Exact and approximate sum representations for the Dirichlet process
摘要:
AbstractThe Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the “stick‐breaking” construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonpara‐metric hierarchical models.
Exact and approximate sum representations for the Dirichlet process
摘要:
AbstractThe Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the “stick‐breaking” construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonpara‐metric hierarchical models.
Selective synthesis of 2-ethoxy alkanes through ethoxylation of 1-alkenes with bioethanol over zeolite beta catalyst in a liquid phase continuous process
作者:Sambhu Radhakrishnan、Joris Franken、Johan A. Martens
DOI:10.1039/c2gc35220f
日期:——
1-Hexene was ethoxylated with ethanol and ethanol–water mixtures mimicking bioethanol in a liquid phase, continuous flow process over a fixed bed of zeolite beta catalyst at a reaction temperature of 423 K and a pressure of 6 MPa. The selectivity for ethoxy alkanes on a hexene basis exceeded 90%. GC-MS, 1H & 13C-NMR and 13C DEPT NMR confirmed the main reaction products to be 2-ethoxy hexane and 3-ethoxy hexane in molar ratio 20 : 1. Side products were diethyl ether from ethanol and dodecenes and hexanol from 1-hexene. Under optimized reaction conditions, the catalyst was stable for at least 14 hours on-stream. The 2-ethoxylation activity of 1-alkenes by zeolite beta was confirmed in reactions with 1-octene and 1-decene. 1-Alkenes can be synthesized out of biomass via conversion into synthesis gas and the Fischer–Tropsch process. The here presented ethoxylation process could contribute green chemicals to the diesel pool and presents a pathway for synthesis of high boiling solvents.
Exact and approximate sum representations for the Dirichlet process
作者:Hemant Ishwaran、Mahmoud Zarepour
DOI:10.2307/3315951
日期:2002.6
AbstractThe Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the “stick‐breaking” construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonpara‐metric hierarchical models.