Thursday, Aug 8: 8:30 AM - 10:20 AM
5181
Contributed Papers
Oregon Convention Center
Room: CC-E144
Main Sponsor
Section on Bayesian Statistical Science
Presentations
Sports organizations often want to estimate athlete strengths. For games with scored outcomes, a common approach is to assume observed game scores follow a normal distribution conditional on athletes' latent abilities, which may change over time. In many games, however, this assumption of conditional normality does not hold. To estimate athletes' time-varying latent abilities using non-normal game score data, we propose a Bayesian dynamic linear model with flexible monotone response transformations. Our model learns nonlinear monotone transformations to address non-normality in athlete scores and can be easily fit using standard regression and optimization routines, which we implement in the dlmt package in R. We demonstrate our method on data from several Olympic sports, including biathlon, diving, rugby, and fencing.
Keywords
Sports statistics
Athlete rating
Bayesian statistics
Dynamic linear model
Kalman filter
Non-normal data
It is not uncommon for privacy or summarization purposes to receive data in a table or in histogram format with bins and associated frequencies. In this work we present a method that fits a mixture distribution to model the probability density function of the underlying population. We focus on a mixture of normal distributions, however the method could be generalized to mixtures of other distributions. A prior is placed on the number of mixture components which could be finite or countably infinite and inference is obtained using reversible jump MCMC. We demonstrate attractive properties of the method, which show a great deal of promise to modeling large data problems using a Bayesian nonparametric approach. Additionally, we consider the case of multiple histograms and cluster them using the Dirichlet process. This clustering allows for the sharing of information between populations and provides a posterior probability of homogeneity between populations.
Keywords
Dirichlet Process
Data Privacy
Big Data
Geophysical inversion is the mathematical process of predicting underground geophysical measurements at different depths from the wave signals detected on the ground, like seismic waves. Three-dimensional reconstruction of lithofacies based on geophysical inversion data enables determining the location and depth of drilling. However, the regularization step involved in geophysical inversion leads to significant differences between the geophysical inversion data and drilled rock data. Therefore, geologists usually have to annotate inversion results manually based on experience. The inversion differences of the same lithofacies at different depths will further hamper manual annotation. Therefore, we develop an unsupervised hierarchical Bayesian model to cluster different lithofacies, correct for the depth effects automatically, and finally recover the 3D geological structures from inversion data. We also consider the spatial continuity of lithofacies distribution in our hierarchical model. Finally, we predict the lithofacies distribution of an oil base located in Northeastern China, and the lithofacies prediction based on inversion data is highly consistent with drilling rock samples
Keywords
Integrative analysis
Model-based clustering
Markov chain Monte Carlo
Geophyiscal inversion
Co-Author(s)
Yujian Hou, Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring
Zhanxiang He, Guangdong Provincial Key Laboratory of Geophysical High-resolution Imaging Technology
Fangda Song, The Chinese University of Hong Kong, Shenzhen
First Author
Yibo ZHAI
Presenting Author
Yibo ZHAI
Mixed Poisson families are widely used to model count data with overdispersion, zero inflation, or heavy tails in a variety of applications including finance, biology, and the physical sciences. The Poisson rate is typically assigned a nonnegative-valued mixing distribution. Surprisingly, it is also possible for the mixing distribution to have negative support. For example, the Hermite distribution is analogous to mixing a Poisson with a Gaussian and can be derived using generating functions so long as constraints on the natural parameter are satisfied. Here we provide general conditions on the mixing distribution that are necessary for a mixed Poisson to exist. A key tool is the use of subweibull bounds on the rates of tail decay and Lp norm growth. We illustrate the scope of mixed Poisson families with examples having different tail behaviors. Finally we comment on the mixed Poisson analogs of the skewed stable and extreme stable Tweedie families.
Keywords
probability distribution
Tweedie
count data
compound Poisson
exponential dispersion models
Abstracts
First Author
Will Townes, Carnegie Mellon University
Presenting Author
Will Townes, Carnegie Mellon University
Bayesian studies to date involving the Conway-Maxwell-Poisson (COM-Poisson) distribution have little discussion of non- and weakly-informative priors. This work considers various priors and evaluates their influence on the COM-Poisson model via an empirical study under varying dispersion types and sample sizes.
Keywords
dispersion
over-dispersion
under-dispersion
Bayesian methodology
count data
In this study, we will use infinite multivariate scale mixtures of Normal distributions to model the density of the continuously compounded return, CCR, of five major American stocks. The approach is based on using a finite discretized version of the density, then estimating the parameters of the corresponding multivariate density based on that of the univariate components using UNMIX, which is a newly developed program for estimating and fitting univariate infinite scale mixtures of Normals. The fitted density is compared with the empirical and the Bayesian method of estimation to the same data. The CCR of the weekly closing stock prices of Google, Amazon, Exxon Mobile, Apple and Fannie Mae and maybe few others. We also check the effect of correlation on the fits.
Keywords
Multivariate Scale Mixtures
Bayesian Method
UNMIX
CCR