Luke Bornn

Predicting the outcome of a single sporting event is difficult; predicting all of the outcomes for an entire tournament is a monumental challenge. Despite the dif- ficulties, millions of people compete each year to forecast the outcome of the NCAA men’s basketball tournament, which spans 63 games over 3 weeks. Statistical predic- tion of game outcomes involves a multitude of possible covariates and information sources, large performance variations from game to game, and a scarcity of detailed… Show more

Predicting the outcome of a single sporting event is difficult; predicting all of the outcomes for an entire tournament is a monumental challenge. Despite the dif- ficulties, millions of people compete each year to forecast the outcome of the NCAA men’s basketball tournament, which spans 63 games over 3 weeks. Statistical predic- tion of game outcomes involves a multitude of possible covariates and information sources, large performance variations from game to game, and a scarcity of detailed historical data. In this paper, we present the results of a team of modelers working together to forecast the 2014 NCAA men’s basketball tournament. We present not only the methods and data used, but also several novel ideas for post-processing statistical forecasts and decontaminating data sources. In particular, we highlight the difficulties in using publicly available data and suggest techniques for improving their relevance. Show less

Although basketball is a dualistic sport, with all players competing on both offense and defense, almost all of the sport’s conventional metrics are designed to summarize offensive play. As a result, player valuations are largely based on offensive performances and to a much lesser degree on defensive ones. Steals, blocks and defensive rebounds provide only a limited summary of defensive effectiveness, yet they persist because they summarize salient events that are easy to observe. Due to the… Show more

Although basketball is a dualistic sport, with all players competing on both offense and defense, almost all of the sport’s conventional metrics are designed to summarize offensive play. As a result, player valuations are largely based on offensive performances and to a much lesser degree on defensive ones. Steals, blocks and defensive rebounds provide only a limited summary of defensive effectiveness, yet they persist because they summarize salient events that are easy to observe. Due to the inefficacy of traditional defensive statistics, the state of the art in defensive analytics remains qualitative, based on expert intuition and analysis that can be prone to human biases and imprecision.

Fortunately, emerging optical player tracking systems have the potential to enable a richer quantitative characterization of basketball performance, particularly defensive performance. Unfortunately, due to computational and methodological complexities, that potential remains unmet. This paper attempts to fill this void, combining spatial and spatio-temporal processes, matrix factorization techniques and hierarchical regression models with player tracking data to advance the state of defensive analytics in the NBA. Our approach detects, characterizes and quantifies multiple aspects of defensive play in basketball, supporting some common understandings of defensive effectiveness, challenging others and opening up many new insights into the defensive elements of basketball. Show less

In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide whether the compact object is a black hole or a neutron star. To assist in this process, we develop a Bayesian statistical model that makes use of the fact that X-ray binary systems appear to cluster based on their compact object type when viewed from a three-dimensional coordinate system derived from X-ray spectral data where the first… Show more

In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide whether the compact object is a black hole or a neutron star. To assist in this process, we develop a Bayesian statistical model that makes use of the fact that X-ray binary systems appear to cluster based on their compact object type when viewed from a three-dimensional coordinate system derived from X-ray spectral data where the first coordinate is the ratio of counts in the mid- to low-energy band (color 1), the second coordinate is the ratio of counts in the high- to low-energy band (color 2), and the third coordinate is the sum of counts in all three bands. We use this model to estimate the probabilities of an X-ray binary system containing a black hole, non-pulsing neutron star, or pulsing neutron star. In particular, we utilize a latent variable model in which the latent variables follow a Gaussian process prior distribution, and hence we are able to induce the spatial correlation which we believe exists between systems of the same type. The utility of this approach is demonstrated by the accurate prediction of system types using Rossi X-ray Timing Explorer All Sky Monitor data, but it is not flawless. In particular, non-pulsing neutron systems containing “bursters” that are close to the boundary demarcating systems containing black holes tend to be classified as black hole systems. As a byproduct of our analyses, we provide the astronomer with the public R code which can be used to predict the compact object type of XRBs given training data. Show less

