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In this paper, we develop a new method to estimate the parameters of a deteriorating system under perfect condition-based maintenance. This method is based on the asymptotical behavior of the system, which is studied by using the renewal…

In this paper we describe a general approach to optimal imperfect maintenance activities of a repairable equipment with independent components. Most of the existing works on optimal imperfect maintenance activities of a repairable equipment…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if…

Machine learning (ML) now pervades the field of Automated Program Repair (APR). Algorithms deploy neural machine translation and large language models (LLMs) to generate software patches, among other tasks. But, there are important…

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error…

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes,…

Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates in particular enjoy many desirable…

Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally…

This paper consider an MMLE (Modified Maximum Likelihood Estimation) based scheme to estimate software reliability using exponential distribution. The MMLE is one of the generalized frameworks of software reliability models of Non…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has…

We investigate the dependence of the maximum entropy method (MEM) reconstruction performance on the default model. The maximum entropy method is a reconstruction technique that utilizes prior information, referred to as the default model,…

This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…

In this paper we propose a new optimization model for maximum likelihood estimation of causal and invertible ARMA models. Through a set of numerical experiments we show how our proposed model outperforms, both in terms of quality of the…

Work on instruction-tuned Large Language Models (LLMs) has used automatic methods based on text overlap and LLM judgments as cost-effective alternatives to human evaluation. In this paper, we perform a meta-evaluation of such methods and…

A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…

We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the…

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…

Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and…