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In cluster-specific studies, ordinary logistic regression and conditional logistic regression for binary outcomes provide maximum likelihood estimator (MLE) and conditional maximum likelihood estimator (CMLE), respectively. In this paper,…
We discuss estimation of the differentiated products demand system of Berry et al (1995) (BLP) by maximum likelihood estimation (MLE). We derive the maximum likelihood estimator in the case where prices are endogenously generated by firms…
We propose a fast algorithm for computing the GMM estimator in the BLP demand model (Berry, Levinsohn, and Pakes, 1995). Inspired by nested pseudo-likelihood methods for dynamic discrete choice models, our approach avoids repeatedly solving…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This…
After deploying a clinical prediction model, subsequently collected data can be used to fine-tune its predictions and adapt to temporal shifts. Because model updating carries risks of over-updating/fitting, we study online methods with…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…
Bayesian multinomial logistic-normal (MLN) models are popular for the analysis of sequence count data (e.g., microbiome or gene expression data) due to their ability to model multivariate count data with complex covariance structure.…
The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently,…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
We propose a new approach to estimating the random coefficient logit demand model for differentiated products when the vector of market-product level shocks is sparse. Assuming sparsity, we establish nonparametric identification of the…
We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…
Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…
The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via…
Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying…
Bayesian Optimization (BO) has been widely used to efficiently optimize expensive black-box functions with limited evaluations. In this paper, we investigate the use of BO for prompt engineering to enhance text classification with Large…