The need to draw climate-related inferences from historical data makes understanding the biases and errors in these data critical. While climate data are collected at point-level monitoring sites, they are often postprocessed by averaging sites within a geographic area to align the data to a grid, easing analysis and visualization. Although this aggregation generally provides reasonable estimates of the mean, its use can be problematic for characterizing the full distribution of climate… Show more

The need to draw climate-related inferences from historical data makes understanding the biases and errors in these data critical. While climate data are collected at point-level monitoring sites, they are often postprocessed by averaging sites within a geographic area to align the data to a grid, easing analysis and visualization. Although this aggregation generally provides reasonable estimates of the mean, its use can be problematic for characterizing the full distribution of climate measures. Specifically, the process of averaging point-level data up to grid level can lead to inconsistencies, particularly when the grid box is heterogeneous and extremes are of interest. Point-level data are measured at individual points, while gridded data are the averaged product of many measurements within a larger spatial area. Because of this aggregation, point-level and grid-level distributions differ in many fundamental properties, such as their shape, skew, and tail behavior. This paper highlights these differences and their effects on analyses pertaining to current climatological questions. Mathe- matical relationships are derived to link the distributions of grid-level climate measures to the distributions of point-level climate measures using the notion of effective sample size. Then, these relationships are leveraged to propose a correction factor to use when modeling higher moments and extreme events. Show less

Due to the ease of recording points, assists, and related goal-scoring statistics, the vast majority of advanced basketball metrics developed to date have focused on offensive production. It is straightforward to see who scored the most points in the 1985/86 season (Alex English, with 2414) or took the most 3-point shots in 1991/92 (Vernon Maxwell, with 473). However, try to look up who had the most points against in 2013/14, or who prevented the most shots from being taken that year, and the… Show more

Due to the ease of recording points, assists, and related goal-scoring statistics, the vast majority of advanced basketball metrics developed to date have focused on offensive production. It is straightforward to see who scored the most points in the 1985/86 season (Alex English, with 2414) or took the most 3-point shots in 1991/92 (Vernon Maxwell, with 473). However, try to look up who had the most points against in 2013/14, or who prevented the most shots from being taken that year, and the history books are, remarkably, empty. Thus we stand in a muddled state where offensive ability is naturally quantified with numerous directly-measured numbers, yet we attempt to explain defensive ability through statistics only loosely related to overall defensive ability, such as blocks and steals. Alternatively, we quote regression-based metrics such as adjusted plus/minus which give no insight into how or why a player is effective defensively. This paper bridges this gap, introducing a new suite of defensive metrics that aim to progress the field of basketball analytics by enriching the measurement of defensive play. Our results demonstrate that the combination of player tracking, statistical modeling, and visualization enable a far richer characterization of defense than has previously been possible. Our method, when combined with more traditional offensive statistics, provides a well-rounded summary of a player’s contribution to the final outcome of a game. Show less

We develop a machine learning approach to rep- resent and analyze the underlying spatial struc- ture that governs shot selection among profes- sional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. This makes it difficult to draw comparisons between players and make accurate player specific pre- dictions. Modeling shot attempt data as a point process, we create a low… Show more

We develop a machine learning approach to rep- resent and analyze the underlying spatial struc- ture that governs shot selection among profes- sional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. This makes it difficult to draw comparisons between players and make accurate player specific pre- dictions. Modeling shot attempt data as a point process, we create a low dimensional representa- tion of offensive player types in the NBA. Using non-negative matrix factorization (NMF), an un- supervised dimensionality reduction technique, we show that a low-rank spatial decomposition summarizes the shooting habits of NBA players. The spatial representations discovered by the algorithm correspond to intuitive descriptions of NBA player types, and can be used to model other spatial effects, such as shooting accuracy. Show less

