On marginal likelihood computation in change-point models

Bauwens, Luc; Rombouts, Jeroen V.K.

doi:10.1016/j.csda.2010.06.025

Cited by 23 publications

(23 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Change points are sometimes called turning points (McArdle and Wang, 2008) or break points (Stasinopoulos and Rigby, 1992; Muggeo, 2008). Models with more than one change point are typically applied to time series data, see, e.g., Bauwens and Rombouts (2012).…”

Section: Introductionmentioning

confidence: 99%

Change point models for cognitive tests using semi-parametric maximum likelihood

Hout¹,

Muniz‐Terrera²,

Matthews³

2013

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Random-effects change point models are formulated for longitudinal data obtained from cognitive tests. The conditional distribution of the response variable in a change point model is often assumed to be normal even if the response variable is discrete and shows ceiling effects. For the sum score of a cognitive test, the binomial and the beta-binomial distributions are presented as alternatives to the normal distribution. Smooth shapes for the change point models are imposed. Estimation is by marginal maximum likelihood where a parametric population distribution for the random change point is combined with a non-parametric mixing distribution for other random effects. An extension to latent class modelling is possible in case some individuals do not experience a change in cognitive ability. The approach is illustrated using data from a longitudinal study of Swedish octogenarians and nonagenarians that began in 1991. Change point models are applied to investigate cognitive change in the years before death.

show abstract

Section: Introductionmentioning

confidence: 99%

Change point models for cognitive tests using semi-parametric maximum likelihood

Hout¹,

Muniz‐Terrera²,

Matthews³

2013

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…8 Several objective Bayesian methods that do not rely on improper priors have been 9 developed, including "Bayes factor approximation" using information criteria (Wasserman, 10 2000) and the use of "intrinsic priors" sampled systematically from the observed data 11 (Berger & Pericchi, 1996). The intrinsic prior approach is applied to change-point analysis 12 specifically by Girón et al (2007). Both of these methods, in principle, permit closed-form 13 approximation of non-subjective posterior distributions, albeit given considerable compu- 14 tation.…”

mentioning

confidence: 99%

“…In some cases, reasonable priors 6 can be inferred from prior data; more controversially, they may be "elicited" from expert In the Supplement, each of the conjugate prior implementations includes a "rule-of-9 thumb" subjective prior derived from the data being analyzed, which can be used as a default 10 value. This approach is an 'empirical Bayes method,' (Casella, 1985) and represents a 11 compromise between the standard logic of Bayesian calculation and the practical limitations 12 of experimentation. In the example above where observations x fall in the range 5000 < 13 x < 6000, setting µ µ = median (x) would be more appropriate than µ µ = 0.0. for example, to use the rule-of-thumb prior calculated from pilot data in the analysis of a 20 subsequent experiment.…”

mentioning

confidence: 99%

“…For example, Chen & 9 Gupta (2011) describe a variety of frequentist change-point methods, and consistently find 10 that the maximum likehoods rise when additional change-points are added. This introduces 11 the additional difficulty of developing significance tests to determine whether the models 12 have improved more than expected by chance alone.…”

mentioning

confidence: 99%

“…There are, however, 4851 models with two change-points and 156849 models with three 10 change-points, a factorial progression. Because exhaustive testing of every combination is 11 out of the question, attention must instead focus on models that seem sufficiently plausible 12 to merit evaluation.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Untitled

Supplemental Information 6: Gaussian Data, Uncorrected vs. Corrected With Respect to Small Sample Bias

View full text Add to dashboard Cite

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described. Introduction 1The analysis of time series data is essential to most scientific disciplines. Given the 2 ability to measure the behavior of an agent, we often wish to know how the measured be-3 havior changes over time. This is true whether that agent is a single neuron firing action 4 potentials, a human participant making choices, or a central bank reporting GDP. Some-5 times, conditions do not change, and observations appear consistent (and display consistent 6 variability); in other cases, change happens gradually and continuously, in a manner befit-7 ting a fitted line or curve. Modeling phenomena in these terms is the bedrock of empirical 8 statistics.

show abstract

Comparing hierarchical models via the marginalized deviance information criterion

Quintero

2018

Statistics in Medicine

View full text Add to dashboard Cite

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent.

show abstract

On marginal likelihood computation in change-point models

Cited by 23 publications

References 29 publications

Change point models for cognitive tests using semi-parametric maximum likelihood

Change point models for cognitive tests using semi-parametric maximum likelihood

Untitled

Comparing hierarchical models via the marginalized deviance information criterion

Contact Info

Product

Resources

About