Estimating the Physical Probability for Successful Stock Swap Mergers: An Application of MCMC Methods

2017 ◽  
Author(s):  
Giuseppe Corvasce
Keyword(s):  
Mcmc Methods ◽  
Physical Probability

scholarly journals Modelling ethnic differences in the distribution of insulin resistance via Bayesian nonparametric processes: an application to the SABRE cohort study

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Marco Molinari ◽  
Maria de Iorio ◽  
Nishi Chaturvedi ◽  
Alun Hughes ◽  
Therese Tillin
Keyword(s):  
Insulin Resistance ◽  
Type 2 Diabetes ◽  
Mcmc Methods ◽  
Model Assessment ◽  
Bayesian Nonparametric ◽  
Nonparametric Prior ◽  
Posterior Inference ◽  
Regression Framework ◽  
Analyse Data

AbstractWe analyse data from the Southall And Brent REvisited (SABRE) tri-ethnic study, where measurements of metabolic and anthropometric variables have been recorded. In particular, we focus on modelling the distribution of insulin resistance which is strongly associated with the development of type 2 diabetes. We propose the use of a Bayesian nonparametric prior to model the distribution of Homeostasis Model Assessment insulin resistance, as it allows for data-driven clustering of the observations. Anthropometric variables and metabolites concentrations are included as covariates in a regression framework. This strategy highlights the presence of sub-populations in the data, characterised by different levels of risk of developing type 2 diabetes across ethnicities. Posterior inference is performed through Markov Chains Monte Carlo (MCMC) methods.

scholarly journals Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 735-743 ◽  
Author(s):  
Pekka Uimari ◽  
Ina Hoeschele
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Allele Frequencies ◽  
Mcmc Methods ◽  
Substitution Effects ◽  
Indicator Variable ◽  
Trait Loci

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.

scholarly journals Discovering novel cancer bio-markers in acquired lapatinib resistance using Bayesian methods

2021 ◽  
Author(s):  
A K M Azad ◽  
Salem A Alyami
Keyword(s):  
Breast Cancer ◽  
Cancer Progression ◽  
Sampling Methods ◽  
Differential Expression Analysis ◽  
Breast Cancer Cell Lines ◽  
Mcmc Methods ◽  
Tgf Beta ◽  
Exponential Random Graph Models ◽  
Statistical Process ◽  
Dual Inhibitor

Abstract Signalling transduction pathways (STPs) are commonly hijacked by many cancers for their growth and malignancy, but demystifying their underlying mechanisms is difficult. Here, we developed methodologies with a fully Bayesian approach in discovering novel driver bio-markers in aberrant STPs given high-throughput gene expression (GE) data. This project, namely ‘PathTurbEr’ (Pathway Perturbation Driver) uses the GE dataset derived from the lapatinib (an EGFR/HER dual inhibitor) sensitive and resistant samples from breast cancer cell lines (SKBR3). Differential expression analysis revealed 512 differentially expressed genes (DEGs) and their pathway enrichment revealed 13 highly perturbed singalling pathways in lapatinib resistance, including PI3K-AKT, Chemokine, Hippo and TGF-$\beta $ singalling pathways. Next, the aberration in TGF-$\beta $ STP was modelled as a causal Bayesian network (BN) using three MCMC sampling methods, i.e. Neighbourhood sampler (NS) and Hit-and-Run (HAR) sampler that potentially yield robust inference with lower chances of getting stuck at local optima and faster convergence compared to other state-of-art methods. Next, we examined the structural features of the optimal BN as a statistical process that generates the global structure using $p_1$-model, a special class of Exponential Random Graph Models (ERGMs), and MCMC methods for their hyper-parameter sampling. This step enabled key drivers identification that drive the aberration within the perturbed BN structure of STP, and yielded 34, 34 and 23 perturbation driver genes out of 80 constituent genes of three perturbed STP models of TGF-$\beta $ signalling inferred by NS, HAR and MH sampling methods, respectively. Functional-relevance and disease-relevance analyses suggested their significant associations with breast cancer progression/resistance.

MCMC Methods for Periodic AR-Arch Models

2001 ◽  
Vol 34 (12) ◽  
pp. 67-70
Author(s):  
Wolfgang Polasek
Keyword(s):  
Mcmc Methods ◽  
Arch Models

scholarly journals Bayesian Metric Multidimensional Scaling

2013 ◽  
Vol 21 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Ryan Bakker ◽  
Keith T. Poole
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Optimal Solution ◽  
Full Rank ◽  
Mcmc Methods ◽  
Ratio Scale ◽  
Posterior Distributions ◽  
Point Estimates ◽  
Inflection Points

In this article, we show how to apply Bayesian methods to noisy ratio scale distances for both the classical similarities problem as well as the unfolding problem. Bayesian methods produce essentially the same point estimates as the classical methods, but are superior in that they provide more accurate measures of uncertainty in the data. Identification is nontrivial for this class of problems because a configuration of points that reproduces the distances is identified only up to a choice of origin, angles of rotation, and sign flips on the dimensions. We prove that fixing the origin and rotation is sufficient to identify a configuration in the sense that the corresponding maxima/minima are inflection points with full-rank Hessians. However, an unavoidable result is multiple posterior distributions that are mirror images of one another. This poses a problem for Markov chain Monte Carlo (MCMC) methods. The approach we take is to find the optimal solution using standard optimizers. The configuration of points from the optimizers is then used to isolate a single Bayesian posterior that can then be easily analyzed with standard MCMC methods.

scholarly journals On Estimating Non-standard Discrete Distributions Using Adaptive MCMC Methods

