Analysis on the evolution process of BFW-like model with explosive percolation of multiple giant components

Recently, the modified BFW model on random graph [Phys. Rev. Lett., 106, 115701 (2011)], which shows a strongly discontinuous percolation transition with multiple giant components, has attracted much attention from physicists, statisticians and materials scientists. In this paper, by establishing the theoretical expression of evolution equations on the modified BFW model, the steady-state and evolution process are analyzed and a close correspondence is built between the values of parameter \alpha and the number of giant components in steady-states, which fits very well with the numerical simulations. In fact, with the value of \alpha decreasing to 0.25, the error between theoretical and numerical results is smaller than 4% and trends to 0 rapidly. Furthermore, the sizes of giant components for different evolution strategies can also be obtained by solving some constraints derived from the evolution equations. The analysis of the steady-state and evolution process is of great help to explain why the percolation of modified BFW model is explosive and how explosive it is.Comment: 12 pages, 5 figure

Objective Bayes and Conditional Frequentist Inference

Objective Bayesian methods have garnered considerable interest and support among statisticians, particularly over the past two decades. It has often been ignored, however, that in some cases the appropriate frequentist inference to match is a conditional one. We present various methods for extending the probability matching prior (PMP) methods to conditional settings. A method based on saddlepoint approximations is found to be the most tractable and we demonstrate its use in the most common exact ancillary statistic models. As part of this analysis, we give a proof of an exactness property of a particular PMP in location-scale models. We use the proposed matching methods to investigate the relationships between conditional and unconditional PMPs. A key component of our analysis is a numerical study of the performance of probability matching priors from both a conditional and unconditional perspective in exact ancillary models. In concluding remarks we propose many routes for future research

Biologists meet statisticians: A workshop for young scientists to foster interdisciplinary team work

Life science and statistics have necessarily become essential partners. The need to plan complex, structured experiments, involving elaborated designs, and the need to analyse datasets in the era of systems biology and high throughput technologies has to build upon professional statistical expertise. On the other hand, conducting such analyses and also developing improved or new methods, also for novel kinds of data, has to build upon solid biological understanding and practise. However, the meeting of scientists of both fields is often hampered by a variety of communicative hurdles - which are based on field-specific working languages and cultural differences. As a step towards a better mutual understanding, we developed a workshop concept bringing together young experimental biologists and statisticians, to work as pairs and learn to value each others competences and practise interdisciplinary communication in a casual atmosphere. The first implementation of our concept was a cooperation of the German Region of the International Biometrical Society and the Leibnitz Institute DSMZ-German Collection of Microorganisms and Cell Cultures (short: DSMZ), Braunschweig, Germany. We collected feedback in form of three questionnaires, oral comments, and gathered experiences for the improvement of this concept. The long-term challenge for both disciplines is the establishment of systematic schedules and strategic partnerships which use the proposed workshop concept to foster mutual understanding, to seed the necessary interdisciplinary cooperation network, and to start training the indispensable communication skills at the earliest possible phase of education