Basketball is a game of decisions; at any moment, a player can change the character of a possession by choosing to pass, dribble, or shoot. The current state of basketball analytics, however, provides no way to quantitatively evaluate the vast majority of decisions that players make, as most metrics are driven by events that occur at or near the end of a possession, such as points, turnovers, and assists. We propose a framework for using player-tracking data to assign a point value to each… Show more

Basketball is a game of decisions; at any moment, a player can change the character of a possession by choosing to pass, dribble, or shoot. The current state of basketball analytics, however, provides no way to quantitatively evaluate the vast majority of decisions that players make, as most metrics are driven by events that occur at or near the end of a possession, such as points, turnovers, and assists. We propose a framework for using player-tracking data to assign a point value to each moment of a possession by computing how many points the offense is expected to score by the end of the possession, a quantity we call expected possession value (EPV). EPV allows analysts to evaluate every decision made during a basketball game – whether it is to pass, dribble, or shoot – opening the door for a multitude of new metrics and analyses of basketball that quantify value in terms of points. In this paper, we propose a modeling framework for estimating EPV, present results of EPV computations performed using player- tracking data from the 2012-13 season, and provide several examples of EPV-derived metrics that answer real basketball questions. Show less

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon… Show more

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models. Show less

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a… Show more

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field. Show less

OBJECTIVE: To determine the prevalence and etiology of anemia among school-aged children in Spiti Valley, India, and implement an appropriate management plan.
METHODS: Hemoglobin (Hb) levels were measured in 382 children (3 to 18 years old) living in the Indian Himalayas for three consecutive years. Blood smears from the 200 most severe cases of anemia were analyzed. Iron treatments were provided for three months, and hemoglobin levels were measured after six weeks.
RESULTS:… Show more

OBJECTIVE: To determine the prevalence and etiology of anemia among school-aged children in Spiti Valley, India, and implement an appropriate management plan.
METHODS: Hemoglobin (Hb) levels were measured in 382 children (3 to 18 years old) living in the Indian Himalayas for three consecutive years. Blood smears from the 200 most severe cases of anemia were analyzed. Iron treatments were provided for three months, and hemoglobin levels were measured after six weeks.
RESULTS: Pre-treatment, 88.4% were anemic in 2007, 78.3% in 2008, and 71.3% in 2009. Analysis of the hemoglobin concentration curve over the three years demonstrated an overall shift to the right. Blood smear results showed that 57% of the samples displayed normocytic, normochromic red blood cells; 30% were hypochromic only; and 11% hypochromic, anisocytic. Post-iron treatment prevalence of anemia was found to be 82.9% in 2007, and 84.9% in 2008.
CONCLUSION: There is a significant prevalence of anemia in the Spiti Valley children, which is multifactorial in etiology. A three-year evaluation of Hb levels combined with interventions addressing linked causes of anemia, such as iron supplementation, deworming, and enhanced nutrition through greenhouses, have demonstrated a significant year-to-year improvement in anemia. The hypochromic anisocytic anemia suggests iron deficiency or thalassemia. The normocytic normochromic anemia may be due to 1) mixed iron, B12, and
folate deficiencies from a low animal protein and fresh vegetable diet in winter months; 2) early iron deficiency; or 3) genetic adaptation in oxygen transport at high-altitude. Due to the multifactorial nature of the anemia, an integrated prevention and treatment approach is warranted. Future goals include administration of iron, multivitamins, and zinc supplements, improvements in water and sanitation, and evaluation of the impact of greenhouses on anemia status Show less

In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed on a particular prior distribution which derives its motivation from the class of product partition models; the properties of this prior relative to existing priors is examined… Show more

In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed on a particular prior distribution which derives its motivation from the class of product partition models; the properties of this prior relative to existing priors is examined through theory and simulation. We then demonstrate the use of graphical models in the field of agriculture, showing how the proposed prior distribution alleviates the inflexibility of previous approaches in properly modeling the interactions between the yield of different crop varieties. Show less

