A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online

The Environmental Consequences of Globalization: A Country-Specific Time-Series Analysis

The dynamic relationships among trade, income and the environment for developed and developing countries are examined using a cointegration analysis. Results suggest that trade and income growth tend to increase environmental quality in developed countries, whereas they have detrimental effects on environmental quality in most developing countries. It is also found that for developed countries the causal relationship appears to run from trade and income to the environment - a change in trade and income growth causes a consequent change in environmental quality, and the opposite relationship holds for developing countries.Developed countries, Developing countries, Environmental quality, Globalization, Time-series analysis, Trade, Environmental Economics and Policy, International Relations/Trade,

Novel Bayesian Networks for Genomic Prediction of Developmental Traits in Biomass Sorghum.

The ability to connect genetic information between traits over time allow Bayesian networks to offer a powerful probabilistic framework to construct genomic prediction models. In this study, we phenotyped a diversity panel of 869 biomass sorghum (Sorghum bicolor (L.) Moench) lines, which had been genotyped with 100,435 SNP markers, for plant height (PH) with biweekly measurements from 30 to 120 days after planting (DAP) and for end-of-season dry biomass yield (DBY) in four environments. We evaluated five genomic prediction models: Bayesian network (BN), Pleiotropic Bayesian network (PBN), Dynamic Bayesian network (DBN), multi-trait GBLUP (MTr-GBLUP), and multi-time GBLUP (MTi-GBLUP) models. In fivefold cross-validation, prediction accuracies ranged from 0.46 (PBN) to 0.49 (MTr-GBLUP) for DBY and from 0.47 (DBN, DAP120) to 0.75 (MTi-GBLUP, DAP60) for PH. Forward-chaining cross-validation further improved prediction accuracies of the DBN, MTi-GBLUP and MTr-GBLUP models for PH (training slice: 30-45 DAP) by 36.4-52.4% relative to the BN and PBN models. Coincidence indices (target: biomass, secondary: PH) and a coincidence index based on lines (PH time series) showed that the ranking of lines by PH changed minimally after 45 DAP. These results suggest a two-level indirect selection method for PH at harvest (first-level target trait) and DBY (second-level target trait) could be conducted earlier in the season based on ranking of lines by PH at 45 DAP (secondary trait). With the advance of high-throughput phenotyping technologies, our proposed two-level indirect selection framework could be valuable for enhancing genetic gain per unit of time when selecting on developmental traits

HE Plots for Repeated Measures Designs

Hypothesis error (HE) plots, introduced in Friendly (2007), provide graphical methods to visualize hypothesis tests in multivariate linear models, by displaying hypothesis and error covariation as ellipsoids and providing visual representations of effect size and significance. These methods are implemented in the heplots for R (Fox, Friendly, and Monette 2009a) and SAS (Friendly 2006), and apply generally to designs with fixed-effect factors (MANOVA), quantitative regressors (multivariate multiple regression) and combined cases (MANCOVA). This paper describes the extension of these methods to repeated measures designs in which the multivariate responses represent the outcomes on one or more âÂÂwithin-subjectâ factors. This extension is illustrated using the heplots for R. Examples describe one- sample profile analysis, designs with multiple between-S and within-S factors, and doubly- multivariate designs, with multivariate responses observed on multiple occasions.

How an Export Boom affects Unemployment

Does trade affect the equilibrium rate of unemployment? To theoretically examine this question, we incorporate firm-union bargaining considerations into a model with a booming external sector and a stagnating manufacturing sector. In the model, a sustained improvement in the terms of trade lowers unemployment. To empirically investigate the predicted determinants of the unemployment rate, we use data for Australia, a country whose prosperity has always depended on the value of its exports. We find strong evidence that higher export prices, capital accumulation in tradeable goods industries and a lower unemployment benefit replacement rate each reduce the equilibrium unemployment rate.