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1. Slice Sampling Reparameterization Gradients

   Zoltowski, David; Cai, Diana; Adams, Ryan P. (January 2021, Advances in neural information processing systems)

   Many probabilistic modeling problems in machine learning use gradient-based optimization in which the objective takes the form of an expectation. These problems can be challenging when the parameters to be optimized determine the probability distribution under which the expectation is being taken, as the na\"ive Monte Carlo procedure is not differentiable. Reparameterization gradients make it possible to efficiently perform optimization of these Monte Carlo objectives by transforming the expectation to be differentiable, but the approach is typically limited to distributions with simple forms and tractable normalization constants. Here we describe how to differentiate samples from slice sampling to compute \textit{slice sampling reparameterization gradients}, enabling a richer class of Monte Carlo objective functions to be optimized. Slice sampling is a Markov chain Monte Carlo algorithm for simulating samples from probability distributions; it only requires a density function that can be evaluated point-wise up to a normalization constant, making it applicable to a variety of inference problems and unnormalized models. Our approach is based on the observation that when the slice endpoints are known, the sampling path is a deterministic and differentiable function of the pseudo-random variables, since the algorithm is rejection-free. We evaluate the method on synthetic examples and apply it to a variety of applications with reparameterization of unnormalized probability distributions. 

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2. Dynamic ordered panel logit models

   https://doi.org/10.3982/QE2052  

   Honoré, Bo E; Muris, Chris; Weidner, Martin (January 2025, Quantitative Economics)

   This paper studies a dynamic ordered logit model for panel data with fixed effects. The main contribution of the paper is to construct a set of valid moment conditions that are free of the fixed effects. The moment functions can be computed using four or more periods of data, and the paper presents sufficient conditions for the moment conditions to identify the common parameters of the model, namely the regression coefficients, the autoregressive parameters, and the threshold parameters. The availability of moment conditions suggests that these common parameters can be estimated using the generalized method of moments, and the paper documents the performance of this estimator using Monte Carlo simulations and an empirical illustration to self‐reported health status using the British Household Panel Survey. 

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3. Growing pains: understanding the impact of likelihood uncertainty on hierarchical Bayesian inference for gravitational-wave astronomy

   https://doi.org/10.1093/mnras/stad2968  

   Talbot, Colm; Golomb, Jacob (October 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Observations of gravitational waves emitted by merging compact binaries have provided tantalizing hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems (mass, spin, distance) used to extract these inferences about the Universe are subject to large uncertainties. The most widely used method of performing these analyses requires performing many Monte Carlo integrals to marginalize over the uncertainty in the properties of the individual binaries and the survey selection bias. These Monte Carlo integrals are subject to fundamental statistical uncertainties. Previous treatments of this statistical uncertainty have focused on ensuring that the precision of the inferred inference is unaffected; however, these works have neglected the question of whether sufficient accuracy can also be achieved. In this work, we provide a practical exploration of the impact of uncertainty in our analyses and provide a suggested framework for verifying that astrophysical inferences made with the gravitational-wave transient catalogue are accurate. Applying our framework to models used by the LIGO–Virgo–KAGRA collaboration and in the wider literature, we find that Monte Carlo uncertainty in estimating the survey selection bias is the limiting factor in our ability to probe narrow population models and this will rapidly grow more problematic as the size of the observed population increases. 

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4. Modeling of fluidized systems using a novel Monte Carlo approach for granular interactions

   https://doi.org/10.1002/aic.70212  

   Black, Matthew; Morris, Aaron (April 2026, AIChE Journal)

   Abstract A kinetic theory‐based Monte Carlo algorithm for simulating particle dynamics within a gas–solid flow is presented. The technique, called the energy direct simulation Monte Carlo (EDSMC) method, has a formulation that is unique in the field of fluidization modeling. EDSMC has previously been applied to simple granular flows, but has never been used to model fluidization. Several additions to the algorithm designed to improve behavior under fluidization conditions are described. The method is then validated by simulating the homogeneous cooling state, where the relaxation rate of the granular temperature is found to be consistent with theory. EDSMC is also used to simulate particles in the turbulent and fast‐fluidization regimes. Compared with DEM simulations under the same conditions, EDSMC is found to exhibit similar bed dynamics and bubble properties while running between 4 and 20 times faster. 

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5. Derivative Based Global Sensitivity Analysis using Conjugate Unscented Transforms

   Nandi, Souransu; Singh, Tarunraj (July 2019, 2019 American Control Conference (ACC))

   In this paper, a novel way to compute derivativebased global sensitivity measures is presented. Conjugate Unscented Transform (CUT) is used to evaluate the multidimensional definite integrals which lead to the sensitivity measures. The method is compared with Monte Carlo estimates as well as the screening method of Morris. It is shown that using CUT provides a much more accurate estimate of sensitivity measures as compared to Monte Carlo (with far lesser computational cost) as well as the Morris method (with similar computational cost). Illustrations on three test functions are presented as evidence. 

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