MCMC Methods for Periodic AR-Arch Models

2001 ◽  
Vol 34 (12) ◽  
pp. 67-70
Author(s):  
Wolfgang Polasek
Keyword(s):  
2011 ◽  
Vol 07 (02) ◽  
pp. 347-361 ◽  
Author(s):  
MARINHO G. ANDRADE ◽  
SANDRA C. OLIVEIRA

The purpose of this study is to address the inference problem of the parameters of autoregressive conditional heteroscedasticity (ARCH) models. Specifically, we present a comparison of the two approaches — Bayesian and Maximum Likelihood (ML) for ARCH models, and the specific mathematical and algorithmic formulations of these approaches. In the ML, estimation we obtain confidence intervals by using the Bootstrap simulation technique. In the Bayesian estimation, we present a reparametrization of the model which allows us to apply prior normal densities to the transformed parameters. The posterior estimates are obtained using Monte Carlo Markov Chain (MCMC) methods. The methodology is exemplified by considering two Brazilian financial time series: the Bovespa Stock Index — IBovespa and the Telebrás series. The order of each ARCH model is selected by using the Bayesian Information Criterion (BIC).


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Marco Molinari ◽  
Maria de Iorio ◽  
Nishi Chaturvedi ◽  
Alun Hughes ◽  
Therese Tillin

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.


Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 735-743 ◽  
Author(s):  
Pekka Uimari ◽  
Ina Hoeschele

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.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiroyuki Kawakatsu

AbstractThis paper considers a class of multivariate ARCH models with scalar weights. A new specification with hyperbolic weighted moving average (HWMA) is proposed as an analogue of the EWMA model. Despite the restrictive dynamics of a scalar weight model, the proposed model has a number of advantages that can deal with the curse of dimensionality. The empirical application illustrates that the (pseudo) out-of-sample multistep forecasts can be surprisingly more accurate than those from the DCC model.


Author(s):  
A K M Azad ◽  
Salem A Alyami

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.


2018 ◽  
Vol 46 (1) ◽  
pp. 26-58
Author(s):  
Marie Hušková ◽  
Natalie Neumeyer ◽  
Tobias Niebuhr ◽  
Leonie Selk

2008 ◽  
Vol 36 (2) ◽  
pp. 742-786 ◽  
Author(s):  
Piotr Fryzlewicz ◽  
Theofanis Sapatinas ◽  
Suhasini Subba Rao

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