Related papers: Marginalization using the metric of the likelihood

Parameter estimation in ordinary differential equations, although applied and refined in various fields of the quantitative sciences, is still confronted with a variety of difficulties. One major challenge is finding the global optimum of a…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

Likelihood-based inference, central in modern particle physics data analysis requires the extensive evaluation of a likelihood function that depends on set of parameters defined by the statistical model under consideration. If an analytical…

We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing…

We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…

Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters…

Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…

Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…

As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an…

The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power {\delta}, which quantifies the degree of discounting of the…

In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to…

In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. This representation relates the mean effect and the heterogeneity variance estimation problems. An explicit form of…

The reconstruction of low-rank matrix from its noisy observation finds its usage in many applications. It can be reformulated into a constrained nuclear norm minimization problem, where the bound $\eta$ of the constraint is explicitly given…