Optimal testing of equivalence hypotheses

In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest. The null hypothesis asserts g(\theta)\notin (a,b) versus the alternative g(\theta)\in (a,b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drugs, a brand name and a proposed generic version, have the same therapeutic effect. Little optimal theory is available for such testing problems, and it is the purpose of this paper to provide an asymptotic optimality theory. Thus, we provide asymptotic upper bounds for what is achievable, as well as asymptotically uniformly most powerful test constructions that attain the bounds. The asymptotic theory is based on Le Cam's notion of asymptotically normal experiments. In order to approximate a general problem by a limiting normal problem, a UMP equivalence test is obtained for testing the mean of a multivariate normal mean.Comment: Published at http://dx.doi.org/10.1214/009053605000000048 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Terrapene ornata

Number of Pages: 4Integrative BiologyGeological Science

Natural selection and genetic variation in a promising Chagas disease drug target: Trypanosoma cruzi trans-sialidase

Rational drug design is a powerful method in which new and innovative therapeutics can be designed based on knowledge of the biological target aiming to provide more efficacious and responsible therapeutics. Understanding aspects of the targeted biological agent is important to optimize drug design and preemptively design to slow or avoid drug resistance. Chagas disease, an endemic disease for South and Central America and Mexico is caused by Trypanosoma cruzi, a protozoan parasite known to consist of six separate genetic clusters or DTUs (discrete typing units). Chagas disease therapeutics are problematic and a call for new therapeutics is widespread. Many researchers are working to use rational drug design for developing Chagas drugs and one potential target that receives a lot of attention is the T. cruzi trans-sialidase protein. Trans-sialidase is a nuclear gene that has been shown to be associated with virulence. In T. cruzi, trans-sialidase (TcTS) codes for a protein that catalyzes the transfer of sialic acid from a mammalian host coating the parasitic surface membrane to avoid immuno-detection. Variance in disease pathology depends somewhat on T. cruzi DTU, as well, there is considerable genetic variation within DTUs. However, the role of TcTS in pathology variance among and within DTU’s is not well understood despite numerous studies of TcTS. These previous studies include determining the crystalline structure of TcTS as well as the TS protein structure in other trypanosomes where the enzyme is often inactive. However, no study has examined the role of natural selection in genetic variation in TcTS. In order to understand the role of natural selection in TcTS DNA sequence and protein variation, we sequenced 540 bp of the TcTS gene from 48 insect vectors. Because all 48 sequences had multiple polymorphic bases, we examined cloned sequences from two of the insect vectors. The data are analyzed to understand the role of natural selection in shaping genetic variation in TcTS and interpreted in light of the possible role of TcTS as a drug target

Religious Affiliation and Individual International-Policy Preferences in the United States

Empirical examination of individual-level survey data on national identity, in general, reveals a significant relationship between religious affiliation and an individual’s international-policy preferences and that this relationship varies across Protestant denominations. Specifically, we test attitudes toward import and immigration policies, the role of international institutions, and unilateral policy actions. The empirical results indicate that individuals affiliated with conservative Protestant denominations are more likely to support positions on international issues that can be regarded as consistent with the anti-globalist right. We also find evidence of a reinforcing regional effect among conservatives in the south, and differences in the preferences of Baptist and non-Baptist African Americans

The G\mathcal{G}-invariant and catenary data of a matroid

The catenary data of a matroid $M$ of rank $r$ on $n$ elements is the vector $(\nu(M;a_0,a_1,\ldots,a_r))$, indexed by compositions $(a_0,a_1,\ldots,a_r)$, where $a_0 \geq 0$,\, $a_i > 0$ for $i \geq 1$, and $a_0+ a_1 + \cdots + a_r = n$, with the coordinate $\nu (M;a_0,a_1, \ldots,a_r)$ equal to the number of maximal chains or flags $(X_0,X_1, \ldots,X_r)$ of flats or closed sets such that $X_i$ has rank $i$,\, $|X_0| = a_0$, and $|X_i - X_{i-1}| = a_i$. We show that the catenary data of $M$ contains the same information about $M$ as its $\mathcal{G}$-invariant, which was defined by H. Derksen [\emph{J.\ Algebr.\ Combin.}\ 30 (2009) 43--86]. The Tutte polynomial is a specialization of the $\mathcal{G}$-invariant. We show that many known results for the Tutte polynomial have analogs for the $\mathcal{G}$-invariant. In particular, we show that for many matroid constructions, the $\mathcal{G}$-invariant of the construction can be calculated from the $\mathcal{G}$-invariants of the constituents and that the $\mathcal{G}$-invariant of a matroid can be calculated from its size, the isomorphism class of the lattice of cyclic flats with lattice elements labeled by the rank and size of the underlying set. We also show that the number of flats and cyclic flats of a given rank and size can be derived from the $\mathcal{G}$-invariant, that the $\mathcal{G}$-invariant of $M$ is reconstructible from the deck of $\mathcal{G}$-invariants of restrictions of $M$ to its copoints, and that, apart from free extensions and coextensions, one can detect whether a matroid is a free product from its $\mathcal{G}$-invariant.Comment: 25 page