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We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…

Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…

Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…

Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of…

In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficienty when the parametric model is correct.…

The super-parametric density estimators and its related algorism were suggested by Y. -S. Tsai et al [7]. The number of parameters is unlimited in the super- parametric estimators and it is a general theory in sense of unifying or…

Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform…

This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…

The maximum-likelihood method for quantum estimation is reviewed and applied to the reconstruction of density matrix of spin and radiation as well as to the determination of several parameters of interest in quantum optics.

In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be…

Abundance estimation from capture-recapture data is of great importance in many disciplines. Analysis of capture-recapture data is often complicated by the existence of one-inflation and heterogeneity problems. Simultaneously taking these…

This study proposes a computationally efficient semiparametric distribution estimator, which is a slight modification of the naive mixture proposed by Schuster and Yakowitz (1985) and Olkin and Spiegelman (1987). The proposed method is…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…

Bayesian synthetic likelihood (BSL) is a popular method for performing approximate Bayesian inference when the likelihood function is intractable. In synthetic likelihood methods, the likelihood function is approximated parametrically via…

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…