2018 ◽  
Vol 7 (3) ◽  
pp. 1 ◽  
Author(s):  
Hatem Baffoun ◽  
Mekki Hajlaoui ◽  
Abdeljelil Farhat
Keyword(s):  
Performance Criterion ◽  
Discrete Distributions ◽  
Mcmc Methods ◽  
Adaptive Mcmc ◽  
Testing Problem ◽  
Sampling Schemes ◽  
Bayesian Hypothesis Testing ◽  
Hypothesis Testing Problem ◽  
Delayed Rejection ◽  
Frequency Estimator

In this paper, we compare empirically the performance of some adaptive MCMC methods, that is, Adaptive Metropolis (AM) algorithm, Single Component Adaptive Metropolis (SCAM) algorithm and Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The context is the simulation of non-standard discrete distributions. The performance criterion used is the precision of the frequency estimator. An application to a Bayesian hypothesis testing problem shows the superiority of the DRAM algorithm over the other considered sampling schemes.

scholarly journals A Bayesian approach to analyzing phenotype microarray data enables estimation of microbial growth parameters

2016 ◽  
Vol 14 (03) ◽  
pp. 1650007 ◽  
Author(s):  
Matthias Gerstgrasser ◽  
Sarah Nicholls ◽  
Michael Stout ◽  
Katherine Smart ◽  
Chris Powell ◽  
...  
Keyword(s):  
High Throughput ◽  
Bayesian Approach ◽  
Microarray Data ◽  
Time Course ◽  
Microbial Growth ◽  
Mcmc Methods ◽  
Lag Phase ◽  
Maximum Output ◽  
Phenotype Microarray ◽  
Phenotype Microarrays

Biolog phenotype microarrays (PMs) enable simultaneous, high throughput analysis of cell cultures in different environments. The output is high-density time-course data showing redox curves (approximating growth) for each experimental condition. The software provided with the Omnilog incubator/reader summarizes each time-course as a single datum, so most of the information is not used. However, the time courses can be extremely varied and often contain detailed qualitative (shape of curve) and quantitative (values of parameters) information. We present a novel, Bayesian approach to estimating parameters from Phenotype Microarray data, fitting growth models using Markov Chain Monte Carlo (MCMC) methods to enable high throughput estimation of important information, including length of lag phase, maximal “growth” rate and maximum output. We find that the Baranyi model for microbial growth is useful for fitting Biolog data. Moreover, we introduce a new growth model that allows for diauxic growth with a lag phase, which is particularly useful where Phenotype Microarrays have been applied to cells grown in complex mixtures of substrates, for example in industrial or biotechnological applications, such as worts in brewing. Our approach provides more useful information from Biolog data than existing, competing methods, and allows for valuable comparisons between data series and across different models.

scholarly journals A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 393
Author(s):  
Jan F. Haase ◽  
Luca Dellantonio ◽  
Alessio Celi ◽  
Danny Paulson ◽  
Angus Kan ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Hamiltonian Formulation ◽  
Mcmc Methods ◽  
Continuous Limit ◽  
Abelian Gauge ◽  
Gauge Groups

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

scholarly journals Measuring hospital spatial wingspan by using a discrete choice model with utility-threshold

2018 ◽  
Author(s):  
Saley Issa ◽  
Ribatet Mathieu ◽  
Molinari Nicolas
Keyword(s):  
Monte Carlo ◽  
Discrete Choice ◽  
Choice Model ◽  
Discrete Choice Models ◽  
Mcmc Methods ◽  
Hospital Competition ◽  
Policy Makers ◽  
New Approach ◽  
Asthma Patients ◽  
The One

AbstractPolicy makers increasingly rely on hospital competition to incentivize patients to choose high-value care. Travel distance is one of the most important drivers of patients’ decision. The paper presents a method to numerically measure, for a given hospital, the distance beyond which no patient is expected to choose the hospital for treatment by using a new approach in discrete choice models. To illustrate, we compared 3 hospitals attractiveness related to this distance for asthma patients admissions in 2009 in Hérault (France), showing, as expected, CHU Montpellier is the one with the most important spatial wingspan. For estimation, Monte Carlo Markov Chain (MCMC) methods are used.

scholarly journals Bayesian Change Point Detection of Vegetation Cover Dynamics of Akure Forest Reserve, Ondo State in Southwestern, Nigeria

2021 ◽  
Vol 25 (8) ◽  
pp. 1449-1452
Author(s):  
P.A. Ukoha ◽  
S.J. Okonkwo ◽  
A.R. Adewoye
Keyword(s):  
Time Series ◽  
Change Point ◽  
Vegetation Index ◽  
Google Earth ◽  
Change Point Detection ◽  
Mcmc Methods ◽  
Landsat Images ◽  
Southwestern Nigeria ◽  
Forest Reserve ◽  
Point Detection

This study uses satellite acquired vegetation index data to monitor changes in Akure forest reserve. Enhanced Vegetation Index (EVI) time series datasets were extracted from Landsat images; extraction was performed on the Google Earth Engine (GEE) platform. The datasets were analyzed using Bayesian Change Point (BCP) to monitor the abrupt changes in vegetation dynamics associated with deforestation. The BCP shows the magnitude of changes over the years, from the posterior data obtained. BCP focuses on changes in the long‐range using Markov Chain Monte Carlo (MCMC) methods, this returns posterior probability at > 0.5% of a change point occurring at each time index in the time series. Three decades of Landsat data were classified using the random forest algorithm to assess the rate of deforestation within the study area. The results shows forest in 2000 (97.7%), 2010 (89.4%), 2020 (84.7%) and non-forest increase 2000 (2.0%), 2010 (10.6%), 2020 (15.3%). Kappa coefficient was also used to determine the accuracy of the classification.

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