A general probabilistic model for group independent component analysis and its estimation methods

Independent component analysis (ICA) has become an important tool for analyzing data from functional magnetic resonance imaging (fMRI) studies. ICA has been successfully applied to single-subject fMRI data. The extension of ICA to group inferences in neuroimaging studies, however, is challenging due to the unavailability of a prespecified group design matrix and the uncertainty in between-subjects variability in fMRI data. We present a general probabilistic ICA (PICA) model that can accommodate varying group structures of multisubject spatiotemporal processes. An advantage of the proposed model is that it can flexibly model various types of group structures in different underlying neural source signals and under different experimental conditions in fMRI studies. A maximum likelihood (ML) method is used for estimating this general group ICA model. We propose two expectation-maximization (EM) algorithms to obtain the ML estimates. The first method is an exact EM algorithm, which provides an exact E-step and an explicit noniterative M-step. The second method is a variational approximation EM algorithm, which is computationally more efficient than the exact EM. In simulation studies, we first compare the performance of the proposed general group PICA model and the existing probabilistic group ICA approach. We then compare the two proposed EM algorithms and show the variational approximation EM achieves comparable accuracy to the exact EM with significantly less computation time. An fMRI data example is used to illustrate application of the proposed methods.     

Nomograms for determining the parameters for a probabilistic model of radiosensitivity

Nomograms are introduced for the determination, from the experimental survival curves, of a and b parameters of the probabilistic model of cell radiosensitivity (proposed by Kapul'tsevich, 1978). The parameter errors are estimated too. Some examples of using these nomograms for bacteria, yeast and mammalian cells are considered.     

Validation of a general method for activity estimation of cyanide evolving oxidoreductases

Ethylene is a key molecule in organic synthesis currently produced by steam cracking of fossil hydrocarbons. In nature, ethylene is produced in higher plants by 1-aminocyclopropane-1-carboxylic acid oxidase (ACCO). Biocatalytic alternatives for ethylene production are still far from being competitive with traditional production plants. Furthermore, data dispersion shown in the literature adds uncertainty to the introduction of ACCO as a biocatalyst, especially when larger numbers of isoforms or mutants are to be compared. Here we propose a new method for measuring ACCO activity based on cyanide detection. Data provided here indicate that cyanide detection is more precise, more responsive, and much more stable than any other method tested for ACCO activity estimation so far. Briefly, enzymatically produced cyanide can be detected by its derivatization with naphthalene-2,3-dicarboxyaldehide (NDA) to generate 1-cyanobenz[f]isoindole (CBI), which is further detected by high-performance liquid chromatography (HPLC) coupled with a fluorescence detector. Cyanide can be detected in the range between 0.99 and 60.17 pmol, which is three orders of magnitude more sensitive than the currently used ethylene estimation method.     

On a probabilistic model for the numerical estimation of nocturnal migration of birds

The study of nocturnal bird migration by cone methods of observation has a century-long history but has continued to be used up to the present. To describe the flux and estimate the number of passing birds a probabilistic model is proposed. This model is based on the concept of dynamic Poisson ensemble of points in appropriate phase space and has two parameters. One is scalar and the other one is functional. We constructed consistent estimations of these parameters and discuss their use for the numerical estimation of the flux of birds observed in a narrow light cone generated by the bright lunar disk and formed by an open angle of telescope. Selection on the same type of birds was suggested as the necessary condition for the model application. Ground speed of each bird was introduced into the model as a new but obligatory value determining the quantification of the flux of bird.     

Statistical estimation of parameters in a phylogenetic tree using a dynamic model of the substitutional process

Using a modified version of the substitutional process proposed by Neyman, we estimate the parameters of the phylogenetic tree made up of three species (or groups of species). The parameters estimated are the rate of substitution of amino acids along a protein and the ratio of the times of divergence of the species (or group of species). A method is given for determining the tree structure when it is not known. Both the maximum likelihood and Bayes methods are used in the estimation. The basic model of the substitutional process within the proteins is validated by showing that the estimates of the ratio of the times of divergence of three species computed from two different protein molecules (haemoglobin α and fibrinopeptides) are within one standard deviation of each other. Next we consider the construction of the correct phylogenetic tree made up of three or more taxonomic categories like phyla or class utilizing the structure of the various types of protein molecules of the species in the three categories. The generalization of the procedure for the construction of the entire phylogenetic tree is also indicated. The main advantage of this method of tree construction over the traditional method is that the latter method can use the information of only one type of protein (for example cytochrome c) while the method of this paper can use all the available data from the different molecules. We also discuss the recent controversy over the constancy of the molecular clock.     

Validation of a model for process development and scale-up of packed-bed solid-state bioreactors.

