Higher-order, multiplicatively weighted Voronoi diagrams: A new approach to trade area analysis

Trade area models have traditionally been classified into one of two groups: spatial monopoly models or market penetration approaches. Spatial monopoly models define trade areas in a deterministic manner, while market penetration models construct market areas that are probabilistic. Past research has grouped Voronoi diagram models exclusively with the spatial monopoly approach. However, the research contained within this thesis demonstrates that Voronoi diagrams can be used to generate trade areas that are consistent with market penetration models. This thesis introduces two new Voronoi diagrams: the order-k, multiplicatively weighted Voronoi diagram (OKMWVD) and the ordered order-k, multiplicatively weighted Voronoi diagram (OOKMWVD). When interpreted as trade area models, these diagrams generate market areas for a set of facilities which are overlapping and probabilistic. These new Voronoi diagrams allow for the simultaneous inclusion of a weight (measuring facility attraction) and consumer choice sets. The new models are demonstrated on data collected for the supermarkets located within the cities of Kitchener and Waterloo. This application shows how Voronoi diagrams can be used to generate sales estimates for retail facilities. The OOKMWVD allows for the examination of the effect of different consumer preference levels on the sales estimates of an individual facility

Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

We introduce a new class of sequential Monte Carlo methods called Nested Sampling via Sequential Monte Carlo (NS-SMC), which reframes the Nested Sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows convergence results to be obtained in the setting when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. As the original NS algorithm is a special case of NS-SMC, this provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. For applications of NS-SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. Finally, a numerical study is conducted where the performance of NS-SMC and temperature-annealed SMC is compared on several challenging and realistic problems. MATLAB code for our experiments is made available at https://github.com/LeahPrice/SMC-NS .Comment: 45 pages, some minor typographical errors fixed since last versio

The Pawley House (38GE15), Georgetown County, South Carolina

https://scholarcommons.sc.edu/archanth_books/1013/thumbnail.jp

Archeological Survey of the North End of the Isle of Palms, Charleston County, South Carolina

https://scholarcommons.sc.edu/archanth_books/1044/thumbnail.jp

Adaptively switching between a particle marginal Metropolis-Hastings and a particle Gibbs kernel in SMC2^2

Sequential Monte Carlo squared (SMC$^2$; Chopin et al., 2012) methods can be used to sample from the exact posterior distribution of intractable likelihood state space models. These methods are the SMC analogue to particle Markov chain Monte Carlo (MCMC; Andrieu et al., 2010) and rely on particle MCMC kernels to mutate the particles at each iteration. Two options for the particle MCMC kernels are particle marginal Metropolis-Hastings (PMMH) and particle Gibbs (PG). We introduce a method to adaptively select the particle MCMC kernel at each iteration of SMC$^2$, with a particular focus on switching between a PMMH and PG kernel. The resulting method can significantly improve the efficiency of SMC$^2$ compared to using a fixed particle MCMC kernel throughout the algorithm. Code for our methods is available at https://github.com/imkebotha/kernel_switching_smc2

Atlas Estadistico Republica Argentina

xiv+228hlm.;23c

Brief of Amici Curiae The Defender Initiative and ACLU of South Carolina

Brief of Amici Curiae The Defender Initiative and ACLU of South Carolin

Brief of Amici Curiae The Defender Initiative and ACLU of South Carolina

Brief of Amici Curiae The Defender Initiative and ACLU of South Carolin