Exact Bayesian curve fitting and signal segmentation.

We consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments. We present an algorithm for perfect simulation from the posterior distribution of such a model, even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment. The algorithm is simple, can scale well to large data sets, and avoids the problem of diagnosing convergence that is present with Monte Carlo Markov Chain (MCMC) approaches to this problem. We demonstrate our algorithm on standard denoising problems, on a piecewise constant AR model, and on a speech segmentation problem

Time Course and Hazard Function: A Distributional Analysis of Fixation Duration in Reading

Reading processes affect not only the mean of fixation duration but also its distribution function. This paper introduces a set of hypotheses that link the timing and strength of a reading process to the hazard function of a fixation duration distribution. Analyses based on large corpora of reading eye movements show a surprisingly robust hazard function across languages, age, individual differences, and a number of processing variables. The data suggest that eye movements are generated stochastically based on a stereotyped time course that is independent of reading variables. High-level reading processes, however, modulate eye movement programming by increasing or decreasing the momentary saccade rate during a narrow time window. Implications to theories and analyses of reading eye movement are discussed

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Essays on Dynamic Marketing Intercommunications.

The dissertation examines two distinct problems related to “marketing communication dynamics”. The main goal of this line of research is to help firms provide individually tailored marketing contents to their customers. In these two essays, I develop statistical models to first understand customers’ responses, and then explore methods to optimize firms’ reactions accordingly. Essay 1 examines “scale attraction effects” in a charitable donation context, introducing novel constructs (“compliance degree”, “pulling amount”, “accumulated pulling amount”) to describe attraction effects for multi-point appeals scales. The proposed model jointly accounts for donation incidence and amount using a Tobit 2 formulation, and allows heterogeneity in seasonality and pulling effects. Results suggest substantial scale attraction effects that vary across donors, stronger “pulling down” than “pulling up”, and heterogeneous seasonal donation patterns. A significantly negative error correlation between donation incidence and donation amount underscores the importance of accounting for selectivity effects. The effects of individually tailoring appeals scales is demonstrated through simulation. Essay 2 investigates mate-seeking users’ decision rules in an online dating context. I develop an empirical two-stage mate choice model that can accommodate compensatory and non-compensatory decision rules in each of two stages: browsing and writing. A mixture of logits model with changepoints allows for distinct decision rules across stages and heterogeneity in rule use across site users. Most importantly, it allows us to identify and compare attribute-level decision rules (“deal-breakers” and “deal-makers”) over the two stages. Results suggest the existence of heterogeneity in decision rules across (1) genders, (2) stages, and (3) site users. Additionally, it suggests the existence of potential deal-breakers/makers across both discrete and continuous attributes.PhDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100041/1/keeyeun_1.pd

Bayesian Modelling and Inference on Mixtures of Distributions.

bayesian models;