Updated July 25, 2006: Young-Earth creationists consider the helium diffusion studies of D. Russell Humphreys and others to be one of their greatest achievements in arguing for a 6,000 year old Earth. A geologist shows that these studies are extensively flawed and include: serious miscalculations in their data, sampling the wrong rock type, failing to eliminate possible contamination, using equations that are based on invalid assumptions and relying on questionable data. Appendices C and D have been added in response to Dr. Humphreys' most recent statements in his January 2006 "Trueorigins" essay.

Troubleshooting refrigeration systems can be complex and frustrating, so put aside any assumptions and inspect the system thoroughly before making any diagnosis.

Recent DNA findings from Pompeii reveal complex ancestry and social diversity, challenging earlier assumptions about family structures and cultural roles in the ancient city. Analysing skeletal remains has shown that some groups presumed to be family members were not biologically related, while traditional gender roles were also re-evaluated. This research highlights the cosmopolitan nature of Pompeii’s society and opens a new chapter in understanding life before the eruption of Mount Vesuvius.

Apr 18, 2024

The human tragedy continuing to unfold in Gaza and Israel reminds us how important it is to get strategic forecasting right. While in no way excusing Hamas’ culpability for 7 October, we also cannot dismiss the fact that the failure to anticipate and prepare for such an attack has had grave consequences for communities on both sides of this conflict, undermined efforts to bring peace and prosperity to the region, and affected global interests through the expansion of the conflict to the Red Sea and potentially beyond. 

National Bureau of Economic Research

Michael P. Fay, Michael A. Proschan

Source: Statist. Surv., Volume 4, 1--39.

Abstract:
In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value. Here we collect many such perspectives for the two-sample t-test, the WMW test and other related tests. We discuss validity and consistency under each perspective and discuss recommendations between the tests in light of these many different perspectives. Finally, we briefly discuss a decision rule for testing genetic neutrality where knowledge of the many perspectives is vital to the proper interpretation of the decision rule.

Reinhard Heckel, Nihar B. Shah, Kannan Ramchandran, Martin J. Wainwright.

Source: The Annals of Statistics, Volume 47, Number 6, 3099--3126.

Abstract:
We consider sequential or active ranking of a set of $n$ items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of prespecified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-$k$ items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does depend on whether or not the underlying pairwise probability matrix, satisfies a particular structural property, unlike a significant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley–Terry–Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.

Tobias Zwingmann, Hajo Holzmann.

Source: Bernoulli, Volume 26, Number 1, 323--351.

Abstract:
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo- convergence as introduced in A. Bücher, J. Segers and S. Volgushev (2014), ‘ When Uniform Weak Convergence Fails: Empirical Processes for Dependence Functions and Residuals via Epi- and Hypographs ’, Annals of Statistics 42 . We impose assumptions for which it is known that weak convergence with respect to the supremum norm generally fails to hold. For quantiles, we consider stationary observations, where the marginal distribution function is assumed to be strictly increasing and continuous except for finitely many points and to admit strictly positive – possibly infinite – left- and right-sided derivatives. For expectiles, we focus on independent and identically distributed (i.i.d.) observations. Only a finite second moment and continuity at the boundary points but no further smoothness properties of the distribution function are required. We also show consistency of the bootstrap for this mode of convergence in the i.i.d. case for quantiles and expectiles.

It turns out you can still be a high-performing athlete on a plant-based diet.

Retirement calculators employ different assumptions to help users predict whether their rate of savings will support their current lifestyle after they quit work.

Achieving 10 per cent nominal growth and 1.2x gross tax revenue buoyancy appears stretched