arXiv subjects

Shane T. Jensen

Publications and source records attributed to Shane T. Jensen.

30 records · Page 2Linked to original sources

arXiv2013

Estimating Player Contribution in Hockey with Regularized Logistic Regression

We present a regularized logistic regression model for evaluating player contributions in hockey. The traditional metric for this purpose is the plus-minus statistic, which allocates a single unit of credit (for or against) to each player on the ice for a goal. However, plus-minus scores measure only the marginal effect of players, do not account for sample size, and provide a very noisy estimate of performance. We investigate a related regression problem: what does each player on the ice contribute, beyond aggregate team performance and other factors, to the odds that a given goal was scored by their team? Due to the large-p (number of players) and imbalanced design setting of hockey analysis, a major part of our contribution is a careful treatment of prior shrinkage in model estimation. We showcase two recently developed techniques -- for posterior maximization or simulation -- that make such analysis feasible. Each approach is accompanied with publicly available software and we include the simple commands used in our analysis. Our results show that most players do not stand out as measurably strong (positive or negative) contributors. This allows the stars to really shine, reveals diamonds in the rough overlooked by earlier analyses, and argues that some of the highest paid players in the league are not making contributions worth their expense.

stat.AP↗

arXiv2012

Refining the Protein-Protein Interactome using Gene Expression Data

Proteins interact with other proteins within biological pathways, forming connected subgraphs in the protein-protein interactome (PPI). Proteins are often involved in multiple biological pathways which complicates interpretation of interactions between proteins. Gene expression data can assist our inference since genes within a particular pathway tend to have more correlated expression patterns than genes from distinct pathways. We provide an algorithm that uses gene expression information to remove inter-pathway protein-protein interactions, thereby simplifying the structure of the protein-protein interactome. This refined topology permits easier interpretation and greater biological coherence of multiple biological pathways simultaneously.

q-bio.MN↗

arXiv2012

A Level-Set Hit-and-Run Sampler for Quasi-Concave Distributions

We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of the target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Our sampler performs well in high-dimensional settings, which we illustrate with a comparison to Gibbs sampling on a spike-and-slab mixture model. We also extend our method to exponentially-tilted quasi-concave densities, which arise often in Bayesian models consisting of a log-concave likelihood and quasi-concave prior density. Within this class of models, our method is effective at sampling from posterior distributions with high dependence between parameters, which we illustrate with a simple multivariate normal example. We also implement our level-set sampler on a Cauchy-normal model where we demonstrate the ability of our level set sampler to handle multi-modal posterior distributions.

stat.CO↗

arXiv2010

An Alternative Prior Process for Nonparametric Bayesian Clustering

Prior distributions play a crucial role in Bayesian approaches to clustering. Two commonly-used prior distributions are the Dirichlet and Pitman-Yor processes. In this paper, we investigate the predictive probabilities that underlie these processes, and the implicit "rich-get-richer" characteristic of the resulting partitions. We explore an alternative prior for nonparametric Bayesian clustering -- the uniform process -- for applications where the "rich-get-richer" property is undesirable. We also explore the cost of this process: partitions are no longer exchangeable with respect to the ordering of variables. We present new asymptotic and simulation-based results for the clustering characteristics of the uniform process and compare these with known results for the Dirichlet and Pitman-Yor processes. We compare performance on a real document clustering task, demonstrating the practical advantage of the uniform process despite its lack of exchangeability over orderings.

stat.ME↗

arXiv2009

A Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics

Numerous statistics have been proposed for the measure of offensive ability in major league baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are the most reliable or consistent. We address this issue with a Bayesian hierarchical model for variable selection to capture which offensive metrics are most predictive within players across time. Our sophisticated methodology allows for full estimation of the posterior distributions for our parameters and automatically adjusts for multiple testing, providing a distinct advantage over alternative approaches. We implement our model on a set of 50 different offensive metrics and discuss our results in the context of comparison to other variable selection techniques. We find that 33/50 metrics demonstrate signal. However, these metrics are highly correlated with one another and related to traditional notions of performance (e.g., plate discipline, power, and ability to make contact).

stat.AP↗

arXiv2009

Bayesian testing of many hypotheses $\times$ many genes: A study of sleep apnea

Substantial statistical research has recently been devoted to the analysis of large-scale microarray experiments which provide a measure of the simultaneous expression of thousands of genes in a particular condition. A typical goal is the comparison of gene expression between two conditions (e.g., diseased vs. nondiseased) to detect genes which show differential expression. Classical hypothesis testing procedures have been applied to this problem and more recent work has employed sophisticated models that allow for the sharing of information across genes. However, many recent gene expression studies have an experimental design with several conditions that requires an even more involved hypothesis testing approach. In this paper, we use a hierarchical Bayesian model to address the situation where there are many hypotheses that must be simultaneously tested for each gene. In addition to having many hypotheses within each gene, our analysis also addresses the more typical multiple comparison issue of testing many genes simultaneously. We illustrate our approach with an application to a study of genes involved in obstructive sleep apnea in humans.

