Positive sequential dependencies occur when the response on the current trial n is positively correlated with the response on trial n-1. This was recently observed in a Judgment of Frequency (JOF) task (Malmberg and Annis, 2011). A model of positive sequential dependencies was developed in the REM framework (Shiffrin & Steyvers, 1997) by assuming that features that represent the current test item in a retrieval cue carry over from the previous retrieval cue. To assess the model, we sought a set of data that allows us to distinguish between frequency similarity and item similarity. Therefore, we chose to use a JOF task in which we manipulated the item similarity of the stimuli by presenting either landscape photos (high similarity), or photos of everyday objects such as shoes, cars, etc (low similarity). Similarity was modeled by assuming either that the item representations share a proportion of features or by assuming that the exemplars from different stimulus classes vary in the distinctiveness or diagnosticity. The model fits indicated that the best way to model similarity was to assume that items share a proportions of features.

This dissertation examines the development of coarse-grained models of atomistic systems for the purpose of predicting target quantities of interest in the presence of uncertainties. It addresses fundamental questions in computational science and engineering concerning model selection, calibration, and validation processes that are used to construct predictive reduced order models through a unified Bayesian framework. This framework, enhanced with the concepts of information theory, sensitivity analysis, and Occam's Razor, provides a systematic means of constructing coarse-grained models suitable for use in a prediction scenario. The novel application of a general framework of statistical calibration and validation to molecular systems is presented. Atomistic models, which themselves contain uncertainties, are treated as the ground truth and provide data for the Bayesian updating of model parameters. The open problem of the selection of appropriate coarse-grained models is addressed through the powerful notion of Bayesian model plausibility. A new, adaptive algorithm for model validation is presented. The Occam-Plausibility ALgorithm (OPAL), so named for its adherence to Occam's Razor and the use of Bayesian model plausibilities, identifies, among a large set of models, the simplest model that passes the Bayesian validation tests, and may therefore be used to predict chosen quantities of interest. By discarding or ignoring unnecessarily complex models, this algorithm contains the potential to reduce computational expense with the systematic process of considering subsets of models, as well as the implementation of the prediction scenario with the simplest valid model. An application to the construction of a coarse-grained system of polyethylene is given to demonstrate the implementation of molecular modeling techniques; the process of Bayesian selection, calibration, and validation of reduced-order models; and OPAL. The potential of the Bayesian framework for the process of coarse graining and of OPAL as a means of determining a computationally conservative valid model is illustrated on the polyethylene example. / text

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We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Lévy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.

There may be several mechanisms that drive observed interactions between plants and pollinators in an ecosystem, many of which may involve trait matching or trait complementarity. Hence a model of insect species activity on plant species should be represented as a mixture of these linkage rules. Unfortunately, ecologists do not always know how many, or even which, traits are the main contributors to the observed interactions. This thesis proposes the Latent Dirichlet Allocation (LDA) model from artificial intelligence for modelling the observed interactions in an ecosystem as a finite mixture of (latent) interaction groups in which plant and pollinator pairs that share common linkage rules are placed in the same interaction group. Several model selection criteria are explored for estimating how many interaction groups best describe the observed interactions. This thesis also introduces a new model selection score called ``penalized perplexity". The performance of the model selection criteria, and of LDA in general, are evaluated through a comprehensive simulation study that consider networks of various size along with varying levels of nesting and numbers of interaction groups. Results of the simulation study suggest that LDA works well on networks with mild-to-no nesting, but loses accuracy with increased nestedness. Further, the penalized perplexity tended to outperform the other model selection criteria in identifying the correct number of interaction groups used to simulate the data. Finally, LDA was demonstrated on a real network, the results of which provided insights into the functional roles of pollinator species in the study region.

