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Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of…

Time-series forecasting plays an important role in many domains. Boosted by the advances in Deep Learning algorithms, it has for instance been used to predict wind power for eolic energy production, stock market fluctuations, or motor…

We propose a modified version of the three-step estimation method for the latent class model with covariates, which may be used to estimate latent Markov models for longitudinal data. The three-step estimation approach we propose is based…

Being probabilistic models, during inference large language models (LLMs) display rare events: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage…

Observational studies of recurrent event rates are common in biomedical statistics. Broadly, the goal is to estimate differences in event rates under two treatments within a defined target population over a specified followup window.…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as…

The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM…

The ICH E9 addendum introduces the term intercurrent event to refer to events that happen after randomisation and that can either preclude observation of the outcome of interest or affect its interpretation. It proposes five strategies for…

Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are…

Mixture models postulate the overall population as a mixture of finite subpopulations with unobserved membership. Fitting mixture models usually requires large sample sizes and combining data from multiple sites can be beneficial. However,…

Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in…

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence…

Event time models predict occurrence times of an event of interest based on known features. Recent work has demonstrated that neural networks achieve state-of-the-art event time predictions in a variety of settings. However, standard event…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…

We address causal estimation in semi-competing risks settings, where a non-terminal event may be precluded by one or more terminal events. We define a principal-stratification causal estimand for treatment effects on the non-terminal event,…