Multivariate Probability in Terms of Marginal Probability and Correlation Coefficient

This paper is motivated by a practical problem relating to student performance in a number of subjects of equal standing. Its mathematical formulation is to find an approximation to a multivariate probability of the form Pr {X₁⩾a, X₂⩾a, …, X_N⩾a} for arbitrary a and N, in terms of p = Pr {X₁⩾a} and q = Corr (X_i, X_j), i≠j, where X_i, i = 1, …, N are exchangeable random variables with mean 0 and variance unity.     

Probability distribution on the parse trees

Paper describes probability distribution on the parse trees of natural language by using Bayesian networks. First parts of the paper describes probabilistic context-free grammar and parse trees. In the second part of the paper, Bayesian network was modelled and joint probability distribution on their vertex. On these theoretical ideas, in the third part, we describe our model tested on Database of grammatical sentences of Croatian language (http:/ /infoz.ffzg.hr / tepes /). At the end was presented a backward procedure and evaluation of our results.     

Probability screening model

A comparative analysis is given of various types of systems of selecting biologically active substances. A theoretical probability model of tests on chemical compounds for biological activity (screening) has been constructed which permits an evaluation of the efficacy of screening on the basis of fairly reasonable assumptions. It has been shown that this efficacy decreases in time with a fixed number of types of activity taken into consideration and rises sharply with an increase in the number of types of activity of chemical compounds taken into account in the tests.     

A New Estimator of the Discovery Probability

Summary Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however, exhibiting some peculiar features that make them more challenging: specifically, one has to deal with very large populations (genomic libraries) containing a huge number of distinct species (genes) and only a small portion of the library has been sampled (sequenced). These aspects motivate the Bayesian nonparametric approach we undertake, since it allows to achieve the degree of flexibility typically needed in this framework. Based on an observed sample of size n , focus will be on prediction of a key aspect of the outcome from an additional sample of size m , namely, the so‐called discovery probability. In particular, conditionally on an observed basic sample of size n , we derive a novel estimator of the probability of detecting, at the (n+m+1) th observation, species that have been observed with any given frequency in the enlarged sample of size n+m . Such an estimator admits a closed‐form expression that can be exactly evaluated. The result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species, as m increases. Natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets.     

Probability of internal unwinding in the triple helix of collagen

Helix probability profiles are calculated for collagen models that take into account specific sequence and unwinding from the ends, by internal loops and by chain dissociation, using parameters from a previous study and the technique of the previous paper.² An analysis is made of the occurrence of imino acids in known collagen sequences and no significant difference is found from random occurrence. Studies of model sequences generated by random placement of the imino acids show no tendency for collagen to unwind via internal loops even when one end is covalently linked and a loop is permanently nucleated at that end.     

Use of Probability Weighted Moments in the Analysis of Means

In the analysis of means the estimate of σ is usually calculated using range. In this study it is proposed that the linear estimate of σ based on probability weighted moments should be used. A simulation study based on 1000 values suggested that the linear estimate of σ using probability weighted moments is more close to the original value. In the simulations different distributions such as normal, t, Cauchy and exponential were assumed.     

遗传概率的一个认识误区

长期以来,广大教师对遗传概率普遍有一个认识误区,前不久在K12生物论坛(http://www.k12.com.cn)引起激烈争论,有几万人次的点击浏览,近千人次的回复发贴。因此非常有必要明确认识。     

Probability of fixation in a heterogeneous environment

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.     

Estimation of the Transmission Probability of Lyme Borreliosis

Whether physicians should prophylactically treat tick bites in areas endemic for Lyme disease has been debated. The high rates of tick infection (10–50%) found in Lyme disease-endemic areas suggest that tick bites should be treated; conversely, the low rates of Lyme disease (1–4%) found in recent clinical trials of untreated tick-bite victims suggest caution in treatment. Medical advice given from Lyme-disease World Wide Web sites is equally contradictory, ranging from suggesting that all tick bites should be treated to suggesting that no tick bites be treated. To clarify this issue, we estimate the transmission probability of the causative agent of Lyme disease, Borrelia burgdorferi, for different durations of tick attachment. The data used to estimate this transmission probability is obtained from previously published animal studies. The accuracy of these estimates is assessed by comparing model predictions of the number of Lyme disease cases to that actually observed in clinical studies of Lyme disease. Our results suggest that tick bites should be treated only when it is known that the duration of tick attachment is longer than 48 hours.     

Methods for Estimating the Probability of Clonality in Cell Line Development

Mammalian cell banks for biopharmaceutical production are usually derived from a single progenitor cell. Different methods to estimate the probability that the cell banks are clonally derived, or the probability of clonality (PoC), associated with various cloning workflows have been reported previously. In this review, a systematic analysis and comparison of the methods used to calculate the PoC are provided. As the single cell deposition and high‐resolution imaging technologies continue to advance and the cloning workflow evolves, an aligned understanding and best practice on estimating the PoC is necessary to compare different cloning workflows adopted across the biopharmaceutical industry and it will help to accelerate regulatory acceptance.     

Probability of paternity in paternity testing using the DNA fingerprint procedure

For the purpose of applying DNA fingerprinting to paternity testing, we established a general formula to calculate the probability of paternity and evaluated the ability of DNA fingerprinting to determine paternity.