Use Of Maximum Likelihood Method Research Articles

Extended Odd Lomax Family of Distributions: Properties and Applications

The Lomax distribution has a wide range of applications. Due to this, it has had many extensions to render it more flexible and useful to model real world data. In this study, a new family of distributions called the extended odd Lomax family of distributions is introduced by adding two extra shape parameters and one scale parameter. We derived several statistical properties of the new family of distributions. The parameters of the family of distributions are estimated by the use of maximum likelihood method and the consistency of the estimators investigated via Monte Carlo simulations. The usefulness and flexibility of the new family of distributions are illustrated by the use of two real datasets. The results show that the distributions adequately describe the datasets.

Explore the Characteristics of Age, BMI and Blood Composition of Breast Cancer Patients Based on Multivariate Statistical Analysis

In this paper, through a series of analysis and testing of breast cancer detection data, the statistical rules of multiple objects and multiple indicators are analyzed in the case of their correlation. First of all, univariate diagnosis and multivariate diagnosis were performed on the data. Among them, when studying the correlation between variables, it was found that HOMA had a clear linear positive correlation with insulin content in blood. It is worth noting that some patients with breast cancer show a high degree of insulin resistance and blood insulin content, which is a feature not found in samples without breast cancer. Then, through single factor analysis of variance, we believe that there were significant differences in blood test conditions, ages, and BMI indicators of samples of different health conditions. Next, the principal component analysis was used to reduce the dimension of the data. In this study, the differences in age, BMI, and blood component content between the two groups with different health conditions can be summarized by these two independent factors. Among them, the absolute value of the MCP-1 (monocyte chemoattractant protein 1) coefficient in the main component 1 is large, reflecting the characteristics of the blood component of the sample; the load values of glucose and leptin in the main component 2 are large, reflecting similar results. Then, assuming the use of m = 3 factor model and the use of maximum likelihood method and principal component method, the original data and factor rotation data are re-analyzed, so that the variables are reduced to 3 factors for analysis. Among them, the maximum likelihood method is used to estimate the factor rotation data. The first factor reflects the insulin resistance factor attributed to insulin and HOMA indicators, and the second factor reflects the body fat and thin factor attributed to BMI and leptin. The third factor reflects the glucose content in the blood. Finally, by setting different misjudgment costs for discriminant analysis, the obtained APER is 0.1638 and EAER is 0.1872. Among them, the probability of discriminating patients with breast cancer from not having breast cancer is 0.09375, which is a low rate of misjudgment and also means the model established in this paper is efficient.

Analysis of spliceosome dynamics by maximum likelihood fitting of dwell time distributions.

Colocalization single-molecule methods can provide a wealth of information concerning the ordering and dynamics of biomolecule assembly. These have been used extensively to study the pathways of spliceosome assembly in vitro. Key to these experiments is the measurement of binding times-either the dwell times of a multi-molecular interaction or times in between binding events. By analyzing hundreds of these times, many new insights into the kinetic pathways governing spliceosome assembly have been obtained. Collections of binding times are often plotted as histograms and can be fit to kinetic models using a variety of methods. Here, we describe the use of maximum likelihood methods to fit dwell time distributions without binning. In addition, we discuss several aspects of analyzing these distributions with histograms and pitfalls that can be encountered if improperly binned histograms are used. We have automated several aspects of maximum likelihood fitting of dwell time distributions in the AGATHA software package.

The modified Power function distribution

Recently, a lot of new, improved, flexible and robust probability distributions have been developed from the existing distributions to encourage their applications in diverse fields. This paper proposes a new lifetime distribution called the Modified Power function (MPF) distribution, the distribution belongs to the Marshall-Olkin-G family of distribution and it’s an extension of the one parameter Power function distribution. The MPF distribution enjoys a close form distributional expression. Some of its statistical properties including possible transformations are presented. The paper suggests the use of maximum likelihood method of parameter estimation for estimating the parameters of the new distribution. The applicability of the distribution was illustrated with two real data-sets and its goodness-of-fit was compared with that of the Exponential, Weibull, Lindley Exponential, Exponentiated Exponential, Kumaraswamy, Power function and Beta distributions by using the AIC, AICc, CAIC, BIC, HQC, W∗ and A∗...

Positive selection of three chitinase genes of the family 18 of glycoside hydrolases in mammals

The digestive enzyme chitinase degrades chitin, and is found in a wide range of organisms, from prokaryotes to eukaryotes. Although mammals cannot synthesize or assimilate chitin, several proteins of the glycoside hydrolase (GH) chitinase family GH18, including some with enzymatic activity, have recently been identified from mammalian genomes. Consequently, there is growing interest in molecular evolution of this family of proteins. Here we report on the use of maximum likelihood methods to test for evidence of positive selection in three genes of the chitinase family GH18, all of which are found in mammals. These focal genes are CHIA, CHIT1 and CHI3L1, which encode the chitinase proteins acidic mammalian chitinase, chitotriosidase and cartilage protein 39, respectively. The results of our analyses indicate that each of these genes has undergone independent selective pressure in their evolution. Additionally, we have found evidence of a signature of positive natural selection, with most sites identified as being subject to adaptive evolution located in the catalytic domain. Our results suggest that positive selection on these genes stems from their function in digestion and/or immunity.

