scholarly journals A Maximum Entropy Procedure to Solve Likelihood Equations

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 596
Author(s):  
Antonio Calcagnì ◽  
Livio Finos ◽  
Gianmarco Altoé ◽  
Massimiliano Pastore
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Score Function ◽  
Likelihood Estimation ◽  
Likelihood Equation ◽  
Equation Problem ◽  
Standard Procedures ◽  
Data Separation

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon’s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth’s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation.

Maximum likelihood estimation for stochastic rth -order reactions

1972 ◽  
Vol 9 (01) ◽  
pp. 32-42
Author(s):  
John P. Mullooly
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Solution ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Order System ◽  
Initial Number ◽  
Direct Evaluation ◽  
Likelihood Equation ◽  
Satisfactory Approximation

In this paper we derive the probability distributions of the number of molecules and of the lifetime of a molecule in a stochastic rth-order system by direct evaluation of probabilities, avoiding the use of differential-difference equations. Maximum likelihood estimation of the rate constant is based on an observation of the level of the system at time t > 0. We find the asymptotic solution of the likelihood equation for a large initial number of molecules. By comparison with the numerical solution of the likelihood equation, the asymptotic estimator is shown to be a satisfactory approximation for second order reactions which are far from completion.

Maximum likelihood estimation for stochastic rth -order reactions

1972 ◽  
Vol 9 (1) ◽  
pp. 32-42 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Solution ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Order System ◽  
Initial Number ◽  
Direct Evaluation ◽  
Likelihood Equation ◽  
Satisfactory Approximation

In this paper we derive the probability distributions of the number of molecules and of the lifetime of a molecule in a stochastic rth-order system by direct evaluation of probabilities, avoiding the use of differential-difference equations. Maximum likelihood estimation of the rate constant is based on an observation of the level of the system at time t > 0. We find the asymptotic solution of the likelihood equation for a large initial number of molecules. By comparison with the numerical solution of the likelihood equation, the asymptotic estimator is shown to be a satisfactory approximation for second order reactions which are far from completion.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals Model Regresi Logistik Terboboti Georafis pada Status Kemiskinan Kabupaten/Kota di Provinsi Sulawesi Selatan tahun 2016

2019 ◽  
Vol 1 (3) ◽  
pp. 87
Author(s):  
Sadriana Rustan ◽  
Muhammad Arif Tiro ◽  
Muhammad Nadjib Bustan
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Geographical Location ◽  
Predictor Variable ◽  
Likelihood Estimation ◽  
Local Form ◽  
South Sulawesi ◽  
Weighted Logistic Regression ◽  
Geographically Weighted Logistic Regression

Abstrak. Analisis regresi logistik digunakan untuk menentukan hubungan antara peubah respon bersifat kategori dengan satu atau lebih peubah penjelas dengan asumsi bahwa respon tidak dipengaruhi oleh lokasi geografis (data spasial). Salah satu metode analisis spasial adalah Model Regresi Logistik Terboboti Geografis (RLTG). Model RLTG adalah bentuk regresi logistik lokal di mana lokasi geografis diperhatikan dan diasumsikan memiliki distribusi Bernoulli. Pendugaan parameter model RLTG menggunakan metode Maximum Likelihood Estimation (MLE) dengan memberikan bobot yang berbeda pada lokasi yang berbeda. Data dalam penelitian ini diperoleh dari publikasi Badan Pusat Statistik, yaitu data dan Informasi Kemiskinan di Provinsi Sulawesi Selatan. Penelitian ini bertujuan untuk mengetahui faktor-faktor yang mempengaruhi status kemiskinan di Provinsi Sulawesi Selatan dengan menggunakan model regresi logistik terboboti geografis dengan fungsi pembobot Kernel bisquare. Hasil penelitian menunjukkan bahwa peubah penjelas yang mempengaruhi status kemiskinan di Provinsi Sulawesi Selatan adalah persentase penduduk tidak bekerja dan persentase rumah tangga pengguna jamban bersama.Abstract. Logistic regression a analysis is used to determine the relationship between categorical response variables with one or more predictor variable assuming that the response is not influenced by geographical location (spatial data). One method of spatial analysis is Geographically Weighted Logistic Regression (GWLR). The GWLR model is a local form of logistic regression where the geographical location is considered and assumed to have a Bernoulli distribution. Estimating parameters of the RLTG model uses the Maximum Likelihood Estimation (MLE) method by giving different weights to different locations. The data were obtained from BPS publications, namely Data and Information on Poverty in South Sulawesi Province. This study aims to determine the factors that influence poverty status in South Sulawesi Province using a geographically weighted logistic regression model with kernel bisquare weighting function. The results showed that the explanatory variables that influence the status of poverty in the province of South Sulawesi were the percentage of the population not working and the percentage of common household toilet users.Keywords: logistic regression, kernel bisquare, GWLR and poverty.

scholarly journals Maximum-likelihood estimation of the parameters of a four-parameter class of probability distributions

1988 ◽  
Vol 31 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Siegfried H. Lehnigk
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Initial Shape ◽  
Definition Of ◽  
Image Position

We shall concern ourselves with the class of continuous, four-parameter, one-sided probability distributions which can be characterized by the probability density function (pdf) classIt depends on the four parameters: shift c ∈ R, scale b > 0, initial shape p < 1, and terminal shape β > 0. For p ≦ 0, the definition of f(x) can be completed by setting f(c) = β/bΓ(β−1)>0 if p = 0, and f(c) = 0 if p < 0. For 0 < p < 1, f(x) remains undefined at x = c; f(x)↑ + ∞ as x↓c.

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