### Citations

5891 | A tutorial on hidden Markov models and selected applications in speech recognition,”
- Rabiner
- 1989
(Show Context)
Citation Context ...ore, hidden semi-Markov process have also been referred to as “hidden Markov 12 Models with explicit duration” (Mitchell et al., 1995; Dewar et al., 2012) or “variable-duration hidden Markov Models” (=-=Rabiner, 1989-=-). We generate 1,000 datasets (1000 observations each) using a hidden semi-Markov process with four states and a negative binomial distribution for the state occupancy distribution. More specifically,... |

941 | Hierarchical Dirichlet processes
- Teh, Jordan, et al.
(Show Context)
Citation Context ...end on each single clone or the the distance between adjacent clones (Marioni et al., 2006). Using a Bayesian nonparametric approach, Du et al. propose a sticky Hierarchical DP-HMM (Fox et al., 2011; =-=Teh et al., 2006-=-) to infer the number of states in an HMM, while also imposing state persistence. Yau et al. (2011) also propose a nonparametric Bayesian HMM, but use instead a DP mixture to model the likelihood in e... |

652 | Bayesian density estimation and inference using mixtures,”
- Escobar, West
- 1995
(Show Context)
Citation Context ...g by a HMM with 4 states. where Ai and Bi are defined as above and B(x,y) = Γ(x)Γ(y)/Γ(x+ y) denotes the Beta function. Equation (12) is an adaptation of well known results for the Dirichlet Process (=-=Escobar and West, 1995-=-). 4 AComparison with Hidden Semi-Markov Models In many problems (e.g. change point detection), hidden Markov Models are used as computationally convenient substitutes for temporal processes that are ... |

628 | Markov chain sampling methods for Dirichlet process mixture models
- Neal
(Show Context)
Citation Context ...θi = θ ∗j , i = 1, . . . ,n. Again, if f (y|θ) and G0 are conjugate, the full conditional of θ ∗j is available in closed form, otherwise we can update θ ∗j by standard Metropolis Hastings algorithms (=-=Neal, 2000-=-). Finally, we note that if pi(α n,β n) is a prior distribution for the Beta hyper-parameters α n and β n, one could implement a Metropolis Hasting scheme to learn about their posterior distribution, ... |

441 |
Ferguson distributions via Polya urn schemes. The Annals of Statistics,
- Blackwell, MacQueen
- 1973
(Show Context)
Citation Context ...00; Hansen and Pitman, 2000; Lee et al., 2008, for more details). The most notable example of exchangeable SS-sequences is the Blackwell MacQueen sampling rule, which defines a Dirichlet Process (see =-=Blackwell and MacQueen, 1973-=-; Ishwaran and Zarepour, 2003). Let p be a DP with mass parameter γ and base measure G0(·), denoted as p ∼ DP(γ,G0). Then, the corresponding sequence of predictive probability function is the well-kno... |

337 | The positive false discovery rate: a Bayesian interpretation and the q-value.
- Storey
- 2003
(Show Context)
Citation Context ...rom our model. The q-value is the FDR analogue of the p-value, as it measures the minimum FDR threshold at which we may determine that a region corresponds to significant copy number gains or losses (=-=Storey, 2003-=-, 2007). More specifically, after conducting a clone based test as described in the previous paragraph, we identify regions of interest by taking into account the strings of consecutive calls. These r... |

228 | Combinatorial stochastic processes
- Pitman
- 2002
(Show Context)
Citation Context ...(see below); however, the proof can be easily extended to a general CID sequence. Two interesting types of CID sampling sequences are the following: a) CID Pitman-Yor sequences. A Pitman-Yor process (=-=Pitman, 2006-=-), is an exchangeable sequence characterized by the following predictive probability functions, P{θn+1 ∈ · |θ1, . . . ,θn}= ∑Knj=1 n jn−α γ+n δθ ∗j (·)+ γ+αKn γ+n G0(·), (5) for γ > 0 and α ∈ [0,1], a... |

223 | Estimating mixture of Dirichlet process models. - MacEachern, Müller - 1998 |

171 |
On a class of Bayesian nonparametric estimates: I Density estimates.
- Lo
- 1984
(Show Context)
Citation Context ... for p. Then, the hierarchical model specification can be concisely described as follows, θ1,θ2, . . . |p∼ p p∼ Q. (2) Model (1)–(2) schematically encompasses both popular Dirichlet Process mixtures (=-=Lo, 1984-=-) as well as Dependent Dirichlet Process mixtures (MacEachern, 1999). The prior process p can often be represented by means of a sequence of predictive distributions that typically encode exchangeabil... |

