We compute the posterior distributions of the initial population and parameter of binary branching processes, in the limit of a large number of generations. We compare this Bayesian procedure with a more näıve one, based on hitting times of some random walks. In both cases, central limit theorems are available, with explicit variances.

Experimentation is a powerful methodology that enables scientists to empirically establish causal claims. However, one important criticism is that experiments merely provide a black-box view of causality and fail to identify causal mechanisms. Specifically, critics argue that although experiments can identify average causal effects, they cannot explain the process through which such effects com...

there have been many productive methods developed so far for optimization of multiple response surface (mrs) problems. this paper tends to review the most seminal approaches in mrs and discuss the strength and weakness of each of the approaches through existing aspects in mrs. a numerical example is included to compare results by different methods. finally some of the prominent areas for future...

the taguchi design of experiments was used to test the relative importance of medium components and environmental factors on poly(β-hydroxybutyrate)(phb) production by ralstonia eutropha. the optimum condition was obtained as: fructose concentration, 15 g/l; c/n ratio, 7.4; agitation speed 200 rpm; culture time, 40 h; temperature, 25 ° c; seed age, 15 h. at optimum condition the yield of phb pr...

in this work, boehmite sol was prepared by a previously applied and validated method; hydrolysis of aluminum chloride hexa-hydrate. in order to obtain precise results, the effect of ph after adding precipitating agent, aging time, peptizing temperature and ultrasonic vibration time on the crystallite size of final precipitate were investigated in a narrow range. the preparation conditions appli...

abstractthe purpose of this study was to investigate the controllable operating parameters influence, including ph, solid content, collector, co-collector, and depressant dose, and conditioning time, on apatite flotation kinetics. four first order flotation kinetic models are tested on batch flotation time-recovery profiles. the results of batch flotation tests and the fitting of first-order ki...

full factorial experimental design (23) for the evaluation of slurry ethylene polymerization in the presence of an industrial ticl4/mgcl2 ziegler-natta catalyst was employed. the following parameters were used as independentvariables: al/ti molar ratio, reaction temperature and hydrogen partial pressure. the total polymerization pressure was 9 bar. catalyst activity, mfi (melt flow index) and m...

Marketers have recently begun to embrace complex experimental designs for marketing and advertising testing. Full-factorial, fractional-factorial and Plackett–Burman designs have given marketers new statistical tools to increase the speed, power, and profitability of their testing programs. This case study shows how well constructed and managed experimental designs offer marketing professionals...