A Hierarchical Bayesian Model of Pitch Framing

Since the advent of high-resolution pitch tracking data (PITCHf/x), many in the sabermetrics community have attempted to quantify a Major League Baseball catcher's ability to "frame" a pitch (i.e. increase the chance that a pitch is called as a strike). Especially in the last three years, there has been an explosion of interest in the "art of pitch framing" in the popular press as well as signs that teams are considering framing when making roster decisions. We introduce a Bayesian hierarchical model to estimate each umpire's probability of calling a strike, adjusting for pitch participants, pitch location, and contextual information like the count. Using our model, we can estimate each catcher's effect on an umpire's chance of calling a strike.We are then able to translate these estimated effects into average runs saved across a season. We also introduce a new metric, analogous to Jensen, Shirley, and Wyner's Spatially Aggregate Fielding Evaluation metric, which provides a more honest assessment of the impact of framing

Estimating an NBA player's impact on his team's chances of winning

Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams' chances of winning. We propose a Bayesian linear regression model to estimate an individual player's impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics.Comment: To appear in the Journal of Quantitative Analysis of Spor

A new BART prior for flexible modeling with categorical predictors

Default implementations of Bayesian Additive Regression Trees (BART) represent categorical predictors using several binary indicators, one for each level of each categorical predictor. Regression trees built with these indicators partition the levels using a ``remove one a time strategy.'' Unfortunately, the vast majority of partitions of the levels cannot be built with this strategy, severely limiting BART's ability to ``borrow strength'' across groups of levels. We overcome this limitation with a new class of regression tree and a new decision rule prior that can assign multiple levels to both the left and right child of a decision node. Motivated by spatial applications with areal data, we introduce a further decision rule prior that partitions the areas into spatially contiguous regions by deleting edges from random spanning trees of a suitably defined network. We implemented our new regression tree priors in the flexBART package, which, compared to existing implementations, often yields improved out-of-sample predictive performance without much additional computational burden. We demonstrate the efficacy of flexBART using examples from baseball and the spatiotemporal modeling of crime.Comment: Software available at https://github.com/skdeshpande91/flexBAR

Simultaneous Variable and Covariance Selection with the Multivariate Spike-and-Slab Lasso

We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Rockova & George (2014) targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes

Estimating an NBA Player’s Impact on is Team’s Chances of Winning

Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams’ chances of winning. We propose a Bayesian linear regression model to estimate an individual player’s impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics

Surface Chemistry Of Application Specific Pads And Copper Chemical Mechanical Planarization

Advances in the interconnection technology have played a key role in the continued improvement of the integrated circuit (IC) density, performance and cost. Copper (Cu) metallization, dual damascenes processing and integration of copper with low dielectric constant material are key issues in the IC industries. Chemical mechanical planarization of copper (CuCMP) has emerged as an important process for the manufacturing of ICs. Usually, Cu-CMP process consists of several steps such as the removal of surface layer by mechanical action of the pad and the abrasive particles, the dissolution of the abraded particles in the CMP solution, and the protection of the recess areas. The CMP process occurs at the atomic level at the pad/slurry/wafer interface, and hence, slurries and polishing pads play critical role in its successful implementation. The slurry for the Cu-CMP contains chemical components to facilitate the oxidation and removal of excess Cu as well as passivation of the polished surface. During the process, these slurry chemicals also react with the pad. In the present study, investigations were carried out to understand the effect of hydrogen peroxide (H2O2) as an oxidant and benzotriazole (BTA) as an inhibitor on the CMP of Cu. Interaction of these slurry components on copper has been investigated using electrochemical studies, x-ray photoelectron spectroscopy (XPS) and secondary ion mass spectroscopy (SIMS). In the presence of 0.1M glycine, Cu removal rate was found to be high in the solution containing 5% H2O2 at pH 2 because of the Cu-glycine complexation reaction. The dissolution rate of the Cu was found to increase due to the formation of highly soluble Cu-glycine complex in the presence of H2O2. Addition of 0.01M BTA in the solution containing 0.1M glycine and 5% H2O2 at pH 2 exhibited a reduction in the Cu removal rate due to the formation of Cu-BTA complex on the surface of the Cu further inhibiting the dissolution. XPS and SIMS investigations revealed the formation of such Cu-glycine complex, which help understand the mechanism of the Cu-oxidant-inhibitor interaction during polishing. Along with the slurry, pads used in the Cu-CMP process have direct influence an overall process. To overcome problems associated with the current pads, new application specific pad (ASP) have been developed in collaboration with PsiloQuest Inc. Using plasma enhanced chemical vapor deposition (PECVD) process; surface of such ASP pads were modified. Plasma treatment of a polymer surface results in the formation of various functional groups and radicals. Post plasma treatment such as chemical reduction or oxidation imparts a more uniform distribution of such functional groups on the surface of the polymer resulting in unique surface properties. The mechanical properties of such coated pad have been investigated using nanoindentation technique in collaboration with Dr. Vaidyanathan’s research group. The surface morphology and the chemistry of the ASP are studied using scanning electron microcopy (SEM), x-ray photoelectron spectroscopy (XPS), and fourier transform infrared spectroscopy (FTIR) to understand the formation of different chemical species on the surface. It is observed that the mechanical and the chemical properties of the pad top surface are a function of the PECVD coating time. Such PECVD treated pads are found to be hydrophilic and do not require being stored in aqueous medium during the not-in-use period. The metal removal rate using such surface modified polishing pad is found to increase linearly with the PECVD coating time. Overall, this thesis is an attempt to optimize the two most important parameters of the Cu-CMP process viz. slurry and pads for enhanced performance and ultimately reduce the cost of ownership (CoO)

Sparse Gaussian chain graphs with the spike-and-slab LASSO: Algorithms and asymptotics

The Gaussian chain graph model simultaneously parametrizes (i) the direct effects of $p$ predictors on $q$ correlated outcomes and (ii) the residual partial covariance between pair of outcomes. We introduce a new method for fitting sparse Gaussian chain graph models with spike-and-slab LASSO (SSL) priors. We develop an Expectation-Conditional Maximization algorithm to obtain sparse estimates of the $p \times q$ matrix of direct effects and the $q \times q$ residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior concentration rate for our model, buttressing our method's excellent empirical performance with strong theoretical guarantees. We use our method to reanalyze a dataset from a study of the effects of diet and residence type on the composition of the gut microbiome of elderly adults

Size dependency variation in lattice parameter and valency states in nanocrystalline cerium oxide

A correlation between the particle size and the lattice parameter has been established in nanocerium oxide particles (3-30 nm). The variation in the lattice parameter is attributed to the lattice strain induced by the introduction of Ce3+ due to the formation of oxygen vacancies. Lattice strain was observed to decrease with an increase in the particle size. Ce3+ ions concentration increased from 17% to 44% with the reduction in the particle size