170 |
Negative Binomial Regression,
- Hilbe
- 2007
(Show Context)
Citation Context ...y distribution. More specifically, we parametrize the negative binomial in terms of its mean and an ancillary parameter, which is directly related to the amount of overdispersion of the distribution (=-=Hilbe, 2011-=-; Airoldi et al., 2006). If the data are not overdispersed, the Negative Binomial reduces to the Poisson, and the ancillary parameter is zero. For the simulations presented here, we consider a NegBin(... |

145 | Detecting differential gene expression with a semiparametric hierarchical mixture method,” - Newton, Noueiry, et al. - 2004 |

136 | Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory; Papers in honor of
- Pitman
- 1996
(Show Context)
Citation Context ...of predictive probability functions, P{θn+1 ∈ · |θ1, . . . ,θn}= n ∑ i=1 qn,iδθi(·)+qn,n+1G0(·), (3) 4 where δx(·) denotes a point mass at x, and G0 is a non-atomic probability measure (base measure, =-=Pitman, 1996-=-). The weights qn,i, i = 1, . . . ,n+ 1, are non–negative functions of (θ1, . . . ,θn), such that ∑n+1i=1 qn,i = 1, and define the probability that the sampled value of θn+1 coincides with one of the ... |

135 |
Genomic and transcriptional aberrations linked to breast cancer pathophysiologies.
- Chin, DeVries, et al.
- 2006
(Show Context)
Citation Context ...nt, in Figure 1 (a) we consider the frequency of genome copy number abnormalities, as estimated from data obtained in a classical study of the genetic determinants of breast cancer pathophysiologies (=-=Chin et al., 2006-=-). The raw data measure genome copy number gains and losses over 145 primary breast tumor samples, across the 23 chromosomes, obtained using BAC array Comparative Genomic Hybridization (CGH). Regions ... |

130 |
Dependent nonparametric processes
- MacEachern
- 1999
(Show Context)
Citation Context ...oncisely described as follows, θ1,θ2, . . . |p∼ p p∼ Q. (2) Model (1)–(2) schematically encompasses both popular Dirichlet Process mixtures (Lo, 1984) as well as Dependent Dirichlet Process mixtures (=-=MacEachern, 1999-=-). The prior process p can often be represented by means of a sequence of predictive distributions that typically encode exchangeability assumptions on the model parameters and the data (see Section 2... |

78 |
Variable duration models for speech,”
- Ferguson
- 1980
(Show Context)
Citation Context ...emporal processes that are known to be more complex than what could be implied by first order Markovian dynamics. Here, we generate non-exchangeable sequences from a hidden semi-Markov process (HSMM; =-=Ferguson, 1980-=-; Yu, 2010) and study how the Beta-GOS process performs in fitting this type of data. Hidden semi-Markov processes are an extension of the popular hidden Markov model where the time spent in each stat... |

77 | BioHMM: a heterogeneous hidden markov model for segmenting array CGH data. - Marioni - 2006 |

56 | Distance dependent Chinese restaurant processes - Blei, Frazier |

44 |
A sticky HDP-HMM with application to speaker diarization.
- Fox, Sudderth, et al.
- 2011
(Show Context)
Citation Context ...between states depend on each single clone or the the distance between adjacent clones (Marioni et al., 2006). Using a Bayesian nonparametric approach, Du et al. propose a sticky Hierarchical DP-HMM (=-=Fox et al., 2011-=-; Teh et al., 2006) to infer the number of states in an HMM, while also imposing state persistence. Yau et al. (2011) also propose a nonparametric Bayesian HMM, but use instead a DP mixture to model t... |

42 |
Bayesian hidden markov modeling of array cgh data
- Guha, Li, et al.
- 2008
(Show Context)
Citation Context ...se gamma distribution for τ centered around τ = 0.1. This choice of τ is motivated by the typical scale of array CGH data and is in accordance with similar choices in the literature (see, for example =-=Guha et al., 2008-=-). Figure 4 exemplifies the fit to chromosome 8 on two tumor samples. The model is able to identify regions of reduced copy number variation and high amplification. Note how contiguous clones tend to ... |

