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The tensor Ising model is a discrete exponential family used for modeling binary data on networks with not just pairwise, but higher-order dependencies. A particularly important class of tensor Ising models are the tensor Curie-Weiss…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
Phase II dose finding studies in clinical drug development are typically conducted to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to…
Modeling sparse data such as microbiome and transcriptomics (RNA-seq) data is very challenging due to the exceeded number of zeros and skewness of the distribution. Many probabilistic models have been used for modeling sparse data,…
Local Interpretable Model-Agnostic Explanations (LIME) is a popular method to perform interpretability of any kind of Machine Learning (ML) model. It explains one ML prediction at a time, by learning a simple linear model around the…
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods…
We consider a re-sampling scheme for estimation of the population parameters in the mixed effects nonlinear regression models of the type use for example in clinical pharmacokinetics, say. We provide an estimation procedure which {\it…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
Large Language Models (LLMs) have shown remarkable capabilities as AI agents. However, existing methods for enhancing LLM-agent abilities often lack a focus on data quality, leading to inefficiencies and suboptimal results in both…
In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression,…
Missing data are inevitable in longitudinal studies. Traditional methods, such as the full information maximum likelihood (FIML), are commonly used to handle ignorable missing data. However, they may lead to biased model estimation due to…
The inherent bias pathology of the maximum likelihood (ML) estimation method is confirmed for models with unknown parameters $\theta$ and $\psi$ when MLE $\hat \psi$ is function of MLE $\hat \theta.$ To reduce $\hat \psi$'s bias the…
One of the most common methods for statistical inference is the maximum likelihood estimator (MLE). The MLE needs to compute the normalization constant in statistical models, and it is often intractable. Using unnormalized statistical…
A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression…
Combining information from multiple samples is often needed in biomedical and economic studies, but the differences between these samples must be appropriately taken into account in the analysis of the combined data. We study estimation for…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
Linear mixed-effects models have increasingly replaced mixed-model analyses of variance for statistical inference in factorial psycholinguistic experiments. Although LMMs have many advantages over ANOVA, like ANOVAs, setting them up for…
The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…