Statistics Seminar

Copula-Based Bivariate for Poisson Time Series Models

Abstract: The class of bivariate integer-valued time series models is gaining rapid popularity. However, its efficiency and adaptability are being challenged because of zero-inflation of count time series (ZITS) and algorithm techniques. In this presentation, the bivariate copula is presented with ZITS. The computational algorithm is proposed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probability functions with Poisson and zero-inflated Poisson margins. The copula theory is also used to capture bivariate ZITS where the dependence between the two series using the bivariate Gaussian and t-copula functions. Likelihood based inference is used to estimate the models’ parameters for simulated and real data with the bivariate integrals of the Gaussian and t-copula functions being evaluated using standard randomized Monte Carlo methods.

 

 

Date:
Location:
MDS 220
Event Series:

An MM algorithm for estimation of a two-component semiparametric density mixture with a known component

Abstract:  We consider a semiparametric mixture of two density functions where one of them is known while the weight and the other function are unknown. We do not assume any additional structure on the unknown density function.  We suggest a novel approach to estimation of this model that is based on an idea of applying a maximum smoothed likelihood to what would otherwise have been an ill-posed problem. We introduce an iterative MM (Majorization-Minimization) algorithm that estimates all of the model parameters. Unlike possible competing methods, this algorithm works well in both univariate as well as multivariate case. We establish that the algorithm possesses a descent property with respect to a log-likelihood objective functional and prove that the algorithm, indeed, converges. Finally, we also illustrate the performance of our algorithm in a simulation study and using a real dataset.

Date:
Location:
MDS 220
Event Series:

A Program for Pharmacokinetic Analysis: An Exercise in Computational Modeling

 

Abstract: This talk is about Pharmacokinetic models, algorithms used to analyze data from them, and a program I am writing to make the analysis easy. There will be a tutorial on Pharmacokinetic models followed by a short description of my method for solving differential equations. We will take a look at the Tetracycline data and then analyze it using my program.

 

Date:
Location:
Zoom
Event Series:

Some Topics in Finite Mixture Models, Tolerance Regions, and Zero-Inflated Models

 

Abstract: This talk will provide an overview of three major areas in my research agenda: finite mixture models, tolerance regions, and zero-inflated models.  Two projects from each area will be highlighted, along with a brief discussion of theoretical or methodological advancements produced during the research, and the data that were analyzed.  I will provide some commentary about my two R packages, mixtools and tolerance.  Research undertaken by former and current PhD advisees will also be highlighted.

 

Date:
-
Location:
https://uky.zoom.us/j/89975253600
Event Series:

Parameterization of Reduced Rank and Co-integrated Vector Autoregression

Abstract: We provide a parametrization of Vector Autoregression (VAR) that enables one to look  at  the  parameters  associated  with  unit  root  dynamics  and  those  associated  with stable dynamics separately.  The task is achieved via a factorization of the VAR polynomialthat partitions  the  polynomial  spectrum  into  unit  root  and  stable  and  zero  roots  via  polynomial factors.   The  proposed  factorization  adds  to  the  literature  of  spectral  factorization  of  matrix polynomials.   The  main  benefit  is  that  using  the  parameterization,  actions  could  be  taken  to model  the  dynamics  due  to  a  particular  class  of  roots,  e.g.   unit  roots  or  zero  roots,  without changing  the  properties  of  the dynamics  due  to  other  roots.   For  example,  using  the  parameterization one is able toestimate cointegrating space with appropriate rank that maintains the root  structure  of  the  original  VAR  processes  or  one  can  estimate  a  reduced  rank  causal  VAR process maintainingthe constraints of causality.  In essence, this parameterization provides the practitioner anoption to perform estimation of VAR processes with constrained root structure (e.g.,  conintegrated VAR  or  reduced  rank  VAR)  such  that  the  estimated  model  maintains  the assumed rootstructure.
 
This is a joint work with Ticker McElroy
 
Date:
Location:
https://uky.zoom.us/j/89401153149
Event Series:

Statistics Seminar Series - Spring 2021 - Week 13

  • 3:00pm - Introductory Remarks by Dr. Derek Young
  • 3:10pm - Announcement of the R.L. Anderson Award Winners

    • R.L. Anderson Outstanding Teaching Award(s) - presented by Dr. Melissa Pittard
    • R.L. Anderson Outstanding Research Award(s) - presented by Dr. Katherine Thompson
  • 3:30pm - Introduction of Dr. Kryscio by Dr. Arnold Stromberg
  • 4:00pm - R.L. Anderson lecture by Dr. Richard Kryscio
  • 5:00pm - Event Wrap-Up
Date:
Location:
https://uky.zoom.us/j/82243594692?pwd=VGw1Y2RCV0lsMGtQa2ROSVhseG5SQT09
Event Series:

Direct Sampling in Bayesian Regression Models with Additive Disclosure Avoidance Noise

 

Abstract: Disclosure avoidance techniques are used by agencies to prepare releases of statistics and microdata when internal data contain information considered sensitive to individual subjects. Differential privacy (DP) techniques have become popular in the literature and are finding increasing use in practical applications. One fundamental DP technique to protect sensitive data is to add noise from a selected distribution in such a way that mathematical privacy criteria are satisfied. An analyst making use of such data in a statistical model may wish to account for uncertainty introduced by the added noise. This work considers Bayesian regression models which regard the agency noise - or equivalently, the unreleased sensitive data - as augmented data. Given other random variables in the model, conditional distributions of these augmented data form weighted densities, but a method of drawing from them may not be apparent. We revisit the direct sampling method proposed by Walker et al. (JCGS 2011) and explore several customizations to address issues encountered in the basic version of the algorithm. Draws from the desired conditional distributions may be then taken reliably, largely avoiding the need for rejections or manual tuning. The customized direct sampler is used to complete the specification of a Gibbs sampler to fit a Lognormal regression model where agency noise has been added to both the outcome and some of the covariates. Demonstrations compare inference using the sensitive internal data versus the privacy-protected release.

 

Date:
Location:
https://uky.zoom.us/j/81507661849
Event Series:

Probability of Correct Model Choice Using R^2 or AIC in Model Selection

 
Abstract: Although recent attention has focused largely on improving predictive models, less consideration has been given to the prevalence of incorrect models selected by traditional statistical methods. In this work, the difficulty in choosing a scientifically correct model is quantified through theoretical and simulation work. Furthermore, the performance of traditional model selection techniques is compared with that of more recent methods. Specifically, when data sets contain a large number of explanatory variables, these results show that often the model with the highest R^2 (or adjusted R^2) or lowest AIC is not the scientifically correct model, suggesting that traditional model selection techniques be inappropriate. This work starts with the derivation of the probability of choosing the scientifically correct model in data sets as a function of regression model parameters when using R^2 or AIC. Next, simulation results show that these traditional model selection criteria are outperformed by methods that produce multiple candidate models for researchers' consideration. Potential extensions for dissertation topics will be discussed, along with a range of applications for this work!
 
**Please note: This talk has been tailored for students currently in the MS and PhD programs.
 
 
Date:
Location:
https://uky.zoom.us/j/89792547951
Event Series:
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