Browsing by Author "Page, Garritt L."

Now showing 1 - 19 of 19
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    A Bayesian Approach to Establishing a Reference Particle Size Distribution in the Presence of Outliers
    (2012) Page, Garritt L.; Vardeman, Stephen B.
    The presence of observations or measurements that are unlike the majority is fairly common in studies conducted to establish particle size (or weight fraction) distributions. Therefore, there is a need to develop methods that are capable of producing estimates of particle size distributions that are not overly sensitive to the presence of a few observations that might be considered outliers. This article proposes a type of contamination mixture model that probabilistically allocates each observation to either a majority component or a contamination component. Observations that are allocated to a contamination component are down-weighted when estimating the particle size distribution (while the uncertainty of contamination classification is automatically accounted for in estimation). Computational methods are developed and the utility of the proposed methodology is demonstrated via a simulation study. The method is then applied to data produced from an inter-laboratory study conducted to establish a particle size distribution in cement.
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    A Projection Approach to Local Regression with Variable-Dimension Covariates
    (2024) Heiner, Matthew J.; Page, Garritt L.; Quintana, Fernando Andres
    Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that uses only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject's incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model's effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data. Supplemental materials for this article are available online.
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    Bayes Statistical Analyses for Particle Sieving Studies
    (2013) Leyva, Norma; Page, Garritt L.; Vardeman, Stephen B.; Wendelberger, Joanne R.
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    Calibrating covariate informed product partition models
    (2018) Page, Garritt L.; Quintana Quintana, Fernando
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    Classification via Bayesian Nonparametric Learning of Affine Subspaces
    (2013) Page, Garritt L.; Bhattacharya, Abhishek; Dunson, David
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    Clustering and Prediction With Variable Dimension Covariates
    (2022) Page, Garritt L.; Quintana, Fernando A.; Muller, Peter
    In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a method based on covariate dependent random partition models that seamlessly handles missing covariates while completely avoiding any type of imputation. The method we develop allows in-sample as well as out-of-sample predictions, even if the missing pattern in the new subjects'incomplete covariate vectorwas not seen in the training data. Any data type, including categorical or continuous covariates are permitted. In simulation studies, the proposed method compares favorably. We illustrate themethod in two application examples. Supplementary materials for this article are available here.
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    Density regression using repulsive distributions
    (2018) Quinlan, Jose J.; Page, Garritt L.; Quintana Quintana, Fernando
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    Dependent Modeling of Temporal Sequences of Random Partitions
    (2022) Page, Garritt L.; Quintana, Fernando A.; Dahl, David B.
    We consider modeling a dependent sequence of random partitions. It is well known in Bayesian non-parametrics that a random measure of discrete type induces a distribution over random partitions. The community has therefore assumed that the best approach to obtain a dependent sequence of random partitions is through modeling dependent random measures. We argue that this approach is problematic and show that the random partition model induced by dependent Bayesian nonparametric priors exhibits counter-intuitive dependence among partitions even though the dependence for the sequence of random probability measures is intuitive. Because of this, we suggest directly modeling the sequence of random partitions when clustering is of principal interest. To this end, we develop a class of dependent random partition models that explicitly models dependence in a sequence of partitions. We derive conditional and marginal properties of the joint partition model and devise computational strategies when employing the method in Bayesian modeling. In the case of temporal dependence, we demonstrate through simulation how the methodology produces partitions that evolve gently and naturally overtime. We further illustrate the utility of the method by applying it to an environmental dataset that exhibits spatio-temporal dependence. Supplemental files for this article are available online.
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    DISCOVERING INTERACTIONS USING COVARIATE INFORMED RANDOM PARTITION MODELS
    (2021) Page, Garritt L.; Quintana, Fernando A.; Rosner, Gary L.
    Combination chemotherapy treatment regimens created for patients diagnosed with childhood acute lymphoblastic leukemia have had great success in improving cure rates. Unfortunately, patients prescribed these types of treatment regimens have displayed susceptibility to the onset of osteonecrosis. Some have suggested that this is due to pharmacokinetic interaction between two agents in the treatment regimen (asparaginase and dexamethasone) and other physiological variables. Determining which physiological variables to consider when searching for interactions in scenarios like these, minus a priori guidance, has proved to be a challenging problem, particularly if interactions influence the response distribution in ways beyond shifts in expectation or dispersion only. In this paper we propose an exploratory technique that is able to discover associations between covariates and responses in a general way. The procedure connects covariates to responses flexibly through dependent random partition distributions and then employs machine learning techniques to highlight potential associations found in each cluster. We provide a simulation study to show utility and apply the method to data produced from a study dedicated to learning which physiological predictors influence severity of osteonecrosis multiplicatively.
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    Effect of position, usage rate, and per game minutes played on NBA player production curves
    (2013) Page, Garritt L.; Barney, Bradley J.; Mcguire, Aaron T.
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    Exploring complete school effectiveness via quantile value added
    (2017) Page, Garritt L.; San Martín, Ernesto; Orellana, Javiera; González Burgos, Jorge Andrés
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    Joint Random Partition Models for Multivariate Change Point Analysis
    (2024) Quinlan, Jose J.; Page, Garritt L.; Castro, Luis M.
    Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underly-ing distribution. When multiple processes are observed, it is often the case that information regarding the change point positions is shared across the different processes. This work describes a method that takes advantage of this type of infor-mation. Since the number and position of change points can be described through a partition with contiguous clusters, our approach develops a joint model for these types of partitions. We describe computational strategies associated with our ap-proach and illustrate improved performance in detecting change points through a small simulation study. We then apply our method to a financial data set of emerging markets in Latin America and highlight interesting insights discovered due to the correlation between change point locations among these economies.
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    Nonparametric bayesian inference in applications
    (2018) Müeller, Peter; Quintana Quintana, Fernando; Page, Garritt L.
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    On a class of repulsive mixture models
    (2020) Quinlan, Jose J.; Quintana Quintana, Fernando; Page, Garritt L.
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    Regression with Variable Dimension Covariates
    (2024) Mueller, Peter; Quintana, Fernando Andres; Page, Garritt L.
    Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the ubiquitous nature of regression problems and the abundance of related methods and results there is a surprising gap in the literature. There are no well established methods for regression with a varying dimension covariate vectors, despite the common occurrence of such problems. In this paper we review some recent related papers proposing varying dimension regression by way of random partitions.
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    Rejoinder
    (2016) Page, Garritt L.; Quintana Quintana, Fernando
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    Spatial Product Partition Models
    (2016) Page, Garritt L.; Quintana Quintana, Fernando
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    Temporally Dynamic, Cohort-Varying Value-Added Models
    (2024) Page, Garritt L.; San Martin, Ernesto; Irribarra, David Torres; Van Bellegem, Sebastien
    We aim to estimate school value-added dynamically in time. Our principal motivation for doing so is to establish school effectiveness persistence while taking into account the temporal dependence that typically exists in school performance from one year to the next. We propose two methods of incorporating temporal dependence in value-added models. In the first we model the random school effects that are commonly present in value-added models with an auto-regressive process. In the second approach, we incorporate dependence in value-added estimators by modeling the performance of one cohort based on the previous cohort's performance. An identification analysis allows us to make explicit the meaning of the corresponding value-added indicators: based on these meanings, we show that each model is useful for monitoring specific aspects of school persistence. Furthermore, we carefully detail how value-added can be estimated over time. We show through simulations that ignoring temporal dependence when it exists results in diminished efficiency in value-added estimation while incorporating it results in improved estimation (even when temporal dependence is weak). Finally, we illustrate the methodology by considering two cohorts from Chile's national standardized test in mathematics.