Browsing by Subject "MCMC"

Now showing 1 - 5 of 5
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    Estimating a noncompensatory IRT model using a modified metropolis algorithm.
    (2009-12) Babcock, Benjamin Grant Eugene
    Two classes of dichotomous multidimensional item response theory (MIRT) models, compensatory and noncompensatory, are reviewed. After a review of the literature, it is concluded that relatively little research has been conducted with the noncompensatory class of models. A monte-carlo simulation study was conducted exploring the estimation of a 2-parameter noncompensatory IRT model. The estimation method used was a modification of the Metropolis-Hastings algorithm that used multivariate prior distributions to help determine whether or not a newly sampled value was retained or rejected. Results showed that the noncompensatory model required a sample size of 4,000 people, 6 unidimensional items per dimension, and latent traits that are not highly correlated, for acceptable item parameter estimation using the modified Metropolis method. It is then argued that the noncompensatory model might not warrant further research due to the great requirements for acceptable estimation. The multidimensional interactive IRT model (MIIM) is proposed, which is more flexible than previous multidimensional models and explicitly accounts for correlated latent traits by using an interaction term within the logit. Item response surfaces for the MIIM model can be shaped either like compensatory or noncompensatory IRT model response surfaces.
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    Geometric ergodicity of a random-walk Metropolis algorithm for a transformed density
    (2010-11-22) Johnson, Leif; Geyer, Charles J.
    Curvature conditions on a target density in R^k for the geometric ergodicity of a random-walk Metropolis algorithm have previously been established (Mengersen and Tweedie(1996), Roberts and Tweedie(1996), Jarner and Hansen(2000)). However, the conditions for target densities in R^k that have exponentially light tails, but are not super-exponential are difficult to apply. In this paper I establish a variable transformation to apply to such target densities, that along with a regularity condition on the target density, ensures that a random-walk Metropolis algorithm for the transformed density is geometrically ergodic. Inference can be drawn for the original target density using Markov chain Monte Carlo estimates based on the transformed density. An application to inference on the regression parameter in multinomial logit regression with a conjugate prior is given.
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    Process-based Bayesian melding of occupational exposure models and industrial workplace data
    (2012-09) Monteiro, Joao Vitor Dias
    In industrial hygiene a worker's exposure to chemical, physical and biological agents is increasingly being modeled using deterministic physical models. However, predicting exposure in real workplace settings is challenging and approaches that simply regress on a physical model (e.g. straightforward non-linear regression) are less effective as they do not account for biases attributable, at least in part, to extraneous variability. This also impairs predictive performance. We recognize these limitations and provide a rich and flexible Bayesian hierarchical framework, which we call process-based Bayesian melding (PBBM), to synthesize the physical model with the field data. We reckon that the physical model, by itself, is inadequate for enhanced inferential performance and deploy (multivariate) Gaussian processes to capture extraneous uncertainties and underlying associations. We propose rich covariance structures for multiple outcomes using latent stochastic processes. We also pay attention to computational feasibility. In particular, we explore Markov chain Monte Carlo (MCMC) as well as Integrated Nested Laplace Approximation (INLA) to estimate PBBM parameters.
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    Topics in Multivariate Statistics with Dependent Data
    (2019-02) Ekvall, Karl Oskar
    This dissertation comprises four chapters. The first is an introduction to the topics of the dissertation and the remaining chapters contain the main results. Chapter 2 gives new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. The presented theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. The theory is applied to two multivariate mixed models for which it was unknown whether maximum likelihood estimators are consistent. In Chapter 3 an algorithm is proposed for maximum likelihood estimation of a covariance matrix when the corresponding correlation matrix can be written as the Kronecker product of two lower-dimensional correlation matrices. The proposed method is fully likelihood-based. Some desirable properties of separable correlation in comparison to separable covariance are also discussed. Chapter 4 is concerned with Bayesian vector autoregressions (VARs). A collapsed Gibbs sampler is proposed for Bayesian VARs with predictors and the convergence properties of the algorithm are studied. The Markov chain generated by the algorithm is proved to be geometrically ergodic, regardless of whether the number of observations in the VAR is small or large in comparison to the order and dimension of the VAR. It is also established that the geometric convergence rate is bounded away from one as the number of observations tends to infinity.
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    Understanding Multi-product Health Insurance Marketplaces: An Advancement in Aggregated Demand Estimation Using Bayesian Statistics
    (2020-11) Huang, Tsan-Yao
    Demand functions estimated by aggregated data used in economics and marketingoften employ the approach of Berry, Levinsohn and Pakes (Berry et al., 1995). To apply the method, researchers are required to collect market shares for each product of interest along with product-level attributes. Yet in many applications observed market shares are aggregated by firms or brands which sell multiple products. My thesis addresses this empirical issue by advancing existing BLP estimation procedure from Musalem et al. (2009) by using aggregated market shares at the firm level (port- folio market shares) and product-level attributes. I provide a solution to recovering the distributions of preference weights and price elasticities when researchers are limited to data containing only market shares at firm-level but consumers make choices over product-level attributes. The applications are specifically applied to the Health Insurance Marketplaces in the US.