Efficient MCMC for temporal epidemics via parameter reduction

Xiang, Fei; Neal, Peter

doi:10.1016/j.csda.2014.07.002

Cited by 19 publications

(28 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore we seek generic guidelines for updating multiple components of y at a time and optimising the performance of the resulting independent sampler. Specifically, this work formalises findings in [Xiang and Neal(2014)] and [Neal and Huang(2015)] in using the independence sampler for data augmentation giving simple guidelines for producing close to optimal independence samplers. The guidelines obtained are similar to those given in [Roberts et al(1997)] for the random walk Metropolis algorithm and comparisons with the random walk Metropolis algorithm are made.…”

Section: Introductionmentioning

confidence: 69%

“…For each individual, i say, infected during the course of the epidemic there will be an infection time, I i and a removal (recovery) time, R i , which mark the start and end of the infectious period, respectively. We follow [O' Neill and Roberts(1999)], [Neal and Roberts(2005)] and [Xiang and Neal(2014)] in assuming that the removal times, R = (R 1 , . .…”

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

“…We use the MCMC algorithm proposed in [Xiang and Neal(2014)], Section 3 with the modification that the number of components to be updated is fixed to k ∈ {1, 2, . .…”

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

“…, m}. As with [Xiang and Neal(2014)], the MCMC algorithm is applied to the extensively studied Abakaliki smallpox outbreak, [Bailey(1975), p.125], [O'Neill and Roberts(1999), O' Neill and Becker(2001), McKinley et al(2014)], where m = 30 and N = 120. We considered various fixed values of α = 1, 3, 10 with optimal k = 9, 17 and 30, respectively, based upon the maximised mean number of components updated over 100000 iterations, see Figure 3.…”

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

See 3 more Smart Citations

Optimal scaling of the independence sampler: Theory and practice

Lee¹,

Neal²

2018

Bernoulli

Self Cite

View full text Add to dashboard Cite

The independence sampler is one of the most commonly used MCMC algorithms usually as a component of a Metropolis-within-Gibbs algorithm. The common focus for the independence sampler is on the choice of proposal distribution to obtain an as high as possible acceptance rate. In this paper we have a somewhat different focus concentrating on the use of the independence sampler for updating augmented data in a Bayesian framework where a natural proposal distribution for the independence sampler exists. Thus we concentrate on the proportion of the augmented data to update to optimise the independence sampler. Generic guidelines for optimising the independence sampler are obtained for independent and identically distributed product densities mirroring findings for the random walk Metropolis algorithm. The generic guidelines are shown to be informative beyond the narrow confines of idealised product densities in two epidemic examples.

show abstract

Section: Introductionmentioning

confidence: 69%

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

“…We use the MCMC algorithm proposed in [Xiang and Neal(2014)], Section 3 with the modification that the number of components to be updated is fixed to k ∈ {1, 2, . .…”

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

Section: Homogeneously Mixing Sir Epidemicmentioning

confidence: 99%

See 2 more Smart Citations

Optimal scaling of the independence sampler: Theory and practice

Lee¹,

Neal²

2018

Bernoulli

Self Cite

View full text Add to dashboard Cite

show abstract

“…Within mathematical infectious disease modelling, the Abakaliki smallpox data set has been frequently cited, the first appearance being Bailey and Thomas (1971). The data are almost always used to illustrate new data analysis methodology, but in virtually all cases most aspects of the data are ignored apart from the population of 120 FTC individuals and the case detection times, while the models used are not particularly appropriate for smallpox (see for example Becker (1976), Yip (1989), O'Neill and Roberts (1999), O'Neill and Becker (2001), Huggins et al (2004), Boys and Giles (2007), Lau and Yip (2008), Clancy and O'Neill (2008), Kypraios (2009), Shanmugan (2011), Xiang and Neal (2014), McKinley et al (2014), Golightly et al (2014), Oh (2014), Xu et al (2016) and references therein). Ray and Marzouk (2008) use a more realistic smallpox model and take account of the compounds where individuals lived, but again ignore all non-FTC individuals.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Bayesian analysis of the Abakaliki smallpox data

2017

View full text Add to dashboard Cite

The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. The only previous analysis of the full data set relied on approximation methods to derive a likelihood and did not assess model adequacy. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian statistical analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations and which yield a wider range of results than previous analyses. We also carry out model assessment using simulation-based methods. Our findings suggest that the outbreak was largely driven by the interaction structure of the population, and that the introduction of control measures was not the sole reason for the end of the epidemic. We also obtain quantitative estimates of key quantities including reproduction numbers.

show abstract

A network epidemic model for online community commissioning data

2017

View full text Add to dashboard Cite

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli random graph, in which any two nodes have the same probability of being connected, does. Therefore, to study the propogation of "infection" across a social network, we propose a network epidemic model by combining a stochastic epidemic model and a preferential attachment model. A simulation study based on the subsequent Markov Chain Monte Carlo algorithm reveals an identifiability issue with the model parameters. Finally, the network epidemic model is applied to a set of online commissioning data.

show abstract

Efficient MCMC for temporal epidemics via parameter reduction

Cited by 19 publications

References 13 publications

Optimal scaling of the independence sampler: Theory and practice

Optimal scaling of the independence sampler: Theory and practice

Modelling and Bayesian analysis of the Abakaliki smallpox data

A network epidemic model for online community commissioning data

Contact Info

Product

Resources

About