Bayesian model selection methodology for road safety

Road accidents are a very relevant issue in many countries and macroeconomic models are very frequently applied by academia and administrations to reduce their frequency and consequences. The selection of explanatory variables and response transformation parameter within the Bayesian framework for the selection of the set of explanatory variables a TIM and 3IM (two input and three input models) procedures are proposed. The procedure also uses the DIC and pseudo -R2 goodness of fit criteria. The model to which the methodology is applied is a dynamic regression model with Box-Cox transformation (BCT) for the explanatory variables and autorgressive (AR) structure for the response. The initial set of 22 explanatory variables are identified. The effects of these factors on the fatal accident frequency in Spain, during 2000-2012, are estimated. The dependent variable is constructed considering the stochastic trend component.

Bayesian model selection of structural explanatory models.

In this study we are proposing a Bayesian model selection methodology, where the best model from the list of candidate structural explanatory models is selected. The model structure is based on the Zellner's (1971)explanatory model with autoregressive errors. For the selection technique we are using a parsimonious model, where the model variables are transformed using Box and Cox (1964) class of transformations.

Bayesian model selection of structural explanatory models: Application to road accident data

Using the Bayesian approach as the model selection criteria, the main purpose in this study is to establish a practical road accident model that can provide a better interpretation and prediction performance. For this purpose we are using a structural explanatory model with autoregressive error term. The model estimation is carried out through Bayesian inference and the best model is selected based on the goodness of fit measures. To cross validate the model estimation further prediction analysis were done. As the road safety measures the number of fatal accidents in Spain, during 2000-2011 were employed. The results of the variable selection process show that the factors explaining fatal road accidents are mainly exposure, economic factors, and surveillance and legislative measures. The model selection shows that the impact of economic factors on fatal accidents during the period under study has been higher compared to surveillance and legislative measures.

Forecasting stock returns using model-selection criteria

This paper examines the economic significance of return predictability in Australian equities. In light of considerable model uncertainty, formal model-selection criteria are used to choose a specification for the predictive model. A portfolio-switching strategy is implemented according to model predictions. Relative to a buy-and-hold market investment, the returns to the portfolio-switching strategy are impressive under several model-selection criteria, even after accounting for transaction costs. However, as these findings are not robust across other model-selection criteria examined, it is difficult to conclude that the degree of return predictability is economically significant.

Model selection and the vectorial misspecification-resistant information criterion in multivariate time series

The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care

This paper develops stochastic search variable selection (SSVS) for zero-inflated count models which are commonly used in health economics. This allows for either model averaging or model selection in situations with many potential regressors. The proposed techniques are applied to a data set from Germany considering the demand for health care. A package for the free statistical software environment R is provided.

Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

Prior selection for panel vector autoregressions

There is a vast literature that specifies Bayesian shrinkage priors for vector autoregressions (VARs) of possibly large dimensions. In this paper I argue that many of these priors are not appropriate for multi-country settings, which motivates me to develop priors for panel VARs (PVARs). The parametric and semi-parametric priors I suggest not only perform valuable shrinkage in large dimensions, but also allow for soft clustering of variables or countries which are homogeneous. I discuss the implications of these new priors for modelling interdependencies and heterogeneities among different countries in a panel VAR setting. Monte Carlo evidence and an empirical forecasting exercise show clear and important gains of the new priors compared to existing popular priors for VARs and PVARs.

Do pseudo-absence selection strategies influence species distribution models and their predictions? An information-theoretic approach based on simulated data

Background Multiple logistic regression is precluded from many practical applications in ecology that aim to predict the geographic distributions of species because it requires absence data, which are rarely available or are unreliable. In order to use multiple logistic regression, many studies have simulated "pseudo-absences" through a number of strategies, but it is unknown how the choice of strategy influences models and their geographic predictions of species. In this paper we evaluate the effect of several prevailing pseudo-absence strategies on the predictions of the geographic distribution of a virtual species whose "true" distribution and relationship to three environmental predictors was predefined. We evaluated the effect of using a) real absences b) pseudo-absences selected randomly from the background and c) two-step approaches: pseudo-absences selected from low suitability areas predicted by either Ecological Niche Factor Analysis: (ENFA) or BIOCLIM. We compared how the choice of pseudo-absence strategy affected model fit, predictive power, and information-theoretic model selection results. Results Models built with true absences had the best predictive power, best discriminatory power, and the "true" model (the one that contained the correct predictors) was supported by the data according to AIC, as expected. Models based on random pseudo-absences had among the lowest fit, but yielded the second highest AUC value (0.97), and the "true" model was also supported by the data. Models based on two-step approaches had intermediate fit, the lowest predictive power, and the "true" model was not supported by the data. Conclusion If ecologists wish to build parsimonious GLM models that will allow them to make robust predictions, a reasonable approach is to use a large number of randomly selected pseudo-absences, and perform model selection based on an information theoretic approach. However, the resulting models can be expected to have limited fit.

Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Benchmarking consensus model quality assessment for protein fold recognition

Background: Selecting the highest quality 3D model of a protein structure from a number of alternatives remains an important challenge in the field of structural bioinformatics. Many Model Quality Assessment Programs (MQAPs) have been developed which adopt various strategies in order to tackle this problem, ranging from the so called "true" MQAPs capable of producing a single energy score based on a single model, to methods which rely on structural comparisons of multiple models or additional information from meta-servers. However, it is clear that no current method can separate the highest accuracy models from the lowest consistently. In this paper, a number of the top performing MQAP methods are benchmarked in the context of the potential value that they add to protein fold recognition. Two novel methods are also described: ModSSEA, which based on the alignment of predicted secondary structure elements and ModFOLD which combines several true MQAP methods using an artificial neural network. Results: The ModSSEA method is found to be an effective model quality assessment program for ranking multiple models from many servers, however further accuracy can be gained by using the consensus approach of ModFOLD. The ModFOLD method is shown to significantly outperform the true MQAPs tested and is competitive with methods which make use of clustering or additional information from multiple servers. Several of the true MQAPs are also shown to add value to most individual fold recognition servers by improving model selection, when applied as a post filter in order to re-rank models. Conclusion: MQAPs should be benchmarked appropriately for the practical context in which they are intended to be used. Clustering based methods are the top performing MQAPs where many models are available from many servers; however, they often do not add value to individual fold recognition servers when limited models are available. Conversely, the true MQAP methods tested can often be used as effective post filters for re-ranking few models from individual fold recognition servers and further improvements can be achieved using a consensus of these methods.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.