scholarly journals A Flexible Skewed Link Model for Ordinal Outcomes: An Application to Infertility

2020 ◽  
Vol 8 (A) ◽  
pp. 119-124
Author(s):  
Mohammad Chehrazi ◽  
Seyed Hassan Saadat ◽  
Mahmoud Hajiahmadi ◽  
Mirko Spiroski
Keyword(s):  
Monte Carlo ◽  
Ordinal Data ◽  
Monte Carlo Algorithm ◽  
Link Function ◽  
Posterior Distributions ◽  
Response Data ◽  
Improper Priors ◽  
Ordinal Regression Model ◽  
Link Model ◽  
Categorical Response

BACKGROUND: An important issue in modeling categorical response data is the choice of the links. The commonly used complementary log-log link is inclined to link misspecification due to its positive and fixed skewness parameter. AIM: The objective of this paper is to introduce a flexible skewed link function for modeling ordinal data with some covariates. METHODS: We introduce a flexible skewed link model for the cumulative ordinal regression model based on Chen model. RESULTS: The main advantage suggested by the proposed links is the skewed link provide much more identifiable than the existing skewed links. The propriety of posterior distributions under proper and improper priors is explored in detail. An efficient Markov chain Monte Carlo algorithm is developed for sampling from the posterior distribution. CONCLUSION: The proposed methodology is motivated and illustrated by ovary hyperstimulation syndrome data.

scholarly journals Quantum-Inspired Magnetic Hamiltonian Monte Carlo

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258277
Author(s):  
Wilson Tsakane Mongwe ◽  
Rendani Mbuvha ◽  
Tshilidzi Marwala
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Learning Community ◽  
Broad Class ◽  
Hamiltonian Dynamics ◽  
Mass Matrix ◽  
Monte Carlo Algorithm ◽  
Posterior Distributions ◽  
Hamiltonian Monte Carlo ◽  
Random Mass

Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be random with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Monte Carlo (MHMC) has been recently proposed as an extension to HMC and adds a magnetic field to HMC which results in non-canonical dynamics associated with the movement of a particle under a magnetic field. In this work, we utilise the non-canonical dynamics of MHMC while allowing the mass matrix to be random to create the Quantum-Inspired Magnetic Hamiltonian Monte Carlo (QIMHMC) algorithm, which is shown to converge to the correct steady state distribution. Empirical results on a broad class of target posterior distributions show that the proposed method produces better sampling performance than HMC, MHMC and HMC with a random mass matrix.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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