Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure

Assisted specification of discrete choice models

Determining appropriate utility specifications for discrete choice models is time-consuming and prone to errors. With the availability of larger and larger datasets, as the number of possible specifications exponentially grows with the number of variables under consideration, the analysts need to spend increasing amounts of time on searching for good models through trial-and-error, while expert knowledge is required to ensure these models are sound. This paper proposes an algorithm that aims at assisting modelers in their search. Our approach translates the task into a multi-objective combinatorial optimization problem and makes use of a variant of the variable neighborhood search algorithm to generate sets of promising model specifications. We apply the algorithm both to semi-synthetic data and to real mode choice datasets as a proof of concept. The results demonstrate its ability to provide relevant insights in reasonable amounts of time so as to effectively assist the modeler in developing interpretable and powerful models

The impact of pillar I support on farm choices: conceptual and methodological challenges

In the near future the CAP will continue to be structured around two pillars. In the first pillar the main instrument for producers’ support is the decoupled Single Farm Payment. In this paper we review the methodological framework for analysing decoupled payments in models of agricultural production. Market and technological uncertainty, credit constraints, farm household choices involving extra-agricultural decisions, policy uncertainty and long-run impact of decoupling on investment and land values are the relevant issues that should be pursued by methodological and empirical analysis. Future research should refine the analysis of decoupled payments, mainly trying to provide results that can be useful for policy simulation, to bridge the gap between analysis at the individual level and sector policy models.decoupled payments, agricultural production models, Common Agricultural Policy, Agricultural and Food Policy, Q12, Q18,

Prior distributions for objective Bayesian analysis

We provide a review of prior distributions for objective Bayesian analysis. We start by examining some foundational issues and then organize our exposition into priors for: i) estimation or prediction; ii) model selection; iii) highdimensional models. With regard to i), we present some basic notions, and then move to more recent contributions on discrete parameter space, hierarchical models, nonparametric models, and penalizing complexity priors. Point ii) is the focus of this paper: it discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. We also present some recent contributions in the area of objective priors on model space.With regard to point iii) we only provide a short summary of some default priors for high-dimensional models, a rapidly growing area of research

String and Membrane Gaussian Processes

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as string Gaussian processes (string GPs), which are not to be mistaken for Gaussian processes operating on text. We construct string GPs so that their finite-dimensional marginals exhibit suitable local conditional independence structures, which allow for scalable, distributed, and flexible nonparametric Bayesian inference, without resorting to approximations, and while ensuring some mild global regularity constraints. Furthermore, string GP priors naturally cope with heterogeneous input data, and the gradient of the learned latent function is readily available for explanatory analysis. Secondly, we provide some theoretical results relating our approach to the standard GP paradigm. In particular, we prove that some string GPs are Gaussian processes, which provides a complementary global perspective on our framework. Finally, we derive a scalable and distributed MCMC scheme for supervised learning tasks under string GP priors. The proposed MCMC scheme has computational time complexity $\mathcal{O}(N)$ and memory requirement $\mathcal{O}(dN)$, where $N$ is the data size and $d$ the dimension of the input space. We illustrate the efficacy of the proposed approach on several synthetic and real-world datasets, including a dataset with $6$ millions input points and $8$ attributes.Comment: To appear in the Journal of Machine Learning Research (JMLR), Volume 1