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Dissertations / Theses on the topic 'Bayesian models'
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Alharthi, Muteb. "Bayesian model assessment for stochastic epidemic models." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33182/.
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Acrucial practical advantage of infectious diseases modelling as a public health tool lies in its application to evaluate various disease-control policies. However, such evaluation is of limited use, unless a sufficiently accurate epidemic model is applied. If the model provides an adequate fit, it is possible to interpret parameter estimates, compare disease epidemics and implement control procedures. Methods to assess and compare stochastic epidemic models in a Bayesian framework are not well-established, particularly in epidemic settings with missing data. In this thesis, we develop novel methods for both model adequacy and model choice for stochastic epidemic models. We work with continuous time epidemic models and assume that only case detection times of infected individuals are available, corresponding to removal times. Throughout, we illustrate our methods using both simulated outbreak data and real disease data. Data augmented Markov Chain Monte Carlo (MCMC) algorithms are employed to make inference for unobserved infection times and model parameters. Under a Bayesian framework, we first conduct a systematic investigation of three different but natural methods of model adequacy for SIR (Susceptible-Infective-Removed) epidemic models. We proceed to develop a new two-stage method for assessing the adequacy of epidemic models. In this two stage method, two predictive distributions are examined, namely the predictive distribution of the final size of the epidemic and the predictive distribution of the removal times. The idea is based onlooking explicitly at the discrepancy between the observed and predicted removal times using the posterior predictive model checking approach in which the notion of Bayesian residuals and the and the posterior predictive p−value are utilized. This approach differs, most importantly, from classical likelihood-based approaches by taking into account uncertainty in both model stochasticity and model parameters. The two-stage method explores how SIR models with different infection mechanisms, infectious periods and population structures can be assessed and distinguished given only a set of removal times. In the last part of this thesis, we consider Bayesian model choice methods for epidemic models. We derive explicit forms for Bayes factors in two different epidemic settings, given complete epidemic data. Additionally, in the setting where the available data are partially observed, we extend the existing power posterior method for estimating Bayes factors to models incorporating missing data and successfully apply our missing-data extension of the power posterior method to various epidemic settings. We further consider the performance of the deviance information criterion (DIC) method to select between epidemic models.
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Volinsky, Christopher T. "Bayesian model averaging for censored survival models /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/8944.
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Kim, Yong Ku. "Bayesian multiresolution dynamic models." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180465799.
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Quintana, José Mario. "Multivariate Bayesian forecasting models." Thesis, University of Warwick, 1987. http://wrap.warwick.ac.uk/34805/.
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This thesis concerns theoretical and practical Bayesian modelling of multivariate time series. Our main goal is to intruduce useful, flexible and tractable multivariate forecasting models and provide the necessary theory for their practical implementation. After a brief review of the dynamic linear model we formulate a new matrix-v-ariate generalization in which a significant part of the variance-covariance structure is unknown. And a new general algorithm, based on the sweep operator is provided for its recursive implementation. This enables important advances to be made in long-standing problems related with the specification of the variances. We address the problem of plug-in estimation and apply our results in the context of dynamic linear models. We extend our matrix-variate model by considering the unknown part of the variance-covariance structure to be dynamic. Furthermore, we formulate the dynamic recursive model which is a general counterpart of fully recursive econometric models. The latter part of the dissertation is devoted to modelling aspects. The usefulness of the methods proposed is illustrated with several examples involving real and simulated data.
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Kaufmann, Sylvia, and Sylvia Frühwirth-Schnatter. "Bayesian Analysis of Switching ARCH Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/744/1/document.pdf.
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We consider a time series model with autoregressive conditional heteroskedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov Chain Monte Carlo simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by combining the candidate's formula with importance sampling. The usefulness of the sampler is demonstrated by applying it to the dataset previously used by Hamilton and Susmel who investigated models with switching autoregressive conditional heteroskedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model select ion, and to potential straightforward extensions of the model presented here. (author's abstract)Series: Forschungsberichte / Institut für Statistik
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Vaidyanathan, Sivaranjani. "Bayesian Models for Computer Model Calibration and Prediction." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1435527468.
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Guo, Yixuan. "Bayesian Model Selection for Poisson and Related Models." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439310177.
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Gramacy, Robert B. "Bayesian treed Gaussian process models /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2005. http://uclibs.org/PID/11984.
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Husain, Syeda Tasmine. "Bayesian analysis of longitudinal models /." Internet access available to MUN users only, 2003. http://collections.mun.ca/u?/theses,163598.
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Ozbozkurt, Pelin. "Bayesian Inference In Anova Models." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611532/index.pdf.
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Estimation of location and scale parameters from a random sample of size n is of paramount importance in Statistics. An estimator is called fully efficient if it attains the Cramer-Rao minimum variance bound besides being unbiased. The method that yields such estimators, at any rate for large n, is the method of modified maximum likelihood estimation. Apparently, such estimators cannot be made more efficient by using sample based classical methods. That makes room for Bayesian method of estimation which engages prior distributions and likelihood functions. A formal combination of the prior knowledge and the sample information is called posterior distribution. The posterior distribution is maximized with respect to the unknown parameter(s). That gives HPD (highest probability density) estimator(s). Locating the maximum of the posterior distribution is, however, enormously difficult (computationally and analytically) in most situations. To alleviate these difficulties, we use modified likelihood function in the posterior distribution instead of the likelihood function. We derived the HPD estimators of location and scale parameters of distributions in the family of Generalized Logistic. We have extended the work to experimental design, one way ANOVA. We have obtained the HPD estimators of the block effects and the scale parameter (in the distribution of errors)they have beautiful algebraic forms. We have shown that they are highly efficient. We have given real life examples to illustrate the usefulness of our results. Thus, the enormous computational and analytical difficulties with the traditional Bayesian method of estimation are circumvented at any rate in the context of experimental design.