PRECISION AND BIAS OF METHODS FOR ESTIMATING POINT SURVEY DETECTION PROBABILITIES

Wildlife surveys often seek to determine the presence or absence of species at sites. Such data may be used in population monitoring, impact assessment, and species– habitat analyses. An implicit assumption of presence/absence surveys is that if a species is not detected in one or more visits to a site, it is absent from that site. However, it is rarely if ever possible to be completely sure that a species is absent, and false negative observation errors may arise when detection probabilities are less than 1. The detectability of species in wildlife surveys is one of the most important sources of uncertainty in determining the proportion of a landscape that is occupied by a species. Recent studies emphasize the need to acknowledge and incorporate false negative observation error rates in the analysis of site occupancy data, although a comparative study of the range of available methods for estimating detectability and occupancy is notably absent. The motivation for this study stems from the lack of guidance in the literature about the relative merits of alternative methods for estimating detection probabilities and site occupancy proportions from presence/absence survey data. Six approaches to estimating underlying detection probabilities and the proportion of sites occupied from binary observation data are reviewed. These include three parametric methods based on binomial mixtures, one nonparametric approach based on mark–recapture theory, and two approaches based on simplistic assumptions about occupancy rates. We compare the performance of each method using simulated data for which the “true” underlying detection rate is known. Simulated data were realized from a beta‐binomial distribution, incorporating a realistic level of variation in detection rates. Estimation methods varied in their precision and bias. The “binomial‐with‐added‐zeros” mixture model, estimated by maximum likelihood, was the least biased estimator of detection probability and, therefore, occupancy rate. We provide an Excel spreadsheet to execute all of the methods reviewed. Stand‐alone programs such as PRESENCE may be used to estimate all models including the “binomial with added zeros” model. Our findings lend support to the use of maximum likelihood methods in estimating site occupancy and detectability rates.

The use of maximum likelihood methods to estimate the risk of tuberculous infection and disease in a Canadian First Nations population.

Tuberculosis (TB) notification rates among First Nations people in British Columbia, Canada, are higher than those among non-First Nations people, although rates are declining more rapidly in the First Nations population. The epidemiology of tuberculous infection and disease during the period 1926-2000 in this population was investigated. The trend in the annual risk of infection (ARI) since 1926 was estimated using tuberculous meningitis mortality statistics and skin testing data. Risks of progression from infection to disease were estimated by fitting model predictions of disease incidence to TB notifications, using maximum likelihood methods. Infectious TB notifications were matched with ARI estimates to obtain the number of transmissions per infectious case over time. We estimate that the ARI decreased from more than 10% during the prechemotherapy era to less than 0.1% by 2000. The risks of primary, reactivation, and exogenous re-infection disease among adults aged 25-44 years were 22%, 0.1%, and 6%, respectively. The number of transmissions per infectious case decreased from 16 to 2 from the early 1970s to the late 1990s. This study shows that the risk of infection among British Columbia First Nations people is decreasing, while the relative contribution of reactivation to disease incidence is increasing. Once infected, First Nations people may have a higher risk of developing disease than other populations.

Instrumentalism, Parsimony, and the Akaike Framework

Akaike's framework for thinking about model selection in terms of the goal of predictive accuracy and his criterion for model selection have important philosophical implications. Scientists often test models whose truth values they already know, and they often decline to reject models that they know full well are false. Instrumentalism helps explain this pervasive feature of scientific practice, and Akaike's framework helps provide instrumentalism with the epistemology it needs. Akaike's criterion for model selection also throws light on the role of parsimony considerations in hypothesis evaluation. I explain the basic ideas behind Akaike's framework and criterion; several biological examples, including the use of maximum likelihood methods in phylogenetic inference, are considered.

Classifying genealogical origins in hybrid populations using dominant markers.

In hybrid studies, potential for error is high when classifying genealogical origins of individuals (e.g., parental, F1, F2) based on their genotypic arrays. For codominant markers, previous researchers have considered the probability of misclassification by genotypic inspection and proposed alternative maximum-likelihood approaches to estimating genealogical class frequencies. Recently developed dominant marker systems may significantly increase the number of diagnostic loci available for hybrid studies. I examine probabilities of classification error based on the number of dominant loci. As in earlier studies, I assume that only parental and first- and second-generation hybrid crosses between two taxa potentially exist. Thirteen loci with dominant expression from each parental taxon (i.e., 26 total loci) are needed to reduce classification error below 5% for F2 individuals, compared to 13 codominant loci for the same error rate. Use of loci in similar numbers from both taxa most efficiently increases power to characterize all genealogical classes. In contrast, classification of backcrosses to one parental taxon is wholly dependent on loci from the other taxon. Use of dominant diagnostic markers may increase the power and expand the use of maximum-likelihood methods for evaluating hybrid mixtures.

