Statistical Models Commons^™

Bayesian Inference For A Periodic Stochastic Volatility Model Of Intraday Electricity Prices, Michael S. Smith

Michael Stanley Smith

The Gaussian stochastic volatility model is extended to allow for periodic autoregressions (PAR) in both the level and log-volatility process. Each PAR is represented as a first order vector autoregression for a longitudinal vector of length equal to the period. The periodic stochastic volatility model is therefore expressed as a multivariate stochastic volatility model. Bayesian posterior inference is computed using a Markov chain Monte Carlo scheme for the multivariate representation. A circular prior that exploits the periodicity is suggested for the log-variance of the log-volatilities. The approach is applied to estimate a periodic stochastic volatility model for half-hourly electricity prices …

Bayesian Skew Selection For Multivariate Models, Michael S. Smith, Anastasios Panagiotelis

Michael Stanley Smith

We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio (2003) or Sahu, Dey and Branco~(2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, …

Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes

Philip T. Reiss

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …

A Statistical Framework For The Analysis Of Chip-Seq Data, Pei Fen Kuan, Dongjun Chung, Guangjin Pan, James A. Thomson, Ron Stewart, Sunduz Keles

Sunduz Keles

Chromatin immunoprecipitation followed by sequencing (ChIP-Seq) has revolutionalized experiments for genome-wide profiling of DNA-binding proteins, histone modifications, and nucleosome occupancy. As the cost of sequencing is decreasing, many researchers are switching from microarray-based technologies (ChIP-chip) to ChIP-Seq for genome-wide study of transcriptional regulation. Despite its increasing and well-deserved popularity, there is little work that investigates and accounts for sources of biases in the ChIP-Seq technology. These biases typically arise from both the standard pre-processing protocol and the underlying DNA sequence of the generated data.

We study data from a naked DNA sequencing experiment, which sequences non-cross-linked DNA after deproteinizing and …

Are (The Log-Odds Of) Hospital Mortality Rates Normally Distributed In Ontario? Implications For Studying Variations In Outcomes Of Medical Care, Peter C. Austin

Peter Austin

Objective: Hierarchical regression models are used to examine variations in outcomes following the provision of medical care across providers. These models frequently assume a normal distribution for the provider-specific random effects. Poincaré said, “Everyone believes in the normal law, the experimenters because they imagine it a mathematical theorem, and the mathematicians because they think it an experimental fact”. Our objective was to examine the appropriateness of this assumption when examining variations in mortality.

Study design and setting: We used Bayesian model selection methods to compare hierarchical regression models in which the provider-specific random effects were either a normal distribution or …

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

Are Credit Constraints In Italy Really More Binding In The South?, Claudio Lupi

Claudio Lupi

This paper is motivated by a very practical question: are there significant geographical differences in the accessibility to the credit market on the part of Italian households? The investigation is carried using robust probit model. Estimation is carried out in a Bayesian framework. The results are somewhat surprising, showing that the area where households are more likely to be credit constrained is not the South, as could be easily imagined, but rather the highly developed and industrialized North-West.

Ensuring The Comparability Of Comparison Groups: Is Randomization Enough?, Vance Berger, Sherri Rose

Sherri Rose

It is widely believed that baseline imbalances in randomized trials must necessarily be random. In fact, there is a type of selection bias that can cause substantial, systematic and reproducible baseline imbalances of prognostic covariates even in properly randomized trials. It is possible, given complete data, to quantify both the susceptibility of a given trial to this type of selection bias and the extent to which selection bias appears to have caused either observable or unobservable baseline imbalances. Yet, in articles reporting on randomized trials, it is uncommon to find either these assessments or the information that would enable a …

Semiparametric Regression: An Exposition And Application To Print Advertising Data, Michael S. Smith, Robert Kohn, Sharat K. Mathur

Michael Stanley Smith

A new regression based approach is proposed for modeling marketing databases. The approach is Bayesian and provides a number of significant improvements over current methods. Independent variables can enter into the model in either a parametric or nonparametric manner, significant variables can be identified from a large number of potential regressors and an appropriate transformation of the dependent variable can be automatically selected from a discrete set of pre-specified candidate transformations. All these features are estimated simultaneously and automatically using a Bayesian hierarchical model coupled with a Gibbs sampling scheme. Being Bayesian, it is straightforward to introduce subjective information about …

Additive Nonparametric Regression With Autocorrelated Errors, Michael S. Smith, C Wong, Robert Kohn

Michael Stanley Smith

A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially nonlinear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterised in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach also allows the selection of a suitable transformation of the dependent variable. All aspects of the model are estimated simultaneously using Markov chain Monte Carlo. It is shown empirically that the proposed approach works well …

A Bayesian Approach To Bivariate Nonparametric Regression, Michael Smith, Robert Kohn

Michael Stanley Smith

No abstract provided.

Nonparametric Regression Using Bayesian Variable Selection, Michael Smith, Robert Kohn

Michael Stanley Smith

No abstract provided.

Finite Sample Performance Of Robust Bayesian Regression, Michael Smith, Sheather Simon, Kohn Robert

Michael Stanley Smith

No abstract provided.

Derivation Of A Scaled Binomial As An Instance Of A General Discrete Exponential Distribution, Joseph Hilbe

Joseph M Hilbe

No abstract provided.

A Bayesian Approach To Additive Nonparametric Regression, Michael S. Smith, Robert Kohn

Michael Stanley Smith

This proceedings paper was the first to suggest using a Gaussian g-prior combined with a point mass to undertake Bayesian variable selection in a Gaussian linear regression model. It also was the first to suggest integrating out the regression parameters and variance in closed form, resulting in an efficient Gibbs sampling scheme. The idea was applied to estimate regression functions in an additive model by using a linear basis expansion for each component function in an additive model. The conference proceeding was eventually published in a slightly tighter form in Journal of Econometrics (1996).

Log-Negative Binomial Regression As A Generalized Linear Model, Joseph Hilbe

Joseph M Hilbe

The negative binomial (NB) is a member of the exponential family of discrete probability distributions. The nature of the distribution is itself well understood, but its contribution to regression modeling, in particular as a generalized linear model (GLM), has not been appreciated. The mathematical properties of the negative binomial are derived and GLM algorithms are developed for both the canonical and log form. Geometric regression is seen as an instance of the NB. The log forms of both may be effectively used to model types of POisson-overdispersed count data. A GLM-type algorithm is created for a general log-negative binomial regression …