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Osuna, Echavarría Leyre Estíbaliz. "Semiparametric Bayesian Count Data Models." Diss., lmu, 2004. http://nbn-resolving.de/urn:nbn:de:bvb:19-25573.
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Mohamed, Shakir. "Generalised Bayesian matrix factorisation models." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/237246.
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Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.
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Shon, Aaron P. "Bayesian cognitive models for imitation /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/7013.
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Xiang, Fei. "Bayesian consistency for regression models." Thesis, University of Kent, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587522.
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Bayesian consistency is an important issue in the context of non- parametric problems. The posterior consistency is a validation of a Bayesian approach and guarantees the posterior mass accumulates around the true density, which" is unknown in most circumstances, as the number of observations goes to infinity. This thesis mainly considers the consistency for nonparametric regression models over both random and non random covariates. The techniques to achieve consistency under random covariates are similar to that derived in Walker (2003, 2004) which is designed for the consistency of independent and identically distributed variables. We contribute a new idea to deal with the supremum metric over covariates when the regression model is with non random covariates. That is, if a regression density is away from the true density in the Hellinger sense, then there is a covariate, whose value is picked from a specific design, such that the density indexed by this value is also away from the true density. As a result, the posterior concentrates in the supremum Hellinger neighbourhood of the real model under conditions on the prior such as the Kullback-Leibler property and the summability of the square rooted prior mass on Hellinger covering balls. Furthermore, the predictive is also shown to be consistent and we illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. We also investigate conditions under which a piecewise density model is consistent.
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Young, Simon Christopher. "Bayesian models and repeated games." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/55723/.
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A game is a theoretical model of a social situation where the people involved have individually only partial control over the outcomes. Game theory is then the method used to analyse these models. As a player's outcome from a game depends upon the actions of his opponents, there is some uncertainty in these models. This uncertainty is described probabilistically, in terms of a player's subjective beliefs about the future play of his opponent. Any additional information that is acquired by the player can be incorporated into the analysis and these subjective beliefs are revised. Hence, the approach taken is `Bayesian'. Each outcome from the game has a value to each of the players, and the measure of merit from an outcome is referred to as a player's utility. This concept of utility is combined with a player's subjective probabilities to form an expected utility, and it is assumed that each player is trying to maximise his expected utility. Bayesian models for games are constructed in order to determine strategies for the players that are expected utility maximising. These models are guided by the belief that the other players are also trying to maximise their own expected utilities. It is shown that a player's beliefs about the other players form an infinite regress. This regress can be truncated to a finite number of levels of beliefs, under some assumptions about the utility functions and beliefs of the other players. It is shown how the dichotomy between prescribed good play and observed good play exists because of the lack of assumptions about the rationality of the opponents (i. e. the ability of the opponents to be utility maximising). It is shown how a model for a game can be built which is both faithful to the observed common sense behaviour of the subjects of an experimental game, and is also rational (in a Bayesian sense). It is illustrated how the mathematical form of an optimal solution to a game can be found, and then used with an inductive algorithm to determine an explicit optimal strategy. It is argued that the derived form of the optimal solution can be used to gain more insight into the game, and to determine whether an assumed model is realistic. It is also shown that under weak regularity conditions, and assuming that an opponent is playing a strategy from a given class of strategies, S, it is not optimal for the player to adopt any strategy from S, thus compromising the chosen model.
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Wiseman, Scott. "Bayesian learning in graphical models." Thesis, University of Kent, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311261.
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Kadir, Dler. "Bayesian inference of autoregressive models." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/20610/.
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The principles, models and steps of Bayesian time series analysis and forecasting have been developed extensively during the past forty years. In order to estimate parameters of an autoregressive (AR) model we develop Markov chain Monte Carlo (MCMC) schemes for inference of AR model. It is our interest to propose a new prior distribution placed directly on the AR parameters of the model. Thus, we revisit the stationarity conditions to determine a flexible prior for AR model parameters.
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Gulam, Razul Sirajudeen. "Bayesian methods for unified models." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619713.
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Van, Gael Jurgen. "Bayesian nonparametric hidden Markov models." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610196.
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Streftaris, George. "Bayesian methods for Poisson models." Thesis, University of Edinburgh, 2000. http://hdl.handle.net/1842/14505.