Maximum Likelihood Estimation of Spatial Covariance Parameters

In this paper, the maximum likelihood method for inferring the parameters of spatial covariances is examined. The advantages of the maximum likelihood estimation are discussed and it is shown that this method, derived assuming a multivariate Gaussian distribution for the data, gives a sound criterion of fitting covariance models irrespective of the multivariate distribution of the data. However, this distribution is impossible to verify in practice when only one realization of the random function is available. Then, the maximum entropy method is the only sound criterion of assigning probabilities in absence of information. Because the multivariate Gaussian distribution has the maximum entropy property for a fixed vector of means and covariance matrix, the multinormal distribution is the most logical choice as a default distribution for the experimental data. Nevertheless, it should be clear that the assumption of a multivariate Gaussian distribution is maintained only for the inference of spatial covariance parameters and not necessarily for other operations such as spatial interpolation, simulation or estimation of spatial distributions. Various results from simulations are presented to support the claim that the simultaneous use of maximum likelihood method and the classical nonparametric method of moments can considerably improve results in the estimation of geostatistical parameters.

Evaluating partially observed survival histories: retrospective projection of covariate trajectories

The use of maximum likelihood methods in analysing times to failure in the presence of unobserved randomly changing covariates requires constrained optimization procedures. An alternative approach using a generalized version of the EM-algorithm requires smoothed estimates of covariate values. Similar estimates are needed in evaluating past exposures to hazardous chemicals, radiation or other toxic materials when health effects only become evident long after their use. In this paper, two kinds of equation for smoothing estimates of unobserved covariates in survival problems are derived. The first shows how new information may be used to update past estimates of the covariates' values. The second can be used to project the covariates' trajectory from the present to the past. If the hazard function is quadratic in form, both types of smoothing equation can be derived in a closed analytical form. Examples of both types of equation are presented. Use of these equations in the extended EM-algorithm, and in estimating past exposures to hazardous materials, are discussed. © 1997 by John Wiley & Sons, Ltd.

An application of an OR-Parallel Prolog system to phylogenetic analysis

In this paper we discuss an application of our OR-Parallel Prolog system to a search problem of importance in practice: the construction of phylogenetic trees. The use of a maximum likelihood method to construct such trees is based on concrete models of evolutional processes and is well-motivated statistically. However, the use of maximum likelihood methods has been hindered by the computational cost to calculate the likelihood of possible alternative trees (i.e. their confidence scores) at each search step for the optimal tree. To cope with this problem, we used OR-parallel Prolog as a “coordination language” to orchestrate the search for the optimal tree. A numerical computation written in C computed the likelihood of each alternative tree and a symbolic computation written in Prolog performed a parallel A* tree search. For constructing phylogenetic trees of bacterial organisms, our parallel algorithm allowed us to increase the size of the search space, allowing us to include nearly optimal as well as optimal intermediate trees in the search. Our priority mechanism reduced the generation of useless tasks and resulted in superlinear speedups in some cases.

Maximum-Likelihood-Constrained Deconvolution of Two-Dimensional NMR Spectra. Accuracy of Spectral Quantification

The maximum-likelihood method (MLM) and a related processing protocol involving diagonally symmetrized data, symmetrized maximum-likelihood (SML) spectral deconvolution, yield contrast-enhanced 2D NMR spectra with simultaneous noise suppression and marked resolution enhancement, relative to spectra processed with conventional apodization and FFT. In this paper the MLM deconvolution technique and SML protocol were applied to synthetic and real 2D NOE spectra to evaluate the accuracy of peak-volume quantification under various conditions. It is concluded that use of MLM and SML is remarkably robust for peak discrimination and volume calculations in 2D NMR studies, despite the inherent nonlinear nature of MLM. These protocols clearly facilitate identification and quantification of heavily overlapped cross peaks. In this study, quantitative integration linearity was observed at peak dynamic ranges of up to 1000:1 for 2D spectral reconstructions.

Trip-Distribution Calculations and Sampling Error: Some Theoretical Aspects

Part 1 of this paper discusses the treatment of zero observations in growth-factor methods; part 2 discusses the calibration of gravity models when the data are of different sampling variability. The problem discussed in part 1 is that zero observations are preserved at zero value in the forecast year, no matter how much growth takes place. Since the probability of making a trip is not zero but very small for those matrix cells that are empty by chance, it is shown how to estimate nonzero values for these cells by use of a method of smoothing reported in the statistical literature. It is argued in part 2 that the usual practice of calibrating against ‘grossed-up’ data is incorrect. If the survey method is the same for all trips, but the sampling fraction varies from one cell to another, it is shown, by use of maximum-likelihood methods, that it is the raw sample data against which the model should be calibrated. If the matrix is made up of data from different surveys, it is shown, by use of least-squares methods, that the raw sample data should be modified before estimating the parameters, leading to a minimum χ2 fitting criterion.

THE ESTIMATION OF OUTCROSSING IN NATURAL POPULATIONS

A new method for estimating the proportion of outcrossing was developed by the use of maximum likelihood method. Using a qualitative character which is monogenically inherited, the proportion of outcrossing can be estimated in one or two generations. A numerical example was also given. Further, the outcrossing and natural crossing were differently defined.