able to replicate as MIDs several models proposed in the literature and to build two new models for CEA: one for malignant pleural effusion and another one for mammography screening. Finally, with the help of an expert, we have built a decision-support system for cochlear implant programming (i.e., parameter tuning) based on PGMs. In this thesis, we also describe tuning networks, a new type of PGM we developed because existing PGMs were not suitable to model the behavior of systems with a high number of tunable parameters. This decision-support system is now routinely used at a hearing clinic in Antwerp (Belgium) to assist audiologists in the programming of cochlear implants. All the contributions to PGMs described in this thesis have been implemented in OpenMarkov, an open-source software tool developed at the UNED, and are publicly available.2016-10-22T03:27:27Z
Bermejo Delgado, Iñigo