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To account for overdispersion in count data, that is variation in excess of that justified from the assumed model, one may consider an additional source of variation, by assuming that each observation, Yi, i = 1, ..., m, arises from a conditionally independent Poisson distribution, given its respective mean qi, i = 1, ..., m. We review various frequentist methods for the estimation of the Poisson parameters qi, i = 1, ..., m, which are based on the inadmissibility of the usual unbiased maximum likelihood estimator, in terms of the associated risk in dimensions greater than two. The so called shrinkage estimators adjust the maximum likelihood estimates towards a fixed or data-determined point, abandoning unbiasedness in favour of lower risk. Inferences for the parameters of interest can also be drawn employing Bayesian methods. Conjugate models are often adopted to facilitate the computational procedure. In this thesis we assume a nonconjugate log-normal prior distribution, which allows for more dispersion in the Poisson means and can also accommodate a correlation structure. We derive two empirical Bayes estimators, which approximate the posterior mean. The first is based on a linear shrinkage rule, while the second employs a non-iterative importance sampling technique. The frequency properties of the two estimators in terms of average risk are assessed and compared to other estimating approaches proposed in the literature. A full hierarchical Bayes analysis is also considered, assuming both informative and non-informative prior distributions at the lower stage of the hierarchy. Some analytical posterior inferences, based on simple approximations are obtained. We then employ stochastic simulation techniques, suggesting two Markov chain Monte Carlo methods which involve the Gibbs sampler and a hybrid strategy. They rely on a log-normal/gamma mixture approximation to the full conditional posterior distribution of the parameters qi, i = 1, ,..., m. The shrinkage behaviour of the hierarchical Bayes estimator is explored, and its average risk is examined through frequency simulations. Examples and applications of the considered methods are given throughout the thesis.
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Dallaire, Patrick. "Bayesian nonparametric latent variable models." Doctoral thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/26848.
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L’un des problèmes importants en apprentissage automatique est de déterminer la complexité du modèle à apprendre. Une trop grande complexité mène au surapprentissage, ce qui correspond à trouver des structures qui n’existent pas réellement dans les données, tandis qu’une trop faible complexité mène au sous-apprentissage, c’est-à-dire que l’expressivité du modèle est insuffisante pour capturer l’ensemble des structures présentes dans les données. Pour certains modèles probabilistes, la complexité du modèle se traduit par l’introduction d’une ou plusieurs variables cachées dont le rôle est d’expliquer le processus génératif des données. Il existe diverses approches permettant d’identifier le nombre approprié de variables cachées d’un modèle. Cette thèse s’intéresse aux méthodes Bayésiennes nonparamétriques permettant de déterminer le nombre de variables cachées à utiliser ainsi que leur dimensionnalité. La popularisation des statistiques Bayésiennes nonparamétriques au sein de la communauté de l’apprentissage automatique est assez récente. Leur principal attrait vient du fait qu’elles offrent des modèles hautement flexibles et dont la complexité s’ajuste proportionnellement à la quantité de données disponibles. Au cours des dernières années, la recherche sur les méthodes d’apprentissage Bayésiennes nonparamétriques a porté sur trois aspects principaux : la construction de nouveaux modèles, le développement d’algorithmes d’inférence et les applications. Cette thèse présente nos contributions à ces trois sujets de recherches dans le contexte d’apprentissage de modèles à variables cachées. Dans un premier temps, nous introduisons le Pitman-Yor process mixture of Gaussians, un modèle permettant l’apprentissage de mélanges infinis de Gaussiennes. Nous présentons aussi un algorithme d’inférence permettant de découvrir les composantes cachées du modèle que nous évaluons sur deux applications concrètes de robotique. Nos résultats démontrent que l’approche proposée surpasse en performance et en flexibilité les approches classiques d’apprentissage. Dans un deuxième temps, nous proposons l’extended cascading Indian buffet process, un modèle servant de distribution de probabilité a priori sur l’espace des graphes dirigés acycliques. Dans le contexte de réseaux Bayésien, ce prior permet d’identifier à la fois la présence de variables cachées et la structure du réseau parmi celles-ci. Un algorithme d’inférence Monte Carlo par chaîne de Markov est utilisé pour l’évaluation sur des problèmes d’identification de structures et d’estimation de densités. Dans un dernier temps, nous proposons le Indian chefs process, un modèle plus général que l’extended cascading Indian buffet process servant à l’apprentissage de graphes et d’ordres. L’avantage du nouveau modèle est qu’il admet les connections entres les variables observables et qu’il prend en compte l’ordre des variables. Nous présentons un algorithme d’inférence Monte Carlo par chaîne de Markov avec saut réversible permettant l’apprentissage conjoint de graphes et d’ordres. L’évaluation est faite sur des problèmes d’estimations de densité et de test d’indépendance. Ce modèle est le premier modèle Bayésien nonparamétrique permettant d’apprendre des réseaux Bayésiens disposant d’une structure complètement arbitraire.One of the important problems in machine learning is determining the complexity of the model to learn. Too much complexity leads to overfitting, which finds structures that do not actually exist in the data, while too low complexity leads to underfitting, which means that the expressiveness of the model is insufficient to capture all the structures present in the data. For some probabilistic models, the complexity depends on the introduction of one or more latent variables whose role is to explain the generative process of the data. There are various approaches to identify the appropriate number of latent variables of a model. This thesis covers various Bayesian nonparametric methods capable of determining the number of latent variables to be used and their dimensionality. The popularization of Bayesian nonparametric statistics in the machine learning community is fairly recent. Their main attraction is the fact that they offer highly flexible models and their complexity scales appropriately with the amount of available data. In recent years, research on Bayesian nonparametric learning methods have focused on three main aspects: the construction of new models, the development of inference algorithms and new applications. This thesis presents our contributions to these three topics of research in the context of learning latent variables models. Firstly, we introduce the Pitman-Yor process mixture of Gaussians, a model for learning infinite mixtures of Gaussians. We also present an inference algorithm to discover the latent components of the model and we evaluate it on two practical robotics applications. Our results demonstrate that the proposed approach outperforms, both in performance and flexibility, the traditional learning approaches. Secondly, we propose the extended cascading Indian buffet process, a Bayesian nonparametric probability distribution on the space of directed acyclic graphs. In the context of Bayesian networks, this prior is used to identify the presence of latent variables and the network structure among them. A Markov Chain Monte Carlo inference algorithm is presented and evaluated on structure identification problems and as well as density estimation problems. Lastly, we propose the Indian chefs process, a model more general than the extended cascading Indian buffet process for learning graphs and orders. The advantage of the new model is that it accepts connections among observable variables and it takes into account the order of the variables. We also present a reversible jump Markov Chain Monte Carlo inference algorithm which jointly learns graphs and orders. Experiments are conducted on density estimation problems and testing independence hypotheses. This model is the first Bayesian nonparametric model capable of learning Bayesian learning networks with completely arbitrary graph structures.