41 | Variable selection in clustering via Dirichlet process mixture models.
- Kim, Tadesse, et al.
- 2006
(Show Context)
Citation Context ...tric methods have been widely employed for the analysis of various types of data in genetics, e.g. for identifying disease subtypes and isolating discriminating genes, proteins or samples (see, e.g., =-=Kim et al., 2006-=-; Guindani et al., 2009; Lee et al., 2013). In order to take into account measurement characteristics (e.g., continuos support, long tails, skewness, multimodality or overdispersion of the frequency d... |

38 | Fdr and Bayesian multiple comparisons rules. In: Bernardo, - Muller - 2006 |

33 | The optimal discovery procedure for large-scale significance testing, with applications to comparative microarray experiments,” - Storey, Dai, et al. - 2007 |

30 | Bayesian non-parametric hidden markov models with applications in genomics. - Yau, Papaspiliopoulos, et al. - 2011 |

25 |
Cluster-based analysis of FMRI data.
- Heller, Stanley, et al.
- 2006
(Show Context)
Citation Context ... be pre-specified on the basis of the information available in the literature. The optimality of the type of procedures here described for cluster based FDR is discussed in Sun et al., 2015. See also =-=Heller et al., 2006-=-, Müller et al., 2007 and Ji et al., 2008). In Table 1 we report the q-values from a set of candidate oncogenes in well-known regions of recurrent amplification (notably, 8p12, 8q24, 11q13-14, 12q131... |

23 | Who wrote Ronald Reagan’s radio addresses
- Airoldi
- 2003
(Show Context)
Citation Context ...n. More specifically, we parametrize the negative binomial in terms of its mean and an ancillary parameter, which is directly related to the amount of overdispersion of the distribution (Hilbe, 2011; =-=Airoldi et al., 2006-=-). If the data are not overdispersed, the Negative Binomial reduces to the Poisson, and the ancillary parameter is zero. For the simulations presented here, we consider a NegBin(15,0.15), which corres... |

22 | Prediction rules for exchangeable sequences related to species sampling
- Hansen, Pitman
(Show Context)
Citation Context ...quency n jn = |Π(n)j | of each value θ ∗j in θ(n), j = 1, . . . ,Kn, then the sequence θ1,θ2, . . . is exchangeable. The result characterizes all exchangeable SS-sequencies (see Fortini et al., 2000; =-=Hansen and Pitman, 2000-=-; Lee et al., 2008, for more details). The most notable example of exchangeable SS-sequences is the Blackwell MacQueen sampling rule, which defines a Dirichlet Process (see Blackwell and MacQueen, 197... |

19 | Limit theorems for a class of identically distributed random variables
- Berti, Pratelli, et al.
- 2004
(Show Context)
Citation Context ...pecific choice of the weights pn,i’s determines the clustering behavior of the sequence (θn)n. In this chapter, we focus on the general class of conditionally identically distributed (CID) sequences (=-=Berti et al., 2004-=-). This class generalizes the notion of exchangeable sequences, while still preserving some of their important characteristics. Formally, a sequence (θn)n≥1 is CID with respect to a filtration G = (Gn... |

12 | Bayesian generalized product partition model - Park, Dunson |

10 | Inference in Hidden Markov Models with Explicit State Duration Distributions
- Dewar, Wiggins, et al.
- 2012
(Show Context)
Citation Context ... distribution characterizes ordinary hidden Markov models. Therefore, hidden semi-Markov process have also been referred to as “hidden Markov 12 Models with explicit duration” (Mitchell et al., 1995; =-=Dewar et al., 2012-=-) or “variable-duration hidden Markov Models” (Rabiner, 1989). We generate 1,000 datasets (1000 observations each) using a hidden semi-Markov process with four states and a negative binomial distribut... |

10 | A Bayesian discovery procedure - Guindani, Müller, et al. - 2009 |

9 |
Exchangeability, predictive distributions and parametric models.
- Fortini, Ladelli, et al.
- 2000
(Show Context)
Citation Context ...ch block, i.e. the frequency n jn = |Π(n)j | of each value θ ∗j in θ(n), j = 1, . . . ,Kn, then the sequence θ1,θ2, . . . is exchangeable. The result characterizes all exchangeable SS-sequencies (see =-=Fortini et al., 2000-=-; Hansen and Pitman, 2000; Lee et al., 2008, for more details). The most notable example of exchangeable SS-sequences is the Blackwell MacQueen sampling rule, which defines a Dirichlet Process (see Bl... |

9 | Random partition models with regression on covariates. - Muller, Quintana - 2010 |