We have validated our previously described model for scale-up of packed-bed solid-state fermenters (Weber et al., 1999) with experiments in an adiabatic 15-dm(3) packed-bed reactor, using the fungi Coniothyrium minitans and Aspergillus oryzae. Effects of temperature on respiration, growth, and sporulation of the biocontrol fungus C. minitans on hemp impregnated with a liquid medium were determined in independent experiments, and the first two effects were translated into a kinetic model, which was incorporated in the material and energy balances of the packed-bed model. Predicted temperatures corresponded well with experimental results. As predicted, large amounts of water were lost due to evaporative cooling. With hemp as support no shrinkage was observed, and temperatures could be adequately controlled, both with C. minitans and A. oryzae. In experiments with grains, strong shrinkage of the grains was expected and observed. Nevertheless, cultivation of C. minitans on oats succeeded because this fungus did not form a tight hyphal network between the grains. However, cultivation of A. oryzae failed because shrinkage combined with the strong hyphal network formed by this fungus resulted in channeling, local overheating of the bed, and very inhomogeneous growth of the fungus. For cultivation of C. minitans on oats and for cultivation of A. oryzae on wheat and hemp, no kinetic models were available. Nevertheless, the enthalpy and water balances gave accurate temperature predictions when online measurements of oxygen consumption were used as input. The current model can be improved by incorporation of (1) gas-solids water and heat transfer kinetics to account for deviations from equilibrium observed with fast-growing fungi such as A. oryzae, and (2) the dynamic response of the fungus to changes in temperature, which were neglected in the isothermal kinetic experiments.     

Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters

Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time‐dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real‐life analyses to estimate nonlinear and time‐dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real‐life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure.     

A general model of error-prone PCR

In this paper, we generalize a previously-described model of the error-prone polymerase chain reaction (PCR) reaction to conditions of arbitrarily variable amplification efficiency and initial population size. Generalisation of the model to these conditions improves the correspondence to observed and expected behaviours of PCR, and restricts the extent to which the model may explore sequence space for a prescribed set of parameters. Error-prone PCR in realistic reaction conditions is predicted to be less effective at generating grossly divergent sequences than the original model. The estimate of mutation rate per cycle by sampling sequences from an in vitro PCR experiment is correspondingly affected by the choice of model and parameters.     

Performance of a divergence time estimation method under a probabilistic model of rate evolution

Rates of molecular evolution vary over time and, hence, among lineages. In contrast, widely used methods for estimating divergence times from molecular sequence data assume constancy of rates. Therefore, methods for estimation of divergence times that incorporate rate variation are attractive. Improvements on a previously proposed Bayesian technique for divergence time estimation are described. New parameterization more effectively captures the phylogenetic structure of rate evolution on a tree. Fossil information and other evidence can now be included in Bayesian analyses in the form of constraints on divergence times. Simulation results demonstrate that the accuracy of divergence time estimation is substantially enhanced when constraints are included.     

Some mathematical aspects of the medical diagnostic process. I: a general mathematical model

Making a medical diagnosis consists of correlating knownpatterns of disease with the various classes of clinical data elicited from the history, physical examination, and batteries of tests relative to the diagnostic dynamics symbolized by atree branching into the various possible diagnostic decisions. In this paper a relational mathematical model of the reasoning aspects of the conventional medical diagnostic process is suggested as a way of extracting a general, formal concept of medical diagnosis. Computer implementation of the model is discussed briefly.     

The estimation of parameters from population data on the general stochastic epidemic

This paper provides a method of using maximum likelihood to estimate the two unknown parameters, the contact rate and the removal rate, in the general stochastic epidemic, using only the observed interremoval times and the total number of cases occurring. A goodness-of-fit test is discussed, and the methods described are illustrated by means of data on an actual smallpox epidemic in a restricted community in southeastern Nigeria.     

Validation protocol of models for centre of mass estimation.

The estimation of the body centre-of-mass (COM) position requires the modelling of the human body as a system of rigid segments and the measurement of the position of related external anatomical landmarks. Many models for COM position estimation have been proposed with different levels of complexity and, in some cases, specific protocols have been used for model accuracy evaluation. In this paper, we propose a general method for the quantitative assessment of any COM model in relation to a determined set of movements. It consists of an experimental protocol and of a set of comparative indices, which quantify the congruence among the estimated kinematic variables and their expected values. The general applicability of the method is specifically addressed to models' comparison, aiming to support the user in the process of choice and validation of the most suitable model for her/his purposes. In this frame, the results of the analytical comparison among two kinematic models with different levels of complexity are reported.     

Simulation-based estimation of stochastic process parameters in tumor growth

Models are generally developed at the micro level. Data are generally gathered at the macro level. Obtaining the macromodel which is the natural consequence of the underlying micro model is generally not feasible. SIMEST gives a means whereby the micromodel is used to generate, for a given assumed set of parameters, simulated sets of macro data. These data are compared with the actual clinical macro data. The parameters are then adjusted to obtain concordance with the clinical data. In this manner, simulation gives us a means of parameter estimation without the necessity of generating the macro model.     

Test of mathematical assumptions behind the 'incidence function' estimation process of metapopulations' dynamic parameters.

I question Hanski's [I. Hanski, A practical model of metapopulation dynamics, J. Animal Ecol. 63 (1994) 151] assumption that incidence functions are relevant approximations of the equilibrium dynamics of stochastic metapopulation models to estimate models' parameters based on snapshot data. Based on ten different metapopulation models, this assumption is found to be at least partly unjustified when referring to the asymptotic behaviour of the models. This leads me to recommend the use of explicit extinction-colonisation transition probabilities and process data (rather than snapshot data) in the estimation process of metapopulation models.