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Bush, Christopher A. "Semi-parametric Bayesian linear models /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487856076417948.
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Kunkel, Deborah Elizabeth. "Anchored Bayesian Gaussian Mixture Models." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524134234501475.
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Bouda, Milan. "Bayesian Estimation of DSGE Models." Doctoral thesis, Vysoká škola ekonomická v Praze, 2012. http://www.nusl.cz/ntk/nusl-200007.
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Thesis is dedicated to Bayesian Estimation of DSGE Models. Firstly, the history of DSGE modeling is outlined as well as development of this macroeconometric field in the Czech Republic and in the rest of the world. Secondly, the comprehensive DSGE framework is described in detail. It means that everyone is able to specify or estimate arbitrary DSGE model according to this framework. Thesis contains two empirical studies. The first study describes derivation of the New Keynesian DSGE Model and its estimation using Bayesian techniques. This model is estimated with three different Taylor rules and the best performing Taylor rule is identified using the technique called Bayesian comparison. The second study deals with development of the Small Open Economy Model with housing sector. This model is based on previous study which specifies this model as a closed economy model. I extended this model by open economy features and government sector. Czech Republic is generally considered as a small open economy and these extensions make this model more applicable to this economy. Model contains two types of households. The first type of consumers is able to access the capital markets and they can smooth consumption across time by buying or selling financial assets. These households follow the permanent income hypothesis (PIH). The other type of household uses rule of thumb (ROT) consumption, spending all their income to consumption. Other agents in this economy are specified in standard way. Outcomes of this study are mainly focused on behavior of house prices. More precisely, it means that all main outputs as Bayesian impulse response functions, Bayesian prediction and shock decomposition are focused mainly on this variable. At the end of this study one macro-prudential experiment is performed. This experiment comes up with answer on the following question: is the higher/lower Loan to Value (LTV) ratio better for the Czech Republic? This experiment is very conclusive and shows that level of LTV does not affect GDP. On the other hand, house prices are very sensitive to this LTV ratio. The recommendation for the Czech National Bank could be summarized as follows. In order to keep house prices less volatile implement rather lower LTV ratio than higher.
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KIM, DONG-HYUK. "Bayesian Econometrics for Auction Models." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/193663.
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This dissertation develops Bayesian methods to analyze data from auctions and produce policy recommendations for auction design. The essay, "Auction Design Using Bayesian Methods," proposes a decision theoretic method to choose a reserve price in an auction using data from past auctions. Our method formally incorporates parameter uncertainty and the payoff structure into the decision procedure. When the sample size is modest, it produces higher expected revenue than the plug-in methods. Monte Carlo evidence for this is provided. The second essay, "Flexible Bayesian Analysis of First Price Auctions Using Simulated Likelihood," develops an empirical framework that fully exploits all the shape restrictions arising from economic theory: bidding monotonicity and density affiliation. We directly model the valuation density so that bidding monotonicity is automatically satisfied, and restrict the parameter space to rule out all the nonaffiliated densities. Our method uses a simulated likelihood to allow for a very exible specification, but the posterior analysis is exact for the chosen likelihood. Our method controls the smoothness and tail behavior of the valuation density and provides a decision theoretic framework for auction design. We reanalyze a dataset of auctions for drilling rights in the Outer Continental Shelf that has been widely used in past studies. Our approach gives significantly different policy prescriptions on the choice of reserve price than previous methods, suggesting the importance of the theoretical shape restrictions. Lastly, in the essay, "Simple Approximation Methods for Bayesian Auction Design," we propose simple approximation methods for Bayesian decision making in auction design problems. Asymptotic posterior distributions replace the true posteriors in the Bayesian decision framework, which are typically a Gaussian model (second price auction) or a shifted exponential model (first price auction). Our method first approximates the posterior payoff using the limiting models and then maximizes the approximate posterior payoff. Both the approximate and exact Bayes rules converge to the true revenue maximizing reserve price under certain conditions. Monte Carlo studies show that my method closely approximates the exact procedure even for fairly small samples.
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Rolfe, Margaret Irene. "Bayesian models for longitudinal data." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/34435/1/Margaret_Rolfe_Thesis.pdf.
