On Confidence Regions in Multiple Assays

In multiple assays a ‘Standard’ preparation is compared in a single assay with two or more ‘Test’ preparations (Finney, 1978, ch. 11). In addition to the estimation of the relative potency of the ‘Test’ preparations the question arises as to simultaneous confidence limits, or else a joint confidence region for these relative potencies. This paper compares a joint confidence region using a LR statistic with separate limits based on Fieller's theorem. These results are presented in an Example on a multiple assay of two tuberculin preparations A, B compared with a Standard one (data of Wadley, Finney, 1978, Table 11.1).     

拟似然非线性模型中的置信域：几何法

对拟似然非线性模型在欧氏内积实间建立了修改的Ｂａｔｅｓ＆Ｗａｔｔｓ几何结构,基于此几何结构,导出了参数和子集系数的与统计曲率有关的三种近似置信域,进一步推广和发展了Ｈａｍｉｌｔｏｎ ｅｔ ａｌ．（１９８２）。Ｈａｍｉｌｔｏｎ（１９８６）和Ｗｅｉ（１９９４,１９９８）等人的相应结果。     

Joint Confidence Sets in Multiple Dilution Assays

Let {Q₁, …, Q_k} be the potencies of k substances relative to a standard in a multiple dilution assay. Joint confidence bounds for these are given with confidence coefficient at least 1-α. These bounds are easily interpreted; they appeal to available tables; they improve Scheffe's bounds; they are based on applicable probability inequalities together with extensions of Fieller's theorem; and they are genuinely nonparametric. The procedures are illustrated using data from parallel-line and slope-ratio assays.     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

A Note on Dilution Assays with Errors in Dilutions

Dilution assays involve a number of steps in the preparation of the dilutions and the delivery of the diluent. These steps may give rise to dilution errors. If assays are treated as if the nominal dilutions have been used then under estimates of micro-organism density may occur. In this paper models for dilution errors are introduced.     

Approximate Confidence Interval on Ratio of Two Variances in a Two-way Crossed Model

The model considered is a two-factor cross-classification variance components model with one observation per cell. Let the two factors be A and B, the problem is to obtain an approximate confidence interval for the ratio of variance component A over variance component B. In this paper, a method of solving this problem is established and simulations are performed to check the method.     

Symmetric Intervals and Confidence Intervals

We show that the symmetric “confidence intervals” of WESTLAKE (1972, 1976), widely used and referred to in bioequivalence studies, are not confidence intervals in any accepted sense. Nevertheless, meaningful symmetric intervals can be constructed in the context of Bayesian or fiducial inference.     

An Examination of the Conservative Nature of “Classical” Confidence Limits for a Proportion

The performance of the standard confidence limits for a proportion is studied over the entire range of proportions, and for various prescribed values of the nominal confidence coefficient. In the light of the conservative nature of these limits, modifications are suggested resulting in limits with average confidence coefficients close to the 95% nominal value. A comparison is made with a solution obtained from the application of Bayes's theorem to the problem.     

Lower Confidence Limits for the Positive Linear Combination of two Variances

An alternative method for determining the approximate lower confidence limits for the positive linear combination of two variances based on an approach similar to BULMER (1957) has been proposed. The probability coverage of the proposed alternative limits has been compared with the other existing methods.     

Confidence as an expression of commitment: why misplaced expressions of confidence backfire

Because communication can be abused by senders, it is not inherently stable. One way of stabilizing communication is for senders to commit to their messages. If a sender is committed to a message, she is willing to incur a cost (direct or reputational) if the message is found to be unreliable. This cost provides a reason for receivers to accept messages to which senders are committed. We suggest that expressions of confidence can be used as commitment signals: messages expressed more confidently commit their senders more. On this basis, we make three predictions: that confidently expressed messages are more persuasive (H1’, already well established), that senders whose messages were accepted due to the senders' confidence but were then found to be unreliable should incur costs (H2’), and that if a message is accepted for reasons other than confidence, when it is found to be unreliable the sender should incur lower reputational costs than if the message had been accepted on the basis of the sender's confidence (H3’). A review of the literature revealed broadly supportive but still ambiguous evidence for H2’ and no tests of H3’. In experiments 1, 2, and 3 (testing H2’) participants received the same advice from two senders, one being confident and the other unconfident. Participants were more likely to follow the advice of the confident sender, but once the advice was revealed to have been misguided, participants adjusted their trust so that they trusted the initially unconfident sender more than the confident sender. In experiments 3 and 4 (testing H3’) participants chose between either two senders differing in confidence or two senders differing in competence. Participants followed the advice of the confident sender and of the competent sender. When it was revealed that the advice was misguided, the confident sender suffered from a larger drop in trust than the competent sender. These results are relevant for communicative theories of overconfidence.     