stat.ME↗

arXiv2009

Bayesball: A Bayesian hierarchical model for evaluating fielding in major league baseball

The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding based on high-resolution data consisting of on-field location of batted balls. We combine spatial modeling with a hierarchical Bayesian structure in order to evaluate the performance of individual fielders while sharing information between fielders at each position. We present results across four seasons of MLB data (2002--2005) and compare our approach to other fielding evaluation procedures.

stat.AP↗

arXiv2009

Hierarchical Bayesian Modeling of Hitting Performance in Baseball

We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such as player age and position. We share information across time and across players by using mixture distributions to control shrinkage for improved accuracy. We compare the performance of our model to current sabermetric methods on a held-out season (2006), and discuss both successes and limitations.

stat.AP↗

arXiv2008

Changes in the Distribution of Income Volatility

Recent research has documented a significant rise in the volatility (e.g., expected squared change) of individual incomes in the U.S. since the 1970s. Existing measures of this trend abstract from individual heterogeneity, effectively estimating an increase in average volatility. We decompose this increase in average volatility and find that it is far from representative of the experience of most people: there has been no systematic rise in volatility for the vast majority of individuals. The rise in average volatility has been driven almost entirely by a sharp rise in the income volatility of those expected to have the most volatile incomes, identified ex-ante by large income changes in the past. We document that the self-employed and those who self-identify as risk-tolerant are much more likely to have such volatile incomes; these groups have experienced much larger increases in income volatility than the population at large. These results color the policy implications one might draw from the rise in average volatility. While the basic results are apparent from PSID summary statistics, providing a complete characterization of the dynamics of the volatility distribution is a methodological challenge. We resolve these difficulties with a Markovian hierarchical Dirichlet process that builds on work from the non-parametric Bayesian statistics literature.

q-fin.ST↗

arXiv2007

Bayesian variable selection and data integration for biological regulatory networks

A substantial focus of research in molecular biology are gene regulatory networks: the set of transcription factors and target genes which control the involvement of different biological processes in living cells. Previous statistical approaches for identifying gene regulatory networks have used gene expression data, ChIP binding data or promoter sequence data, but each of these resources provides only partial information. We present a Bayesian hierarchical model that integrates all three data types in a principled variable selection framework. The gene expression data are modeled as a function of the unknown gene regulatory network which has an informed prior distribution based upon both ChIP binding and promoter sequence data. We also present a variable weighting methodology for the principled balancing of multiple sources of prior information. We apply our procedure to the discovery of gene regulatory relationships in Saccharomyces cerevisiae (Yeast) for which we can use several external sources of information to validate our results. Our inferred relationships show greater biological relevance on the external validation measures than previous data integration methods. Our model also estimates synergistic and antagonistic interactions between transcription factors, many of which are validated by previous studies. We also evaluate the results from our procedure for the weighting for multiple sources of prior information. Finally, we discuss our methodology in the context of previous approaches to data integration and Bayesian variable selection.

math.ST↗

arXiv2007

Evaluating Throwing Ability in Baseball

We present a quantitative analysis of throwing ability for major league outfielders and catchers. We use detailed game event data to tabulate success and failure events in outfielder and catcher throwing opportunities. We attribute a run contribution to each success or failure which are tabulated for each player in each season. We use four seasons of data to estimate the overall throwing ability of each player using a Bayesian hierarchical model. This model allows us to shrink individual player estimates towards an overall population mean depending on the number of opportunities for each player. We use the posterior distribution of player abilities from this model to identify players with significant positive and negative throwing contributions.

stat.AP↗

arXiv2006

Bayesian Clustering of Transcription Factor Binding Motifs

Genes are often regulated in living cells by proteins called transcription factors (TFs) that bind directly to short segments of DNA in close proximity to specific genes. These binding sites have a conserved nucleotide appearance, which is called a motif. Several recent studies of transcriptional regulation require the reduction of a large collection of motifs into clusters based on the similarity of their nucleotide composition. We present a principled approach to this clustering problem based upon a Bayesian hierarchical model that accounts for both within- and between-motif variability. We use a Dirichlet process prior distribution that allows the number of clusters to vary and we also present a novel generalization that allows the core width of each motif to vary. This clustering model is implemented, using a Gibbs sampling strategy, on several collections of transcription factor motif matrices. Our clusters provide a means by which to organize transcription factors based on binding motif similarities, which can be used to reduce motif redundancy within large databases such as JASPAR and TRANSFAC. Finally, our clustering procedure has been used in combination with discovery of evolutionarily-conserved motifs to predict co-regulated genes. An alternative to our Dirichlet process prior distribution is explored but shows no substantive difference in the clustering results for our datasets. Our Bayesian clustering model based on the Dirichlet process has several advantages over traditional clustering methods that could make our procedure appropriate and useful for many clustering applications.

math.ST↗