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Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.
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Baker, Jannah F. "Bayesian spatiotemporal modelling of chronic disease outcomes." Thesis, Queensland University of Technology, 2017. https://eprints.qut.edu.au/104455/1/Jannah_Baker_Thesis.pdf.
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This thesis contributes to Bayesian spatial and spatiotemporal methodology by investigating techniques for spatial imputation and joint disease modelling, and identifies high-risk individual profiles and geographic areas for type II diabetes mellitus (DMII) outcomes. DMII and related chronic conditions including hypertension, coronary arterial disease, congestive heart failure and chronic obstructive pulmonary disease are examples of ambulatory care sensitive conditions for which hospitalisation for complications is potentially avoidable with quality primary care. Bayesian spatial and spatiotemporal studies are useful for identifying small areas that would benefit from additional services to detect and manage these conditions early, thus avoiding costly sequelae.
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Overstall, Antony Marshall. "Default Bayesian model determination for generalised linear mixed models." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170229/.
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In this thesis, an automatic, default, fully Bayesian model determination strategy for GLMMs is considered. This strategy must address the two key issues of default prior specification and computation. Default prior distributions for the model parameters, that are based on a unit information concept, are proposed. A two-phase computational strategy, that uses a reversible jump algorithm and implementation of bridge sampling, is also proposed. This strategy is applied to four examples throughout this thesis.
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JIANG, DONGMING. "OBJECTIVE BAYESIAN TESTING AND MODEL SELECTION FOR POISSON MODELS." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1185821399.
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Foreman, Lindsay Anne. "Bayesian computation for hidden Markov models." Thesis, Imperial College London, 1994. http://hdl.handle.net/10044/1/11490.
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Campolieti, Michele. "Bayesian estimation of discrete duration models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0001/NQ27884.pdf.
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Bennett, James Elston. "Bayesian analysis of population pharmacokinetic models." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363017.
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Östling, Robert. "Bayesian Models for Multilingual Word Alignment." Doctoral thesis, Stockholms universitet, Institutionen för lingvistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-115541.
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In this thesis I explore Bayesian models for word alignment, how they can be improved through joint annotation transfer, and how they can be extended to parallel texts in more than two languages. In addition to these general methodological developments, I apply the algorithms to problems from sign language research and linguistic typology. In the first part of the thesis, I show how Bayesian alignment models estimated with Gibbs sampling are more accurate than previous methods for a range of different languages, particularly for languages with few digital resources available—which is unfortunately the state of the vast majority of languages today. Furthermore, I explore how different variations to the models and learning algorithms affect alignment accuracy. Then, I show how part-of-speech annotation transfer can be performed jointly with word alignment to improve word alignment accuracy. I apply these models to help annotate the Swedish Sign Language Corpus (SSLC) with part-of-speech tags, and to investigate patterns of polysemy across the languages of the world. Finally, I present a model for multilingual word alignment which learns an intermediate representation of the text. This model is then used with a massively parallel corpus containing translations of the New Testament, to explore word order features in 1001 languages.
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Wakefield, Jon. "The Bayesian analysis of pharmacokinetic models." Thesis, University of Nottingham, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334806.
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Giles, Philip R. "Bayesian inference for stochastic epidemic models." Thesis, University of Newcastle Upon Tyne, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420008.
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Grigsby, Mark Edwin. "Bayesian inference for log-linear models." Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393934.
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HUAMANI, LUIS ALBERTO NAVARRO. "BAYESIAN INFERENCE ON MULTIVARIATE ARCH MODELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2001. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=1868@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOO objetivo deste trabalho é desenvolver uma estratégia Metropolis-Hastings para inferência Bayesiana, usando a estrutura ARCH multivatriada com representação BEKK.Em problemas complexos, como a generalização ARCH/GARCH univariadas para estruturas multivariadas, o processo de inferência é dificultado por causa do número de parâmetros envolvidos e das restrições a que eles estão sujeitos. Neste trabalho desenvolvemos uma estratégia Metropolis- Hastings para inferência Bayesiana, usando uma estrutura ARCH multivariada com representação BEKK.
The objective of this work is to develop Metropolis-Hasting for strategy Bayesian Inference, based on a Multivariate ARCH model with BEKK representation. In complex problems, such as the multivariate generalization of ARCH/GARCH structures, the inference process in complicated, due to the large number of parameters involved and to the restrictions they must satisfy. We propose Metropolis- Hastings structure to provide inference, in a Bayesian framework, for a multivariate ARCH model with BEKK representation.
EL objetivo de este trabajo es desarrollar una estrategia Metropolis-Hastings para inferencia Bayesiana, usando La extructura ARCH multivatriada con representación BEKK.En problemas complejos, como la generalización ARCH/GARCH univariadas para extructuras multivariadas, el proceso de inferencia se hace dificil por causa del número de parámetros involucrados y de las restricciones a que ellos están sujetos. En este trabajo desarrollamos una estrategia Metropolis- Hastings para inferencia Bayesiana, usando una extructura ARCH multivariada con representación BEKK.
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Mestre, María del Rosario. "Bayesian predictive models of user intention." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708641.
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Al-Kaabawi, Zainab A. A. "Bayesian hierarchical models for linear networks." Thesis, University of Plymouth, 2018. http://hdl.handle.net/10026.1/12829.
