We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalm...

This note studies the bias arises from the MLE estimate of the rate parameter and the mean parameter of an exponential distribution. 1 Motivation Although maximum likelihood estimation (MLE) methods provide estimates that are useful, the estimates themselves are not guaranteed to be unbiased. Nevertheless, MLE methods are still highly regarded in practice due to several of their properties, not...

We investigate the problem of estimation of parameters of a gravitational wave signal from a coalescing binary, at the output of a single interferometric detector. We present, a computationally viable statistical model of the distribution, of the maximum likelihood estimates (MLE), of the parameters. This model reproduces the essential features of the Monte Carlo simulations, thereby explaining...

This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster thanMLE and these are the fo...

This theoretical paper is concerned with a rigorous non-asymptotic analysis of relational learning applied to a single network. Under suitable and intuitive conditions on features and clique dependencies over the network, we present the first probably approximately correct (PAC) bound for maximum likelihood estimation (MLE). To our best knowledge, this is the first sample complexity result of t...

PSA measurements are used to assess the risk for prostate cancer. PSA range and PSA kinetics such as PSA velocity have been correlated with increased cancer detection and assist the clinician in deciding when prostate biopsy should be performed. Our aim is to evaluate the use of a novel, maximum likelihood estimation prostate specific antigen (MLE-PSA) model for predicting the probability of pr...

Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood estimation (MLE). Among the most widely used families of statistical models are mixture models, especially, mixtures of Gaussian distributions. A popular hard-clu...

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions dra...

The estimation of the covariance matrix is a pivotal step in several statistical tasks. In particular, the estimation becomes challenging for high dimensional representations of data when few samples are available. Using the standard Maximum Likelihood estimation (MLE) when the number of samples are lower than the dimension of the data can lead to incorrect estimation e.g. of the covariance mat...

Representing and modeling the motion and spatial support of multiple objects and surfaces from motion video sequences is an important intermediate step towards dynamic image understanding. One such representation, called layered representation, has recently been proposed. Although a number of algorithms have been developed for computing these representations, there has not been a consolidated e...