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

Assessing the Increasing Strength of Charter Laws

Since 2005, the National Alliance for Public Charter Schools (National Alliance) has advocated for high-quality public charter school laws. With the support of a working group with deep expertise in public charter school law, we released a model charter law in 2009 with 20 essential components focused on creating and supporting high-quality public charter schools.After we released the model charter law, we then undertook an extensive review of all existing state charter laws in comparison to the model law and issued annual state charter laws rankings reports in 2010, 2011, 2012, 2013, 2014 and 2015. Each year, we sought input on the rankings reports from a variety of charter stakeholders and made adjustments to the reports' scoring rubrics as needed. In the rankings reports, we showed where state scores shifted as a result of policy change, but we also noted where changes occurred as a result of adjustments in our scoring rubrics or further clarifications about existing policies in states that would affect the state's rankings score.The purpose of this report is to sync the ratings from the multiple rankings reports so that rating changes over time are primarily the result of changes in policy, not from changes to our scoring rubrics and clarifications about existing policies

Club-guessing, stationary reflection, and coloring theorems

We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.Comment: Initial public versio

Wet Strength Resins

Wet strength is defined as a paper which has extraordinary resistance to rupture or disintegration when saturated with water. This definition has been interpreted as if a paper sample retains more than 15% of its dry strength when wetted, it can be considered to have wet strength properties. Wet strength resins are chemicals that aid in wet strength, and they have been around since the 1940\u27s. These wet strength resins help to protect paper and paper products from breaking down in the presence of water and high humidity. There are many uses for wet strength resins these days, Some of these are: To protect from outdoor weather, to aid in drying and wiping, to wrap up food products, and to help in things that must be totally submerged in water. The resins compared are urea formaldehyde, melamine formaldehyde, polyamide epichlorohydrin, and polyamine epichiorohydrin. These resins when compared showed that the newer PAE resins had better wet strength properties than the older formaldehydes. Because of this reason and that formaldehyde is a public hazard and is regulated by OSHA, the PAE resins came out better in cost and overall usage