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A motorway network is handled as a linear network. The purpose of this study is to highlight dangerous motorways via estimating the intensity of accidents and study its pattern across the UK motorway network. Two mechanisms have been adopted to achieve this aim. The first, the motorway-specific intensity is estimated by modelling the point pattern of the accident data using a homogeneous Poisson process. The homogeneous Poisson process is used to model all intensities but heterogeneity across motorways is incorporated using two-level hierarchical models. The data structure is multilevel since each motorway consists of junctions that are joined by grouped segments. In the second mechanism, the segment-specific intensity is estimated by modelling the point pattern of the accident data. The homogeneous Poisson process is used to model accident data within segments but heterogeneity across segments is incorporated using three-level hierarchical models. A Bayesian method via Markov Chain Monte Carlo simulation algorithms is used in order to estimate the unknown parameters in the models and a sensitivity analysis to the prior choice is assessed. The performance of the proposed models is checked through a simulation study and an application to traffic accidents in 2016 on the UK motorway network. The performance of the three-level frequentist model was poor. The deviance information criterion (DIC) and the widely applicable information criterion (WAIC) are employed to choose between the two-level Bayesian hierarchical model and the three-level Bayesian hierarchical model, where the results showed that the best fitting model was the three-level Bayesian hierarchical model.
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Umaras, Jonas Radvilas. "Bayesian Parametrisation ofIn Silico Tumour Models." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-382536.
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Technological progress in recent decades has allowed researchers to utilise accurate but computationally demanding models. One example of this development is the adoption of the multi-scale modelling technique for simulating various tissues. These models can then be utilised to test the efficacy of new drugs, e.g., for cancer treatment. Though multi-scale models can produce accurate representations of complex systems, their parameters often cannot be measured directly and have to be inferred using experimental data, which is a challenge yet to be solved. The goal of this work is to investigate the possibility of parametrising a specific high-performance tumour growth model using a likelihood-free method called Approximate Bayesian Computation (ABC). The first objective is to understand the effect that parameters of the model have on its behaviour. Then, by using the insights gained from the first step, define a set of summary statistics and a distance metric capable of capturing the impact of parameter variations on the growth of simulated tumours. Finally, assess the landscapes of the parameter space by utilising the statistics and the metric. The obtained results indicate that some of the parameters can be inferred by applying an ABC-style method, which motivates to further investigate the prospect of applying ABC for parametrising the model in question. However, the computational costs of such techniques are expected to be high, putting its execution time in the order of weeks, thus requiring future performance improvements of the model and highly efficient implementations of the parametrisation procedure.
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Lu, Peter Guang Yi. "Bayesian inference of stochastic dynamical models." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/79265.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 165-175).
A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.
by Peter Lu.
S.M.
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Vasconcelos, Nuno Miguel Borges de Pinho Cruz de. "Bayesian models for visual information retrieval." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/62947.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2000.Includes bibliographical references (leaves 192-208).
This thesis presents a unified solution to visual recognition and learning in the context of visual information retrieval. Realizing that the design of an effective recognition architecture requires careful consideration of the interplay between feature selection, feature representation, and similarity function, we start by searching for a performance criteria that can simultaneously guide the design of all three components. A natural solution is to formulate visual recognition as a decision theoretical problem, where the goal is to minimize the probability of retrieval error. This leads to a Bayesian architecture that is shown to generalize a significant number of previous recognition approaches, solving some of the most challenging problems faced by these: joint modeling of color and texture, objective guidelines for controlling the trade-off between feature transformation and feature representation, and unified support for local and global queries without requiring image segmentation. The new architecture is shown to perform well on color, texture, and generic image databases, providing a good trade-off between retrieval accuracy, invariance, perceptual relevance of similarity judgments, and complexity. Because all that is needed to perform optimal Bayesian decisions is the ability to evaluate beliefs on the different hypothesis under consideration, a Bayesian architecture is not restricted to visual recognition. On the contrary, it establishes a universal recognition language (the language of probabilities) that provides a computational basis for the integration of information from multiple content sources and modalities. In result, it becomes possible to build retrieval systems that can simultaneously account for text, audio, video, or any other content modalities. Since the ability to learn follows from the ability to integrate information over time, this language is also conducive to the design of learning algorithms. We show that learning is, indeed, an important asset for visual information retrieval by designing both short and long-term learning mechanisms. Over short time scales (within a retrieval session), learning is shown to assure faster convergence to the desired target images. Over long time scales (between retrieval sessions), it allows the retrieval system to tailor itself to the preferences of particular users. In both cases, all the necessary computations are carried out through Bayesian belief propagation algorithms that, although optimal in a decision-theoretic sense, are extremely simple, intuitive, and easy to implement.
by Nuno Miguel Borges de Pinho Cruz de Vasconcelos.
Ph.D.
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Evans, Owain Rhys. "Bayesian computational models for inferring preferences." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101522.
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Thesis: Ph. D. in Linguistics, Massachusetts Institute of Technology, Department of Linguistics and Philosophy, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 130-131).
