Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

Parsimonious Description of Generalized Gibbs Measures : Decimation of the 2d-Ising Model

In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on $\Z^2$ in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and present the construction of global specifications consistent with the extremal decimated measures. We use them to consider these renormalized measures as almost Gibbsian measures and to precise its convex set of DLR measures. We also recall the weakly Gibbsian description and complete it using a potential that admits a quenched correlation decay, i.e. a well-defined configuration-dependent length beyond which this potential decays exponentially. We use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences.Comment: 32 pages, preliminary versio

Bayesian Geoadditive Seemingly Unrelated Regression

Parametric seemingly unrelated regression (SUR) models are a common tool for multivariate regression analysis when error variables are reasonably correlated, so that separate univariate analysis may result in inefficient estimates of covariate effects. A weakness of parametric models is that they require strong assumptions on the functional form of possibly nonlinear effects of metrical covariates. In this paper, we develop a Bayesian semiparametric SUR model, where the usual linear predictors are replaced by more flexible additive predictors allowing for simultaneous nonparametric estimation of such covariate effects and of spatial effects. The approach is based on appropriate smoothness priors which allow different forms and degrees of smoothness in a general framework. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques

Generalized multivariate Markov chains : estimation, inference and implementation in R

Mestrado Bolonha em Econometria Aplicada e PrevisãoEste trabalho propõe uma nova generalização do modelo de Cadeias de Markov Multivariadas. Tipicamente, uma cadeia de Markov é descrita pelos valores passados do pro- cesso, a generalização proposta neste trabalho permiritá também considerar variáveis exó- genas. Especificamente, iremos incorporar os efeitos dos valores passados do processo e os efeitos de variáveis pré-determinadas ou exógenas no modelo. Deste modo, será considerada uma cadeia de Markov não-homogénea em vez de uma cadeia de Markov homogénea. Os resultados da simulação de Monte Carlo mostraram que o modelo pro- posto detectou uma cadeia de Markov não-homogénea e detectou valores específicos dos parâmetros. Porém, quando esses valores eram baixos em magnitude, os resultados da simulação mostraram que o modelo tinha baixo poder de teste. Portanto, para estimativas de baixa magnitude, dever-se-á considerar um nível de significância mais alto ao tes- tar a significância individual dos parâmetros. Adicionalmente, uma ilustração empírica demonstrou a relevância deste novo modelo, ao estimar a matriz de transição de proba- bilidade, para diferentes valores de uma variável exógena. Uma contribuição adicional e prática deste trabalho é o desenvolvimento de uma package R com esta generalização.This essay proposes a new generalization of Multivariate Markov Chains (MMC) model. Typically, a Markov chain is described by the process’ past values, the gener- alization proposed in this work will also consider exogenous variables. Specifically, we will incorporate the effects of the process’ past values and the effects of pre-determined or exogenous covariates in the model. This is achieved by considering a non-homogeneous Markov chain instead of an homogeneous Markov chain. The findings from the Monte Carlo simulation showed that the model proposed detected a non-homogeneous Markov chain and it detected specific values of the parameters. However, when these values were small in magnitude, the results from the simulation showed that the model had low power of test. Hence, for estimates with small magnitude, one should use a higher significance level when testing for individual significance of the parameters. Moreover, an empirical illustration demonstrated the relevance of this new model, by estimating the probabil- ity transition matrix, for different values of the exogenous variable. An additional and practical contribution of this work is the development of a novel R package with this generalization.info:eu-repo/semantics/publishedVersio

Growth and volatility regime switching models for New Zealand GDP data

This paper fits hidden Markov switching models to New Zealand GDP data. A primary objective is to better understand the utility of these methods for modelling growth and volatility regimes present in the New Zealand data and their interaction. Properties of the models are developed together with a description of the estimation methods, including use of the Expectation Maximisation (EM) algorithm. The models are fitted to New Zealand GDP and production sector growth rates to analyse changes in their mean and volatility over time. The paper discusses applications of the methodology to identifying changes in growth performances, and examines the timing of growth and volatility regime switching between production sectors. Conclusions to emerge are that, in contrast to the 1980s, New Zealand GDP growth experienced an unusually long period of time in high growth and low volatility regimes during the 1990s. The paper evaluates sector contributions to this 1990s experience and discusses directions for further development.Hidden Markov models; regime switching; growth; business cycles; volatility; production sectors; GDP.