75 research outputs found
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
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 predictors on 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 matrix of direct effects and the 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
A Bayesian analysis of the time through the order penalty in baseball
As a baseball game progresses, batters appear to perform better the more
times they face a particular pitcher. The apparent drop-off in pitcher
performance from one time through the order to the next, known as the Time
Through the Order Penalty (TTOP), is often attributed to within-game batter
learning. Although the TTOP has largely been accepted within baseball and
influences many managers' in-game decision making, we argue that existing
approaches of estimating the size of the TTOP cannot disentangle continuous
evolution in pitcher performance over the course of the game from
discontinuities between successive times through the order. Using a Bayesian
multinomial regression model, we find that, after adjusting for confounders
like batter and pitcher quality, handedness, and home field advantage, there is
little evidence of strong discontinuity in pitcher performance between times
through the order. Our analysis suggests that the start of the third time
through the order should not be viewed as a special cutoff point in deciding
whether to pull a starting pitcher.Comment: Accepted to JQA
Are you using test log-likelihood correctly?
Test log-likelihood is commonly used to compare different models of the same
data or different approximate inference algorithms for fitting the same
probabilistic model. We present simple examples demonstrating how comparisons
based on test log-likelihood can contradict comparisons according to other
objectives. Specifically, our examples show that (i) approximate Bayesian
inference algorithms that attain higher test log-likelihoods need not also
yield more accurate posterior approximations and (ii) conclusions about
forecast accuracy based on test log-likelihood comparisons may not agree with
conclusions based on root mean squared error.Comment: Presented at the ICBINB Workshop at NeurIPS 202
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