This thesis is about learning the preferences of humans from observations of their choices. It builds on work in economics and decision theory (e.g. utility theory, revealed preference, utilities over bundles), Machine Learning (inverse reinforcement learning), and cognitive science (theory of mind and inverse planning). Chapter 1 lays the conceptual groundwork for the thesis and introduces key challenges for learning preferences that motivate chapters 2 and 3. I adopt a technical definition of 'preference' that is appropriate for inferring preferences from choices. I consider what class of objects preferences should be defined over. I discuss the distinction between actual preferences and informed preferences and the distinction between basic/intrinsic and derived/instrumental preferences. Chapter 2 focuses on the challenge of human 'suboptimality'. A person's choices are a function of their beliefs and plans, as well as their preferences. If they have inaccurate beliefs or make inefficient plans, then it will generally be more difficult to infer their preferences from choices. It is also more difficult if some of their beliefs might be inaccurate and some of their plans might be inefficient. I develop models for learning the preferences of agents subject to false beliefs and to time inconsistency. I use probabilistic programming to provide a concise, extendable implementation of preference inference for suboptimal agents. Agents performing suboptimal sequential planning are represented as functional programs. Chapter 3 considers how preferences vary under different combinations (or &compositions') of outcomes. I use simple mathematical functional forms to model composition. These forms are standard in microeconomics, where the outcomes in question are quantities of goods or services. These goods may provide the same purpose (and be substitutes for one another). Alternatively, they may combine together to perform some useful function (as with complements). I implement Bayesian inference for learning the preferences of agents making choices between different combinations of goods. I compare this procedure to empirical data for two different applications.
by Owain Rhys Evans.
Ph. D. in Linguistics
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Williamson, Sinead Anne. "Nonparametric Bayesian models for dependent data." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610373.
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Paquet, Ulrich. "Bayesian inference for latent variable models." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613111.
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Bracegirdle, C. I. "Inference in Bayesian time-series models." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1383529/.
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Time series-data accompanied with a sequential ordering-occur and evolve all around us. Analysing time series is the problem of trying to discern and describe a pattern in the sequential data that develops in a logical way as the series continues, and the study of sequential data has occurred for a long period across a vast array of fields, including signal processing, bioinformatics, and finance-to name but a few. Classical approaches are based on estimating the parameters of temporal evolution of the process according to an assumed model. In econometrics literature, the field is focussed on parameter estimation of linear (regression) models with a number of extensions. In this thesis, I take a Bayesian probabilistic modelling approach in discrete time, and focus on novel inference schemes. Fundamentally, Bayesian analysis replaces parameter estimates by quantifying uncertainty in the value, and probabilistic inference is used to update the uncertainty based on what is observed in practice. I make three central contributions. First, I discuss a class of latent Markov model which allows a Bayesian approach to internal process resets, and show how inference in such a model can be performed efficiently, before extending the model to a tractable class of switching time series models. Second, I show how inference in linear-Gaussian latent models can be extended to allow a Bayesian approach to variance, and develop a corresponding variance-resetting model, the heteroskedastic linear-dynamical system. Third, I turn my attention to cointegration-a headline topic in finance-and describe a novel estimation scheme implied by Bayesian analysis, which I show to be empirically superior to the classical approach. I offer example applications throughout and conclude with a discussion.
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Frank, Stella Christina. "Bayesian models of syntactic category acquisition." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/6693.
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Discovering a word’s part of speech is an essential step in acquiring the grammar of a language. In this thesis we examine a variety of computational Bayesian models that use linguistic input available to children, in the form of transcribed child directed speech, to learn part of speech categories. Part of speech categories are characterised by contextual (distributional/syntactic) and word-internal (morphological) similarity. In this thesis, we assume language learners will be aware of these types of cues, and investigate exactly how they can make use of them. Firstly, we enrich the context of a standard model (the Bayesian Hidden Markov Model) by adding sentence type to the wider distributional context.We show that children are exposed to a much more diverse set of sentence types than evident in standard corpora used for NLP tasks, and previous work suggests that they are aware of the differences between sentence type as signalled by prosody and pragmatics. Sentence type affects local context distributions, and as such can be informative when relying on local context for categorisation. Adding sentence types to the model improves performance, depending on how it is integrated into our models. We discuss how to incorporate novel features into the model structure we use in a flexible manner, and present a second model type that learns to use sentence type as a distinguishing cue only when it is informative. Secondly, we add a model of morphological segmentation to the part of speech categorisation model, in order to model joint learning of syntactic categories and morphology. These two tasks are closely linked: categorising words into syntactic categories is aided by morphological information, and finding morphological patterns in words is aided by knowing the syntactic categories of those words. In our joint model, we find improved performance vis-a-vis single-task baselines, but the nature of the improvement depends on the morphological typology of the language being modelled. This is the first token-based joint model of unsupervised morphology and part of speech category learning of which we are aware.
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O'Sullivan, Aidan Michael. "Bayesian latent variable models with applications." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/19191.
