Complete Classes for Sequential Tests of Hypotheses

We consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the alternative hypothesis. A complete class for testing closure of null against closure of alternative is an essentially complete class for testing null against alternative. Furthermore, a complete class for testing closure of null against closure of alternative is a complete class for testing null against alternative when the risks have certain continuity properties. Such continuity properties do hold in many cases. Three models are treated. The first is when the closure of the null space is compact and the cost of the first observation is positive. Under very unrestrictive conditions it is shown that the Bayes tests form a complete class. This result differs considerably from most fixed sample analogues that have been studied. The second model is when the closure of the null space is compact, the distributions are exponential family, and the cost of the first observation is zero. The third model is for the one dimensional exponential family case when the hypotheses are one sided

A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications

Suppose a random variable has a density belonging to a one parameter family which has strict monotone likelihood ratio. For inference regarding the parameter (or a monotone function of the parameter) consider the loss function to be bowl shaped for each fixed parameter and also to have each action be a point of increase or a point of decrease for some value of the parameter. Under these conditions, given any nonmonotone decision procedure, a unique monotone procedure is constructed which is strictly better than the given procedure for all the above loss functions. This result has application to the following areas: combining data problems, sufficiency, a multivariate one-sided testing problem

Correction: Complete Classes for Sequential Tests of Hypotheses

Theorems 3.1 and 3.2 as stated are incorrect. Corrected versions of these results are given below. Theorem 3.1 was concerned with an essentially complete class. Theorem 3.2 was concerned with a complete class. The correlations do affect a qualitative change in Theorem 3.2 in that now the result requires an assumption of a one dimensional exponential family and treats only a one-sided testing problem. There is essentially no qualitative change in Theorem 3.1, where the assumptions on distributions are minimal and there are no changes in the rest of the paper. The new version of Theorem 3.1 is also concerned with an essentially complete class. To describe this class let D* be the class of procedures characterized by (γ, ρ, π1*, T1*, T2*) where γ is the probability of stopping at time zero, ρ is the probability of rejection given that the procedure stopped at time zero and (π1*, T1*, T2*) are defined on pages 384 and 385, π1* ≥ c. A procedures δ corresponding to a (γ, ρ, π1*, T1*, T2*) lies in D* if whenever 0 ≤ \u3c 1, δ is conditional Bayes with respect to (π1*, T1*, T2*) given that an observation had been taken

On the Admissibility or Inadmissibility of Fixed Sample Size Tests in a Sequential Setting

Questions pertaining to the admissibility of fixed sample size tests of hypotheses, when sequential tests are available, are considered. For the normal case with unknown mean, suppose the risk function is a linear combination of probability of error and expected sample size. Then any fixed sample size test, with sample size n ⩾ 2, is inadmissible. On the other hand, suppose the risk function consists of the pair of components, probability of error and expected sample size. Then any optimal fixed sample size test for the one sided hypothesis is admissible. When the variance of the normal distribution is unknown, t-tests are studied. For one-sided hypotheses and componentwise risk functions the fixed sample size t-test is inadmissible if and only if the absolute value of the critical value of the test is greater than or equal to one. This implies that for the most commonly used sizes, the fixed sample size t-test is inadmissible. Other loss functions are discussed. Also an example for a normal mean problem is given where a nonmonotone test cannot be improved on by a monotone test when the risk is componentwise

Automatic Extraction of Protein Point Mutations Using a Graph Bigram Association

Protein point mutations are an essential component of the evolutionary and experimental analysis of protein structure and function. While many manually curated databases attempt to index point mutations, most experimentally generated point mutations and the biological impacts of the changes are described in the peer-reviewed published literature. We describe an application, Mutation GraB (Graph Bigram), that identifies, extracts, and verifies point mutations from biomedical literature. The principal problem of point mutation extraction is to link the point mutation with its associated protein and organism of origin. Our algorithm uses a graph-based bigram traversal to identify these relevant associations and exploits the Swiss-Prot protein database to verify this information. The graph bigram method is different from other models for point mutation extraction in that it incorporates frequency and positional data of all terms in an article to drive the point mutation–protein association. Our method was tested on 589 articles describing point mutations from the G protein–coupled receptor (GPCR), tyrosine kinase, and ion channel protein families. We evaluated our graph bigram metric against a word-proximity metric for term association on datasets of full-text literature in these three different protein families. Our testing shows that the graph bigram metric achieves a higher F-measure for the GPCRs (0.79 versus 0.76), protein tyrosine kinases (0.72 versus 0.69), and ion channel transporters (0.76 versus 0.74). Importantly, in situations where more than one protein can be assigned to a point mutation and disambiguation is required, the graph bigram metric achieves a precision of 0.84 compared with the word distance metric precision of 0.73. We believe the graph bigram search metric to be a significant improvement over previous search metrics for point mutation extraction and to be applicable to text-mining application requiring the association of words

What Do Nectaris Basin Impact Melt Rocks Look like and Where Can We Find Them?

The formation of the Nectaris basin is a key event defining the stratigraphy of the Moon. Its absolute age, therefore, is a linchpin for lunar bombardment history. Fernandes et al. gave a thorough account of the history of different samples thought to originate in Nectaris, with the upshot being there is little agreement on what samples represent Nectaris, if any. We are revisiting the effort to identify Nectaris basin impact-melt rocks at the Apollo 16 site, to model their emplacement, and to use these parameters to examine other sites where Nectaris impact melt is more abundant and/or more recognizable for potential further study

System using leo satellites for centimeter-level navigation

Disclosed herein is a system for rapidly resolving position with centimeter-level accuracy for a mobile or stationary receiver [4]. This is achieved by estimating a set of parameters that are related to the integer cycle ambiguities which arise in tracking the carrier phase of satellite downlinks [5,6]. In the preferred embodiment, the technique involves a navigation receiver [4] simultaneously tracking transmissions [6] from Low Earth Orbit Satellites (LEOS) [2] together with transmissions [5] from GPS navigation satellites [1]. The rapid change in the line-of-sight vectors from the receiver [4] to the LEO signal sources [2], due to the orbital motion of the LEOS, enables the resolution with integrity of the integer cycle ambiguities of the GPS signals [5] as well as parameters related to the integer cycle ambiguity on the LEOS signals [6]. These parameters, once identified, enable real-time centimeter-level positioning of the receiver [4]. In order to achieve high-precision position estimates without the use of specialized electronics such as atomic clocks, the technique accounts for instabilities in the crystal oscillators driving the satellite transmitters, as well as those in the reference [3] and user [4] receivers. In addition, the algorithm accommodates as well as to LEOS that receive signals from ground-based transmitters, then re-transmit frequency-converted signals to the ground

Interpersonal prosodic correlation in frontotemporal dementia.

Communication accommodation describes how individuals adjust their communicative style to that of their conversational partner. We predicted that interpersonal prosodic correlation related to pitch and timing would be decreased in behavioral variant frontotemporal dementia (bvFTD). We predicted that the interpersonal correlation in a timing measure and a pitch measure would be increased in right temporal FTD (rtFTD) due to sparing of the neural substrate for speech timing and pitch modulation but loss of social semantics. We found no significant effects in bvFTD, but conversations including rtFTD demonstrated higher interpersonal correlations in speech rate than healthy controls