Exact Bayesian inference for diffusion-based models

We develop methods to carry out Bayesian inference for diffusion-based continuous time models, formulated as stochastic differential equations (SDEs). The transition density implied by such SDEs is intractable, which complicates likelihood-based inference from discrete observations. In spite of this obstacle, we seek methods that are exact in the sense that they target the correct posterior distribution, in contrast to prevailing discretization approaches. We begin by discussing the main approaches to likelihood-based inference under intractability, and their application to diffusion-based models. This discussion is followed by a presentation of the fundamental inference algorithms for ordinary Itō diffusion inference, of computational difficulties they meet in practice, and of recent improvements motivated by our research on more complex diffusion-based models. These include Markov switching diffusions and stochastic volatility models, where a latent continuous time process modifies the dynamics of an observable diffusion process. We follow up by developing Markov chain Monte Carlo (MCMC) and Monte Carlo Expectation Maximization (MCEM) inference algorithms for the more complex settings, and evaluate them systematically. We close with a discussion of practical hurdles to adoption of exact algorithms, and propose solutions to overcome those hurdles

A propósito da formação de professores

O problema da formação de professores está no cerne do problema da universidade. A formação do professor de níveis II e III e os estudos de educação têm sido, no sistema paulista, reiteradamente deficientes e tratados como uma formação superior de segunda categoria. O amplo debate atual sobre a reformulação das licenciaturas e dos cursos de pedagogia tem que envolver, necessariamente, o repensar de toda a universidade