猴 B 病毒血清学和 PCR 检测结果比较

目的：比较猴B病毒血清抗体和病毒PCR检测结果,阐明动物感染后病毒在机体内的存在状况。方法：采集成年猴血清和三叉神经组织,首先通过ELISA方法检测血清中B病毒抗体,然后采用B病毒舡和徊基因引物通过PCR方法扩增血清DNA和三叉神经组织DNA,比较2种方法的检测结果,并对扩增产物进行序列分析。结果：22份猴血清中,B病毒抗体呈阳性的有13份（59．1％）;PCR结果显示,抗体阴性动物及所有血清DNA模板中均无阳性扩增,但在13份抗体阳性动物的三叉神经组织DNA样品中,PCR阳性4份（30．8％）;gL和gD基因扩增条件及产物分析表明,舡基因的GC含量为64．1％,gD为74．2％,且舡的扩增条件和效果明显优于gD。结论：B病毒感染猴后,将在部分动物神经节中建立潜伏,而础基因更适合作为分子鉴定的靶标。     

Approximate Confidence Bounds for Ripley's Statistic for Random Points in a Square

Confidence envelopes for Ripley's L function for N random points in the unit square were obtained by simulation. The 90, 95 and 99th percentiles of 1000 simulations are given in tabular form for N in the range 10 to 350. Results for a number of choices of the maximum interpoint distance are reported.     

Analysis of Plankton Dynamics in a Southwestern U.S.A. Reservoir Using ATP Assays

Plankton biomass in size segregated (i.e. 0.45–10 μm, 10–64 μm, 64–165 μm, and > 165 μm) samples was measured using ATP assays for two years in H. H. Moss Reservoir. The presence of variable numbers of microcrustacean zooplankton in the > 165 μ size class introduced significant, and perhaps inaccurate, variance into temporal dynamics of total ATP concentrations. As many as six physiochemical parameters, measured during 1975–76, were required to produce a significant multiple regression against ATP concentrations; a significant correlation between total ATP measured in the photic zone and surface temperature was observed. A large standing crop of nannoplankton (i.e. 0.45–10 μm) existed in the anaerobic and aphotic hypolimnion during summer stratification both years. This suggested that microbial heterotrophy was an especially important primary trophic event in the reservoir. Particulate (POC) and dissolved (DOC) organic carbon were measured in 1976–77. Organic carbon (POC + DOC) regressed significantly against ATP concentration in the 0.45–10 μm size class and microbial biomass (i.e. 0.45–165 μm) averaged 32 per cent of POC. When biomass was monitored over 24-hour periods in the photic zone, significant changes were documented in various size classes, especially nannoplankton; but total microbial biomass remained relatively constant.     

Confidence Limits on the Ratio of the Mean Failure Times Based on Paired Exponential Observations

This paper discusses interval estimation for the ratio of the mean failure times on the basis of paired exponential observations. This paper considers five interval estimators: the confidence interval using an idea similar to Fieller's theorem (CIFT), the confidence interval using an exact parametric test (CIEP), the confidence interval using the marginal likelihood ratio test (CILR), the confidence interval assuming no matching effect (CINM), and the confidence interval using a locally most powerful test (CIMP). To evaluate and compare the performance of these five interval estimators, this paper applies Monte Carlo simulation. This paper notes that with respect to the coverage probability, use of the CIFT, CILR, or CIMP, although which are all derived based on large sample theory, can perform well even when the number of pairs n is as small as 10. As compared with use of the CILR, this paper finds that use of the CIEP with equal tail probabilities is likely to lose efficiency. However, this loss can be reduced by using the optimal tail probabilities to minimize the average length when n is small (<20). This paper further notes that use of the CIMP is preferable to the CIEP in a variety of situations considered here. In fact, the average length of the CIMP with use of the optimal tail probabilities can even be shorter than that of the CILR. When the intraclass correlation between failure times within pairs is 0 (i.e., the failure times within the same pair are independent), the CINM, which is derived for two independent samples, is certainly the best one among the five interval estimators considered here. When there is an intraclass correlation but which is small (<0.10), the CIFT is recommended for obtaining a relatively short interval estimate without sacrificing the loss of the coverage probability. When the intraclass correlation is moderate or large, either the CILR or the CIMP with the optimal tail probabilities is preferable to the others. This paper also notes that if the intraclass correlation between failure times within pairs is large, use of the CINM can be misleading, especially when the number of pairs is large.