A Conversation With Harry Martz

Harry F. Martz was born June 16, 1942 and grew up in Cumberland, Maryland. He received a Bachelor of Science degree in mathematics (with a minor in physics) from Frostburg State University in 1964, and earned a Ph.D. in statistics at Virginia Polytechnic Institute and State University in 1968. He started his statistics career at Texas Tech University's Department of Industrial Engineering and Statistics right after graduation. In 1978, he joined the technical staff at Los Alamos National Laboratory (LANL) in Los Alamos, New Mexico after first working as Full Professor in the Department of Industrial Engineering at Utah State University in the fall of 1977. He has had a prolific 23-year career with the statistics group at LANL; over the course of his career, Martz has published over 80 research papers in books and refereed journals, one book (with co-author Ray Waller), and has four patents associated with his work at LANL. He is a fellow of the American Statistical Association and has received numerous awards, including the Technometrics Frank Wilcoxon Prize for Best Applications Paper (1996), Los Alamos National Laboratory Achievement Award (1998), R&D 100 Award by R&D Magazine (2003), Council for Chemical Research Collaboration Success Award (2004), and Los Alamos National Laboratory's Distinguished Licensing Award (2004). Since retiring as a Technical Staff member at LANL in 2001, he has worked as a LANL Laboratory Associate.Comment: Published at http://dx.doi.org/10.1214/088342306000000646 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks

We propose a rank-based statistical procedure for comparing performances of top major league baseball players who performed in different eras. The model is based on using the player ranks from voting results for the most valuable player awards in the American and National Leagues. The current voting procedure has remained the same since 1932, so the analysis regards only data for players whose career blossomed after that time. Because the analysis is based on quantiles, its basis is nonparametric and relies on a simple link function. Results are stratified by fielding position, and we compare 73 Hall of Fame players up to 2010. We also consider the players on the 2011 Hall of Fame ballot as well as other potential Hall of Fame candidates. The analysis is based on the method of maximum likelihood, and results are illustrated graphically

The Price is Right: Analyzing Bidding Behavior on Contestants’ Row

The TV game show “The Price is Right” features a bidding auction called Contestant’s Row that rewards the player (out of four) who bids closest to an item’s value without overbidding. By exploring 903 game outcomes from the 2000–2001 season, we show how player strategies are significantly inefficient, and compare the empirical results to probability outcomes for optimal bid strategies found in a recent study. Findings show that the last bidder would do better using the naïve strategy of bidding a dollar more than the highest of the three bids. We apply the EM algorithm in a novel way to extract a maximum amount of information from observed player bids. The gained knowledge about a player’s evaluation of merchandise allows us to uncover new insights into player behavior, including the potential effects of anchoring

Ranked Set Sampling Based on Binary Water Quality Data with Covariates

A ranked set sample (RSS) is composed of independent order statistics, formed by collecting and ordering independent subsamples, then measuring only one item from each subsample. If the cost of sampling is dominated by data measurement rather than collection or ranking, the RSS technique is known to be superior to ordinary sampling. Experiments based on binary data are not designed to exploit the advantages of ranked set sampling because categorical data typically are as easily measured as ranked, making RSS methods impractical. However, in some environmental and biological studies, the success probability of a bivariate outcome is related to one or more covariates. If the covariate information is not easily quantified, but can be objectively ordered with respect to this success probability, the RSS method can be used to improve the analysis of binary data. This article considers the case in which the covariate information is modeled in terms of a mixing distribution for the success probability, and the expected success probability is of primary interest. The inference technique is demonstrated with water-quality data from the Rappahannock river in Virginia. In a general setting, the RSS estimator is shown to be superior, including cases in which error in judgment ranking is present

Electoral Voting and Population Distribution in the United States

In the United States, the electoral system for determining the president is controversial and sometimes confusing to voters keeping track of election outcomes. Instead of directly counting votes to decide the winner of a presidential election, individual states send a representative number of electors to the Electoral College, and they are trusted to cast their collective vote for the candidate who won the popular vote in their state. Under the current rules, the value of a vote differs from state to state. A large state such as California has an immense effect on the national election, but, compared to a sparsely populated state such as Alaska, is grossly under-represented in the U.S. senate, where all senators have an equal vote. Arnold Barnett and Edward Kaplan, in their 2007 CHANCE article, A Cure for the Elector College called the Electoral College the fun-house mirror of American politics and suggested a weighted voting system that would mitigate the problem caused by the present winner-take-all rule

A Conversation with Harry Martz

Harry F. Martz was born June 16, 1942 and grew up in Cumberland, Maryland. He received a Bachelor of Science degree in mathematics (with a minor in physics) from Frostburg State University in 1964, and earned a Ph.D. in statistics at Virginia Polytechnic Institute and State University in 1968. He started his statistics career at Texas Tech University\u27s Department of Industrial Engineering and Statistics right after graduation. In 1978, he joined the technical staff at Los Alamos National Laboratory (LANL) in Los Alamos, New Mexico after first working as Full Professor in the Department of Industrial Engineering at Utah State University in the fall of 1977. He has had a prolific 23-year career with the statistics group at LANL; over the course of his career, Martz has published over 80 research papers in books and refereed journals, one book (with co-author Ray Waller), and has four patents associated with his work at LANL. He is a fellow of the American Statistical Association and has received numerous awards, including the Technometrics Frank Wilcoxon Prize for Best Applications Paper (1996), Los Alamos National Laboratory Achievement Award (1998), R&D 100 Award by R&D Magazine (2003), Council for Chemical Research Collaboration Success Award (2004), and Los Alamos National Laboratory\u27s Distinguished Licensing Award (2004). Since retiring as a Technical Staff member at LANL in 2001, he has worked as a LANL Laboratory Associate

Length Bias in the Measurements of Carbon Nanotubes

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length distribution estimate provides a better fit to the Weibull distribution than the original selection-biased observations, thus reinforcing a previous claim about the underlying distribution of synthesized nanotube lengths

Computational problems with binomial failure rate model and incomplete common cause failure reliability data

In estimating the reliability of a system of components, it is ordinarily assumed that the component lifetimes are independently distributed. This assumption usually alleviates the difficulty of analyzing complex systems, but it is seldom true that the failure of one component in an interactive system has no effect on the lifetimes of the other components. Often, two or more components will fail simultaneously due to a common cause event. Such an incident is called a common cause failure (CCF), and is now recognized as an important contribution to system failure in various applications of reliability. We examine current methods for reliability estimation of system and component lifetimes using estimators derived from the binomial failure rate model. Computational problems require a new approach, like iterative solutions via the EM algorithm

A Probability Model for Strategic Bidding on The Price is Right

The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player\u27s bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large advantage in both scenarios because of receiving the most information from opposing players and being able to bid the minimal amount over an opponent’s bid without incurring extra risk. Finally, we measure how confidence can affect a player’s winning probability

Teaching Statistics with Sports Examples

Class material for introductory and advanced statistics can be colorfully illustrated by using appropriate data and examples from sports. Specific methods, including statistical graphics (e.g., boxplots), ball-and-urn probabilities, and statistical regression are demonstrated. Examples are drawn from popular American sports such as baseball, basketball, soccer and American football. Classroom feedback indicates that most students enjoy sports examples as a way to learn abstract concepts using familiar, recreational settings