A Bayesian marked spatial point processes model for basketball shot chart

The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017--2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups

Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse

Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern. We propose a Bayesian semiparametric regression model where the observed spatial points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is piecewise constant, approached with a powered Chinese restaurant process prior which prevents an unnecessarily large number of pieces. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the proposed methods. The performance of the methods is validated in an extensive simulation study. In application to the locations of Beilschmiedia pendula trees in the Barro Colorado Island forest dynamics research plot in central Panama, the spatial heterogeneity is attributed to a subset of soil measurements in addition to geographic measurements with a spatially varying baseline intensity.Comment: 21 pages, 7 figure

On Bayesian Methods for Spatial Point Processes

Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing and understanding the pattern. Spatial point processes are a widely used to model for such data. Additional measurements are often available along with spatial points, which are called marks. Such data can be modeled using marked spatial point processes. The first part of this dissertation focuses on the heterogeneity of point processes. We propose a Bayesian semiparametric model where the observed points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is approached with a powered Chinese restaurant process (PCRP) prior. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed. The performance of the methods is validated in an extensive simulation study and the Beilschmiedia pendula trees data. Spatial smoothness is often observed in some environmental spatial point pattern data, and the PCRP may have lower efficiency for such data since it allows more flexibility without any spatial constraint. Distance dependent Chinese restaurant process (ddCRP) can be easily realized by introducing a decay function to Chinese restaurant process. The second part of this dissertation introduces the ddCRP model with Bayesian inference methods, whose performance is illustrated using simulation study. In the third part, we investigate the marked spatial point process, which is motivated by the basketball shot data. We develop a Bayesian joint model of the mark and the intensity, where the intensity is incorporated in the mark’s model as a covariate. An MCMC algorithm is developed to draw posterior samples from this model. Two Bayesian model comparison criteria, the modified Deviance Information Criterion and the modified Logarithm of the Pseudo-Marginal Likelihood, are developed to assess the fitness of different models focusing on the mark. Simulation study and application to NBA basketball shot data are conducted to show the performance of proposed methods

Building Blocks for the Molecular Expression of Quantum Cellular Automata. Isolation and Characterization of a Covalently Bonded Square Array of Two Ferrocenium and Two Ferrocene Complexes

The suitability of [{(η5-C5H5)Fe(η5-C5H4)}4(η4-C4)Co(η5-C5H5)][PF6]2, [1][PF6]2, for use as a molecular quantum cellular automata (QCA) cell is demonstrated. To this end the structure of 1 in the solid state and the conversion of 1 to mono- and dicationic mixed-valence complexes have been accomplished. The latter compounds have been isolated as pure materials and characterized by IR, EPR, and Mössbauer spectroscopies and single-crystal XRD (monocation only) and magnetic susceptibility measurements. Near-IR spectra demonstrate the mixed valence character of the cations (valence trapped on the IR, EPR and Mössbauer time scales), and the energies of the intervalence charge-transfer bands provide a measure of the hole hopping frequency

Meroterpenoids with Diverse Ring Systems from the Sponge-Associated Fungus Alternaria sp. JJY-32

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Surface Fluorination for Controlling the PbS Quantum Dot Bandgap and Band Offset

Fully fluorinated perfluorocarbon ligands are shown to modify the energetics and dielectric environment of quantum dots (QDs), resulting in a large hypsochromic shift in the optical gap. The original oleic acid (OA) ligands on PbS QDs can be completely replaced with thiolate and carboxylate-based perfluorocarbons, e.g., -SCF₃ and CF₃(CF₂)₁₄COOH (pFA), respectively. Ultraviolet photoelectron spectroscopy indicates that the work function varies by >1.3 eV depending on the electronegativity of the surface ligand, while cyclic voltammetry shows that an OA:pFA ratio of ∼2:1 increases the oxidation potential by 0.18 eV in solution. The diminished reduction potential of the conduction band is confirmed by photoinduced electron transfer experiments. The short thiolate ligands, -SCF₃ and -SCH₃, enhance the electron-donating ability of PbS QDs up to 7-fold because of an increase in the permeability of the ligand shell. This work shows that electron-withdrawing halogens like fluorine and chlorine can control the bandgap and band offsets of nanocrystals for the future design and optimization of functional organic/inorganic hybrid nanostructures