Related papers: Tutorial: Maximum likelihood estimation in the con…
For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence,…
This paper addresses a data detection problem for multiple-input multiple-output (MIMO) communication systems with hardware impairments. To facilitate maximum likelihood (ML) data detection without knowledge of nonlinear and unknown…
Estimation of autocorrelations and spectral densities is of fundamental importance in many fields of science, from identifying pulsar signals in astronomy to measuring heart beats in medicine. In circumstances where one is interested in…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…
We consider a set of M images, whose pixel intensities at a common point can be treated as the components of a M-dimensional vector. We are interested in the estimation of the modulus of such a vector associated to a compact source. For…
When a population exhibits heterogeneity, we often model it via a finite mixture: decompose it into several different but homogeneous subpopulations. Contemporary practice favors learning the mixtures by maximizing the likelihood for…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
We study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. To analyze its performance, we…
We show that a maximum likelihood approach for parameter estimation in agent-based models (ABMs) of opinion dynamics outperforms the typical simulation-based approach. Simulation-based approaches simulate the model repeatedly in search of a…
The detection reliability of weak signals is a critical issue in many astronomical contexts and may have severe consequences for determining number counts and luminosity functions, but also for optimising the use of telescope time in…
In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…
A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification…
Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
A maximum likelihood (ML) technique for detecting compact sources in images of the x-ray sky is examined. Such images, in the relatively low exposure regime accessible to present x-ray observatories, exhibit Poissonian noise at background…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
In the past years, optical fluorescence microscopy (OFM) made steady progress towards increasing the localisation precision of fluorescent emitters in biological samples. The high precision achieved by these techniques has prompted new…
The performance of modern algorithms on certain computer vision tasks such as object recognition is now close to that of humans. This success was achieved at the price of complicated architectures depending on millions of parameters and it…
Single-image super-resolution (SISR) is a canonical problem with diverse applications. Leading methods like SRGAN produce images that contain various artifacts, such as high-frequency noise, hallucinated colours and shape distortions, which…