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The massive increases in computational power that have occurred over the last two decades have contributed to the increasing prevalence of Bayesian reasoning in statistics. The often intractable integrals required as part of the Bayesian approach to inference can be approximated or estimated using intensive sampling or optimisation routines. This has extended the realm of applications beyond simple models for which fully analytic solutions are possible. Latent variable models are ideally suited to this approach as it provides a principled method for resolving one of the more difficult issues associated with this class of models, the question of the appropriate number of latent variables. This thesis explores the use of latent variable models in a number of different settings employing Bayesian methods for inference. The first strand of this research focusses on the use of a latent variable model to perform simultaneous clustering and latent structure analysis of multivariate data. In this setting the latent variables are of key interest providing information on the number of sub-populations within a heterogeneous data set and also the differences in latent structure that define them. In the second strand latent variable models are used as a tool to study relational or network data. The analysis of this type of data, which describes the interconnections between different entities or nodes, is complicated due to the dependencies between nodes induced by these connections. The conditional independence assumptions of the latent variable framework provide a means of taking these dependencies into account, the nodes are independent conditioned on an associated latent variable. This allows us to perform model based clustering of a network making inference on the number of clusters. Finally the latent variable representation of the network, which captures the structure of the network in a different form, can be studied as part of a latent variable framework for detecting differences between networks. Approximation schemes are required as part of the Bayesian approach to model estimation. The two methods that are considered in this thesis are stochastic Markov chain Monte Carlo methods and deterministic variational approximations. Where possible these are extended to incorporate model selection over the number of latent variables and a comparison, the first of its kind in this setting, of their relative performance in unsupervised model selection for a range of different settings is presented. The findings of the study help to ascertain in which settings one method may be preferred to the other.
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Rios, Felix Leopoldo. "Bayesian structure learning in graphical models." Licentiate thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-179852.
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This thesis consists of two papers studying structure learning in probabilistic graphical models for both undirected graphs anddirected acyclic graphs (DAGs). Paper A, presents a novel family of graph theoretical algorithms, called the junction tree expanders, that incrementally construct junction trees for decomposable graphs. Due to its Markovian property, the junction tree expanders are shown to be suitable for proposal kernels in a sequential Monte Carlo (SMC) sampling scheme for approximating a graph posterior distribution. A simulation study is performed for the case of Gaussian decomposable graphical models showing efficiency of the suggested unified approach for both structural and parametric Bayesian inference. Paper B, develops a novel prior distribution over DAGs with the ability to express prior knowledge in terms of graph layerings. In conjunction with the prior, a search and score algorithm based on the layering property of DAGs, is developed for performing structure learning in Bayesian networks. A simulation study shows that the search and score algorithm along with the prior has superior performance for learning graph with a clearly layered structure compared with other priors.QC 20160111
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Chanialidis, Charalampos. "Bayesian mixture models for count data." Thesis, University of Glasgow, 2015. http://theses.gla.ac.uk/6371/.
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Regression models for count data are usually based on the Poisson distribution. This thesis is concerned with Bayesian inference in more flexible models for count data. Two classes of models and algorithms are presented and studied in this thesis. The first employs a generalisation of the Poisson distribution called the COM-Poisson distribution, which can represent both overdispersed data and underdispersed data. We also propose a density regression technique for count data, which, albeit centered around the Poisson distribution, can represent arbitrary discrete distributions. The key contribution of this thesis are MCMC-based methods for posterior inference in these models. One key challenge in COM-Poisson-based models is the fact that the normalisation constant of the COM-Poisson distribution is not known in closed form. We propose two exact MCMC algorithms which address this problem. One is based on the idea of retrospective sampling; we sample the uniform random variable used to decide on the acceptance (or rejection) of the proposed new state of the unknown parameter first and then only evaluate bounds for the acceptance probability, in the hope that we will not need to know the acceptance probability exactly in order to come to a decision on whether to accept or reject the newly proposed value. This strategy is based on an efficient scheme for computing lower and upper bounds for the normalisation constant. This procedure can be applied to a number of discrete distributions, including the COM-Poisson distribution. The other MCMC algorithm proposed is based on an algorithm known as the exchange algorithm. The latter requires sampling from the COM-Poisson distribution and we will describe how this can be done efficiently using rejection sampling. We will also present simulation studies which show the advantages of using the COM-Poisson regression model compared to the alternative models commonly used in literature (Poisson and negative binomial). Three real world applications are presented: the number of emergency hospital admissions in Scotland in 2010, the number of papers published by Ph.D. students and fertility data from the second German Socio-Economic Panel. COM-Poisson distributions are also the cornerstone of the proposed density regression technique based on Dirichlet process mixture models. Density regression can be thought of as a competitor to quantile regression. Quantile regression estimates the quantiles of the conditional distribution of the response variable given the covariates. This is especially useful when the dispersion changes across the covariates. Instead of estimating the conditional mean , quantile regression estimates the conditional quantile function across different quantiles. As a result, quantile regression models both location and shape shifts of the conditional distribution. This allows for a better understanding of how the covariates affect the conditional distribution of the response variable. Almost all quantile regression techniques deal with a continuous response. Quantile regression models for count data have so far received little attention. A technique that has been suggested is adding uniform random noise ('jittering'), thus overcoming the problem that, for a discrete distribution, the conditional quantile function is not a continuous function of the parameters of interest. Even though this enables us to estimate the conditional quantiles of the response variable, it has disadvantages. For small values of the response variable Y, the added noise can have a large influence on the estimated quantiles. In addition, the problem of 'crossing quantiles' still exists for the jittering method. We eliminate all the aforementioned problems by estimating the density of the data, rather than the quantiles. Simulation studies show that the proposed approach performs better than the already established jittering method. To illustrate the new method we analyse fertility data from the second German Socio-Economic Panel.