出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：Modelling microlensing events is a complex job extending far beyond the optimization of a function
of adopted model parameters by means of standard techniques. Non-linearity of the underlying
models leads to parameter ambiguities and degeneracies, and already the most simple case of
a single point-like observed source star and a single point-mass lens as well as a static observer is
substantially less trivial than one might think, while a proper treatment of the various microlensing
anomalies requires tailored approaches to ensure that all regions in a high-dimensional intricate
model parameter space are identied that could provide a suitable description of the nature of
the observed event. Catastrophic behaviour leading to caustics results in the need to optimize
functions that are not smooth, which causes a signicant problem to standard algorithms. As if
this were not enough, the photometric measurements frequently show complex statistics, varying
amongst different sites, and involving outliers, an increased abundance of larger deviations as
compared to a Gaussian distribution, as well as effects depending on the observing conditions.
It requires advanced statistical methods and numerical strategies to account for the encountered
difculties. In order to be able to identify deviations from an ordinary light curve of ongoing
microlensing events, a real-time modelling is required, and for realizing an optimal monitoring
strategy, accurate predictions of model parameters are a valuable ingredient. The bias of
maximum-likelihood estimates however frequently leads to substantial mispredictions, whereas
maximum a-posteriori estimates with an appropriate prior are doing a better job. Multivariate parameter
probability densities of the model parameters for observed events contain all the relevant
information from which any interval estimates can be derived. Moreover, by means of Bayes'
theorem, these can be converted to yield the probabilistic distributions of any physical properties
with the assumption of respective priors. The identication of characteristic features in the
observed light curve provides the clue to a successful modelling, and tailored articial neural networks
might replace human intuition, eventually leading to fully-automated real-time modelling
systems.
