Stable and invariant adjusted directed likelihoods

For the purpose of making inferences for a one-dimensional interestparameter, or constructing approximate complementary ancillariesor residuals, the directed likelihood or signed square rootof the likelihood ratio statistic can be adjusted so that theresulting modified directed likelihood is under ordinary repeatedsampling approximately standard normal with error of O(n^–3/2),conditional on a suitable ancillary statistic and hence unconditionally.In general, suitable specification of the ancillary statisticmay be difficult. We introduce two adjusted directed likelihoodswhich are similar to the modified directed likelihood but donot require the specification of the ancillary statistic. Theerror of the standard normal approximation to the distributionof these new adjusted directed likelihoods is O(n^–1),conditional on any reasonable ancillary statistic, which isstill an improvement over the unadjusted directed likelihoods.     

Integrated likelihood functions for non-Bayesian inference

Consider a model with parameter = (, ), where is the parameterof interest, and let L(, ) denote the likelihood function. Oneapproach to likelihood inference for is to use an integratedlikelihood function, in which is eliminated from L(, ) by integratingwith respect to a density function (|). The goal of this paperis to consider the problem of selecting (|) so that the resultingintegrated likelihood function is useful for non-Bayesian likelihoodinference. The desirable properties of an integrated likelihoodfunction are analyzed and these suggest that (|) should be chosenby finding a nuisance parameter that is unrelated to and thentaking the prior density for to be independent of . Such anunrelated parameter is constructed and the resulting integratedlikelihood is shown to be closely related to the modified profilelikelihood.     

DPP10 is an inactivation modulatory protein of Kv4.3 and Kv1.4

Voltage-gated K⁺ channels exist in vivo as multiprotein complexes made up of pore-forming and ancillary subunits. To further our understanding of the role of a dipeptidyl peptidase-related ancillary subunit, DPP10, we expressed it with Kv4.3 and Kv1.4, two channels responsible for fast-inactivating K⁺ currents. Previously, DPP10 has been shown to effect Kv4 channels. However, Kv1.4, when expressed with DPP10, showed many of the same effects as Kv4.3, such as faster time to peak current and negative shifts in the half-inactivation potential of steady-state activation and inactivation. The exception was recovery from inactivation, which is slowed by DPP10. DPP10 expressed with Kv4.3 caused negative shifts in both steady-state activation and inactivation of Kv4.3, but no significant shifts were detected when DPP10 was expressed with Kv4.3 + KChIP2b (Kv channel interacting protein). DPP10 and KChIP2b had different effects on closed-state inactivation. At –60 mV, KChIP2b nearly abolishes closed-state inactivation in Kv4.3, whereas it developed to a much greater extent in the presence of DPP10. Finally, expression of a DPP10 mutant consisting of its transmembrane and cytoplasmic 58 amino acids resulted in effects on Kv4.3 gating that were nearly identical to those of wild-type DPP10. These data show that DPP10 and KChIP2b both modulate Kv4.3 inactivation but that their primary effects are on different inactivation states. Thus DPP10 may be a general modulator of voltage-gated K⁺ channel inactivation; understanding its mechanism of action may lead to deeper understanding of the inactivation of a broad range of K⁺ channels. potassium channel inactivation; potassium channel ancillary subunits; closed-state inactivation; voltage-gated potassium channels     

Some Tests on a Single Change in Independent Copies of Short Sequences: A Cancer Diagnostic Study

Testing a single change in mean or variance when the observations are n independent short sequences has not been fully researched in the literature. Two statistical tests, max t and modified likelihood radtio, are used in this study. Power comparisons and examples are also given. As expected the modified likelihood ratio test yields the largest power. However, with the assumptions we have in the examples, the max t might be the optimal method to use. The max t may prove useful in assessing departures from the steady state in which the data are short sequences of diagnostic information.     

A solution to the problem of monotone likelihood in Cox regression

The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.     

Practical use of modified maximum likelihoods for stratified data

Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between-strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum-specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points.     

Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance Correlation Parameters

Chen & Dunson ([3]) have proposed a modified Cholesky decompositionof the form = D L L'D for a covariance matrix where D is adiagonal matrix with entries proportional to the square rootsof the diagonal entries of and L is a unit lower-triangularmatrix solely determining its correlation matrix. This totalseparation of variance and correlation is definitely a majoradvantage over the more traditional modified Cholesky decompositionof the form LD²L', (Pourahmadi, [13]). We show that, thoughthe variance and correlation parameters of the former decompositionare separate, they are not asymptotically orthogonal and thatthe estimation of the new parameters could be more demandingcomputationally. We also provide statistical interpretationfor the entries of L and D as certain moving average parametersand innovation variances and indicate how the existing likelihoodprocedures can be employed to estimate the new parameters.     