This thesis is about some issues in system modeling: The first is a parsimonious representation of MISO Hammerstein system, which is by projecting the multivariate linear function into a univariate input function space. This leads to the so-called semiparamtric Hammerstein model, which overcomes the commonly known “Curse of dimensionality” for nonparametric estimation on MISO systems. The second issue discussed in this thesis is orthogonal expansion analysis on a univariate Hammerstein model and hypothesis testing for the structure of the nonlinear subsystem. The generalization of this technique can be used to test the validity for parametric assumptions of the nonlinear function in Hammersteim models. It can also be applied to approximate a general nonlinear function by a certain class of parametric function in the Hammerstein models. These techniques can also be extended to other block-oriented systems, e.g, Wiener systems, with slight modification. The third issue in this thesis is applying machine learning and system modeling techniques to transient stability studies in power engineering. The simultaneous variable section and estimation lead to a substantially reduced complexity and yet possesses a stronger prediction power than techniques known in the power engineering literature so far.

This paper presents the fully Bayesian analysis of the latent class model using a new approach towards MCMC estimation in the context of mixture models. The approach starts with estimating unidentified models for various numbers of classes. Exact Bayes' factors are computed by the bridge sampling estimator to compare different models and select the number of classes. Estimation of the unidentified model is carried out using the random permutation sampler. From the unidentified model estimates for model parameters that are not class specific are derived. Then, the exploration of the MCMC output from the unconstrained model yields suitable identifiability constraints. Finally, the constrained version of the permutation sampler is used to estimate group specific parameters. Conjoint data from the Austrian mineral water market serve to illustrate the method. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This thesis is about some issues in system modeling: The first is a parsimonious representation of MISO Hammerstein system, which is by projecting the multivariate linear function into a univariate input function space. This leads to the so-called semiparamtric Hammerstein model, which overcomes the commonly known “Curse of dimensionality” for nonparametric estimation on MISO systems. The second issue discussed in this thesis is orthogonal expansion analysis on a univariate Hammerstein model and hypothesis testing for the structure of the nonlinear subsystem. The generalization of this technique can be used to test the validity for parametric assumptions of the nonlinear function in Hammersteim models. It can also be applied to approximate a general nonlinear function by a certain class of parametric function in the Hammerstein models. These techniques can also be extended to other block-oriented systems, e.g, Wiener systems, with slight modification. The third issue in this thesis is applying machine learning and system modeling techniques to transient stability studies in power engineering. The simultaneous variable section and estimation lead to a substantially reduced complexity and yet possesses a stronger prediction power than techniques known in the power engineering literature so far.

<p>We explore the posterior inference available for Bayesian spatial point process models. In the literature, discussion of such models is usually focused on model fitting and rejecting complete spatial randomness, with model diagnostics and posterior inference often left as an afterthought. Posterior predictive point patterns are shown to be useful in performing model diagnostics and model selection, as well as providing a wide array of posterior model summaries. We prescribe Bayesian residuals and methods for cross-validation and model selection for Poisson processes, log-Gaussian Cox processes, Gibbs processes, and cluster processes. These novel approaches are demonstrated using existing datasets and simulation studies.</p> / Dissertation

In this paper we head for a fully Bayesian analysis of the latent class model with a priori unknown number of classes. Estimation is carried out by means of Markov Chain Monte Carlo (MCMC) methods. We deal explicitely with the consequences the unidentifiability of this type of model has on MCMC estimation. Joint Bayesian estimation of all latent variables, model parameters, and parameters determining the probability law of the latent process is carried out by a new MCMC method called permutation sampling. In a first run we use the random permutation sampler to sample from the unconstrained posterior. We will demonstrate that a lot of important information, such as e.g. estimates of the subject-specific regression coefficients, is available from such an unidentified model. The MCMC output of the random permutation sampler is explored in order to find suitable identifiability constraints. In a second run we use the permutation sampler to sample from the constrained posterior by imposing identifiablity constraints. The unknown number of classes is determined by formal Bayesian model comparison through exact model likelihoods. We apply a new method of computing model likelihoods for latent class models which is based on the method of bridge sampling. The approach is applied to simulated data and to data from a metric conjoint analysis in the Austrian mineral water market. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"