Prior sensitivity analysis and cross-validation are important tools in Bayesian statistics. However, due to the computational expense of implementing existing methods, these techniques are rarely used. In this paper, the authors show how it is possible to use sequential Monte Carlo methods to create an efficient and automated algorithm to perform these tasks. They apply the algorithm to the computation of regularization path plots and to assess the sensitivity of the tuning parameter in g-prior… Show more

Prior sensitivity analysis and cross-validation are important tools in Bayesian statistics. However, due to the computational expense of implementing existing methods, these techniques are rarely used. In this paper, the authors show how it is possible to use sequential Monte Carlo methods to create an efficient and automated algorithm to perform these tasks. They apply the algorithm to the computation of regularization path plots and to assess the sensitivity of the tuning parameter in g-prior model selection. They then demonstrate the algorithm in a cross-validation context and use it to select the shrinkage parameter in
Bayesian regression. Show less

The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits,
SHM has been widely studied over the past two decades. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state—a condition that often does not hold in complex ‘‘real-world”… Show more

The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits,
SHM has been widely studied over the past two decades. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state—a condition that often does not hold in complex ‘‘real-world” systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time-series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment. Show less

The use of statistical methods for anomaly detection has become of interest to researchers in many subject areas. Structural health monitoring in particular has benefited from the versatility of statistical damage-detection techniques. We propose modeling structural vibration sensor output data using nonlinear time-series models. We demonstrate the improved performance of these models over currently used linear models. Whereas existing methods typically use a single sensor’s output for damage… Show more

The use of statistical methods for anomaly detection has become of interest to researchers in many subject areas. Structural health monitoring in particular has benefited from the versatility of statistical damage-detection techniques. We propose modeling structural vibration sensor output data using nonlinear time-series models. We demonstrate the improved performance of these models over currently used linear models. Whereas existing methods typically use a single sensor’s output for damage detection, we create a combined sensor analysis to maximize the efficiency of damage detection. From this combined analysis we may also identify the individual sensors that are most influenced by structural damage. Show less

This paper assesses the feasibility of vibration testing to detect structural damage caused by the settlement of buttresses in the Beverley Minster, a Gothic church located in the UK. Over the past eight centuries, the accumulated support settlements of the buttresses of Beverley Minster have pulled the main nave
walls outward, causing severe separation along the edges of the masonry vaults. Bays closer to the main crossing tower have remained intact; however, at the west end of the Minster,… Show more

This paper assesses the feasibility of vibration testing to detect structural damage caused by the settlement of buttresses in the Beverley Minster, a Gothic church located in the UK. Over the past eight centuries, the accumulated support settlements of the buttresses of Beverley Minster have pulled the main nave
walls outward, causing severe separation along the edges of the masonry vaults. Bays closer to the main crossing tower have remained intact; however, at the west end of the Minster, the crack width between the walls and vaults has reached about 150 mm, leading to approximately 200 mm of sag at the crown of
the vaults. Due to uneven settlement of buttresses along the nave of the church, the Minster now has ten nominally identical vaults at different damage states. In this work, two of these vaults representing the two extremes, the most damaged and undamaged structural states, are subjected to vibration testing with impact hammer excitation. From these vibration measurements, damage indicators are extracted in the
modal, frequency, and time domains. In the modal domain, the differences between modal parameters are observed to be comparable to measurement uncertainty and hence insufficient to reach conclusions about the presence of vault damage. However, the amplitudes of frequency response functions in the frequency
domain are observed to indicate a clear difference between the damaged and undamaged states of the structure. A time domain autoregressive model, support vector machine regression, is also found to be successful at indicating the differences between the two structural states of the vaults. We conclude that vibration measurements offer a practical solution to detect wall–vault separation in historic masonry monuments, provided that multiple damage indicators are evaluated. Show less