Logistic and Nonlogistic Density Functions in Binary Regression with Nonstochastic Covariates

A binary random variable depends on nonstochastic covariates through a density function. The equations that determine the maximum likelihood estimators of the parameters are intractable and difficult to solve iteratively. We develop modified maximum likelihood estimators for both logistic and nonlo-gistic densities. These estimators are explicit functions of sample observations and are, therefore, easy to compute. They are asymptotically fully efficient and, for small samples, are almost fully efficient. The appropriateness of the logistic density function is also discussed.     

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves

The usefulness of fluorescence techniques for the study of macromolecular structure and dynamics depends on the accuracy and sensitivity of the methods used for data analysis. Many methods for data analysis have been proposed and used, but little attention has been paid to the maximum likelihood method, generally known as the most powerful statistical method for parameter estimation. In this paper we study the properties and behavior of maximum likelihood estimates by using simulated fluorescence intensity decay data. We show that the maximum likelihood method provides generally more accurate estimates of lifetimes and fractions than does the standard least-squares approach especially when the lifetime ratios between individual components are small. Three novelties to the field of fluorescence decay analysis are also introduced and studied in this paper: a) discretization of the convolution integral based on the generalized integral mean value theorem: b) the likelihood ratio test as a tool to determine the number of exponential decay components in a given decay profile; and c) separability and detectability indices which provide measures on how accurately, a particular decay component can be detected. Based on the experience gained from this and from our previous study of the Padé-Laplace method, we make some recommendations on how the complex problem of deconvolution and parameter estimation of multiexponential functions might be approached in an experimental setting. Offprint requests to: F. G. Prendergast     

A note on profile likelihood for exponential tilt mixture models

Suppose that independent observations are drawn from multipledistributions, each of which is a mixture of two component distributionssuch that their log density ratio satisfies a linear model witha slope parameter and an intercept parameter. Inference forsuch models has been studied using empirical likelihood, andmixed results have been obtained. The profile empirical likelihoodof the slope and intercept has an irregularity at the null hypothesisso that the two component distributions are equal. We derivea profile empirical likelihood and maximum likelihood estimatorof the slope alone, and obtain the usual asymptotic propertiesfor the estimator and the likelihood ratio statistic regardlessof the null. Furthermore, we show the maximum likelihood estimatorof the slope and intercept jointly is consistent and asymptoticallynormal regardless of the null. At the null, the joint maximumlikelihood estimator falls along a straight line through theorigin with perfect correlation asymptotically to the firstorder.     

Light and productivity of Antarctic phytoplankton during austral summer in an ice edge region in the Weddell-Scotia Sea

The photosynthesis-irradiance relationships (P-I curves) ofnatural plankton samples were studied in the Weddell Sea ice-edgezone, between Elephant Island and South Orkney Islands, duringthe austral summer of 1988–89. Three water bodies weredistinguished in the region: Bellingshausen Sea waters modifiedafter flowing through Drake Passage and Bransfield Strait, WeddellSea waters and Weddell Sea waters modified by melting. The stationssituated in modified Bellingshausen waters showed a net phytoplanktoncomposition which was different from that of the other two waterbodies. Weddell Sea waters and Weddell Sea waters modified bymelting of sea ice had the same net phytoplankton composition.In the area of modified Weddell Sea waters, there was an accumulationof phytoplankton in the upper 40 m (>4 mg Chl m^–1).p^B, and     

Phylogenetic estimation with partial likelihood tensors

We present an alternative method for calculating likelihoods in molecular phylogenetics. Our method is based on partial likelihood tensors, which are generalizations of partial likelihood vectors, as used in Felsenstein's approach. Exploiting a lexicographic sorting and partial likelihood tensors, it is possible to obtain significant computational savings. We show this on a range of simulated data by enumerating all numerical calculations that are required by our method and the standard approach.     

Maximum likelihood estimation in the additive hazards model

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model, additive hazards offer a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log-likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non-negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least-squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least-squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided.     

DNA Sequencing Using Ultra Small Amounts of Reagents and Template

One of the key points in the genome project is finding waysto reduce the running cost in DNA sequencing. One way is touse a highly-sensitive fluorescent DNA sequencer, where onlytrace amounts of template DNA and reagents are needed. An experimentalprotocol optimized for the trace amounts of DNA analysis wasestablished by using the hybridization reaction rate coefficientof primers on template DNA, which was estimated to be 7.5x10⁵M^–1 sec^–1 at 37°C. One femtomole of templateDNA with 0.001 unit of modified T7 DNA polymerase (SequenaseVer. 2.0) and also 0.45 fmol of M13 template DNA with 0.01 unitof Taq DNA polymerase were enough to sequence DNA of up to 400bases.