769 research outputs found
Bayesian isotonic logistic regression via constrained splines: an application to estimating the serve advantage in professional tennis
In professional tennis, it is often acknowledged that the server has an initial advantage. Indeed, the majority of points are won by the server, making the serve one of the most important elements in this sport. In this paper, we focus on the role of the serve advantage in winning a point as a function of the rally length. We propose a Bayesian isotonic logistic regression model for the probability of winning a point on serve. In particular, we decompose the logit of the probability of winning via a linear combination of B-splines basis functions, with athlete-specific basis function coefficients. Further, we ensure the serve advantage decreases with rally length by imposing constraints on the spline coefficients. We also consider the rally ability of each player, and study how the different types of court may impact on the player’s rally ability. We apply our methodology to a Grand Slam singles matches dataset
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Zonal And Regional Load Forecasting In The New England Wholesale Electricity Market: A Semiparametric Regression Approach
Power system planning, reliability analysis and economically efficient capacity scheduling all rely heavily on electricity demand forecasting models. In the context of a deregulated wholesale electricity market, using scheduling a region’s bulk electricity generation is inherently linked to future values of demand. Predictive models are used by municipalities and suppliers to bid into the day-ahead market and by utilities in order to arrange contractual interchanges among neighboring utilities. These numerical predictions are therefore pervasive in the energy industry.
This research seeks to develop a regression-based forecasting model. Specifically, electricity demand is modeled as a function of calendar effects, lagged demand effects, weather effects, and a stochastic disturbance. Variables such as temperature, wind speed, cloud cover and humidity are known to be among the strongest predictors of electricity demand and as such are used as model inputs. It is well known, however, that the relationship between demand and weather can be highly nonlinear. Rather than assuming a linear functional form, the structural change in these relationships is explored. Those variables that indicate a nonlinear relationship with demand are accommodated with penalized splines in a semiparametric regression framework. The equivalence between penalized splines and the special case of a mixed model formulation allows for model estimation with currently available statistical packages such as R, STATA and SAS.
Historical data are available for the entire New England region as well as for the smaller zones that collectively make up the regional grid. As such, a secondary research objective of this thesis is to explore whether or not an aggregation of zonal forecasts might perform better than those produced from a single regional model. Prior to this research, neither the applicability of a semiparametric regression-based approach towards load forecasting nor the potential improvement in forecasting performance resulting from zonal load forecasting has been investigated for the New England wholesale electricity market
Quantum Geometry and Quantum Gravity
The purpose of this contribution is to give an introduction to quantum
geometry and loop quantum gravity for a wide audience of both physicists and
mathematicians. From a physical point of view the emphasis will be on
conceptual issues concerning the relationship of the formalism with other more
traditional approaches inspired in the treatment of the fundamental
interactions in the standard model. Mathematically I will pay special attention
to functional analytic issues, the construction of the relevant Hilbert spaces
and the definition and properties of geometric operators: areas and volumes.Comment: To appear in the AIP Conference Proceedings of the XVI International
Fall Workshop on Geometry and Physics, Lisbon - Portugal, 5-8 September 200
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
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