In some application fields, series are affected by two different types of effects: abrupt changes (or change-points) and functional effects. We propose here a Bayesian approach that allows us to estimate these two parts. Here, the underlying piecewise-constant part (associated to the abrupt changes) is expressed as the product of a lower triangular matrix by a sparse vector and the functional part as a linear combination of functions from a large dictionary where we want to select the relevant ones. This problem can thus lead to a global sparse estimation and a stochastic search variable selection approach is used to this end. The performance of our proposed method is assessed using simulation experiments. Applications to three real datasets from geodesy, agronomy and economy fields are also presented.
AltamimiZCollilieuxXM/’etivierL (2011) ITRF2008: An improved solution of the International Terrestrial Reference Frame. Journal of Geodesy, 85, 457–73.
2.
BarbieriMMBergerJO (2004) Optimal predictive model selection. The Annals of Statistics, 32, 870–97.
3.
BarryDHartiganJA (2004) A Bayesian analysis for change point problems. Journal of the American Statistical Society, 88, 309–19.
4.
BertinKCollilieuxXLebarbierEMezaC (2017) Semi-parametric segmentation of multiple series using a DP-Lasso strategy. Journal of Statistical Computation and Simulation, 87, 1255–68.
5.
BickelPJRitovYTsybakovAB (2009) Simultaneous analysis of lasso and Dantzig selector. The Annals of Statistics, 37, 1705–32.
6.
BottoloLRichardsonS (2010) Evolutionary stochastic search for Bayesian model exploration. Bayesian Analysis, 5, 583–618.
7.
BoysRJHendersonDA (2004) A Bayesian approach to DNA sequence segmentation. Biometrics, 60, 573–88.
8.
CaussinusHMestreO (2004) Detection and correction of artificial shifts in climate series. Applied Statistics, 53, 405–25.
9.
DobigeonNTourneretJ-YScargleJ (2007) Joint segmentation of multivariate astronomical time series: Bayesian sampling with a hierarchical model. IEEE Transactions on Signal Processing, 55, 414–23.
10.
DongDFangPBockYChengMKMiyazakiS (2002) Anatomy of apparent seasonal variations from GPS-derived site position time series. Journal of Geophysical Research (Solid Earth), 107, ETG 9-1-ETG 9–16.
11.
ErdmanCEmersonJW (2008) A fast Bayesian change point analysis for the segmentation of microarray data. Bioinformatics, 24, 2143–48.
12.
FearnheadP (2006) Exact and efficient Bayesian inference for multiple changepoint problems. Statistics and Computing, 16, 203–13.
13.
GeorgeEIMcCullochRE (1993) Variable selection via Gibbs sampling. Journal of the American Statistical Association, 88, 881–89.
HannartANaveauP (2009) Bayesian multiple change points and segmentation: Application to homogenization of climatic series. Water Resources Research, 45, 1944–73.
16.
HarchaouiZLevy-LeducC (2010) Multiple change-point estimation with a total variation penalty. Journal of the American Statistical Association, 105, 1480–93.
17.
HardleWKerkyacharianGPicardDTsybakovA (1998) Wavelets, approximation, and statistical applications: Vol. 129. Lecture Notes in Statistics. New York, NY: Springer-Verlag.
18.
HarleFChatelainFGouy-PaillerCAchardS (2016) Bayesian model for multiple change-points detection in multivariate time series. IEEE Transactions on Signal Processing64, 4351–62.
19.
KingMAltamimiZBoehmJBosMDachREloseguiPFundFHernandez-PajaresMLavalleeDCerveiraP (2010) Improved constraints on models of glacial isostatic adjustment: A review of the contribution of ground-based geodetic observations. Surveys in Geophysics, 31, 465–507.
20.
LavielleMLebarbierE (2001) An application of MCMC methods for the multiple change-points problem. Signal processing, 81, 39–53.
21.
Le TaconF (2017) les Truffes: Biologie, ecologie et domestication. AgroParisTech.
22.
Le TaconFMarcaisBCourvoisierMMuratCMontpiedPBeckerM (2014) Climatic variations explain annual fluctuations in French perigord black true wholesale markets but do not explai the decrease in black true production over the last 48 years. Mycorrhiza, 24, S115–25.
23.
LiuJS (1994) The collapsed Gibbs sampler in Bayesian computations with application to a gene regulation problem. Journal of the American Statistical Association, 89, 958–66.
24.
MartinezAMenaR (2014) On a nonparametric change point detection model in Markovian regimes. Bayesian Analysis, 9, 823–58.
25.
MullerPParmigianiGRobertCRousseauJ (2004) Optimal sample size for multiple testing: The case of gene expression microarrays. Journal of the American Statistical Association, 99, 990–1001.
26.
MullerPParmigianiGRiceK (2006) FDR and Bayesian multiple comparisons rules. Proceedings of the Valencia/ISBA 8th World Meeting on Bayesian Statistics. URL http://biostats.bepress.com/jhubiostat/paper115
27.
PicardFLebarbierEHoebekeMRigaillGThiamBRobinS (2011) Joint segmentation, calling and normalization of multiple CGH proles. Biostatistics, 12, 413–28.
28.
R Core Team (2009) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.
29.
RayJAltamimiZCollilieuxXvan DamT (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions, 12, 55–64.
30.
RuggieriE (2013) A Bayesian approach to detecting change points in climatic records. International Journal of Climatology, 33, 520–28.
31.
ScargleJD (1982) Studies in astronomical time series analysis. II: Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal, 263, 835–53.
32.
SmithMKohnR (1997) Non parametric regression using Bayesian variable selection. Journal of Econometrics, 75, 317–44.
33.
TaiTLXingH (2010) A fast Bayesian change point analysis for the segmentation of microarray data. Bioinformatics, 24, 2143–48.
34.
van DykDAParkT (2008) Partially collapsed Gibbs samplers: Theory and methods. Journal of the American Statistical Association, 103, 790–96.
35.
WilliamsS (2003) Offsets in global positioning system time series. Journal of Geophysical Research (Solid Earth), 108, 2310.
36.
WyseJFrielNRueH (2011) Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments. Bayesian Analysis, 6, 501–28.
37.
ZellnerA (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In PK Goel and A Zellner eds. Bayesian inference and decision techniques: Essays in honour of Bruno De Finetti, pages 23343. New York: Elsevier Science Publishers, Inc.