8 | Defining Predictive Probability Functions for Species Sampling Models. Technical report.Currently available at odin.mdacc.tmc.edu/~pm/pap/LQMT08.pdf - Lee, Quintana, et al. - 2008 |

7 | Conditionally identically distributed species sampling sequences
- Bassetti, Crimaldi, et al.
- 2010
(Show Context)
Citation Context ...f the DP, obtained by setting α = 0 in (6), is similar to that of the classical DP: if the Wi’s are i.i.d. with finite variance and mean E[Wi] = m, then Kn/ log(n) converges almost surely to γ/m (see =-=Bassetti et al., 2010-=-, Example 5.8). The situation is less simple for the case in which α 6= 0. b) Beta-GOS sequences. An alternative specification of (4) considers weights obtained as a product of independent Beta random... |

6 | Bayesian random segmentation models to identify shared copy number aberrations for array CGH data. J Am Stat Assoc - Baladandayuthapani, Ji, et al. |

6 |
Bayesian models based on test statistics for multiple hypothesis testing problems",
- Yuan, Lu, et al.
- 2008
(Show Context)
Citation Context ...ion available in the literature. The optimality of the type of procedures here described for cluster based FDR is discussed in Sun et al., 2015. See also Heller et al., 2006, Müller et al., 2007 and =-=Ji et al., 2008-=-). In Table 1 we report the q-values from a set of candidate oncogenes in well-known regions of recurrent amplification (notably, 8p12, 8q24, 11q13-14, 12q1314, 17q21-24, and 20q13). Our findings also... |

5 | Sticky hidden Markov modeling of comparative genomic hybridization
- Du, Chen, et al.
- 2010
(Show Context)
Citation Context ...endence in the intensity ratios, which results in location-dependent transition probabilities and corresponding locally varying state persistence properties of the aberrations (DeSantis et al., 2009; =-=Du et al., 2010-=-; Fox et al., 2011). By considering species sampling sequences where the weights are modeled as functions of latent Beta random variables, we have defined a Beta-GOS process prior that provides an alt... |

5 |
Comparative genomic hybridization: DNA labeling, hybridization and detection. Methods Mol Biol
- Redon, Fitzgerald, et al.
(Show Context)
Citation Context ...ncer and normal female genomic DNA, labeled with distinct fluorescent dyes and co-hybridized on a microarray in the presence of Cot-1 DNA to suppress unspecific hybridization of repeat sequences (see =-=Redon et al., 2009-=-). The reference DNA is assumed to have two copies of each chromosome. If the test sample has no copy number aberrations, the log2 of the intensity ratio is theoretically equal to zero. Array CGH data... |

5 |
RHmm: Hidden Markov Models simulations and estimations. R package version 2.0.3 https://r-forge.r-project.org/R/?group_id=85
- Taramasco, Bauer
- 2013
(Show Context)
Citation Context ... the fit resulting from hidden Markov models, assuming 3, 4 and 5 states, respectively. Results from the simulations are reported in Table 4, where the HMM was implemented using the R package “RHmm” (=-=Taramasco and Bauer, 2012-=-). Table 4 shows that the Beta-GOS is a viable alternative to HMM, as it can provide more accurate inference than a single hidden Markov model where the number of states is fixed a priori. The fit obt... |

3 | False discovery control in large-scale spatial multiple testing
- Sun, Reich, et al.
- 2014
(Show Context)
Citation Context ...e regions of interest could be pre-specified on the basis of the information available in the literature. The optimality of the type of procedures here described for cluster based FDR is discussed in =-=Sun et al., 2015-=-. See also Heller et al., 2006, Müller et al., 2007 and Ji et al., 2008). In Table 1 we report the q-values from a set of candidate oncogenes in well-known regions of recurrent amplification (notably... |

2 |
Generalized Species Sampling Priors With Latent Beta Reinforcements
- Airoldi, Costa, et al.
- 2014
(Show Context)
Citation Context ...CGH data. 3 A Beta-GOS Hierarchical Model In this Section, we focus on the Beta-GOS sequences and discuss how they can be used to define a prior in a hierarchical model (for a broader discussion, see =-=Airoldi et al., 2014-=-). Although the discussion pertains specifically to the Beta-GOS process, the basic modeling idea naturally extends to the CID Pitman-Yor sequences and the general CID sequences. We then discuss the p... |

2 | Bayesian hierarchical mixture modeling to assign copy number from a targeted cnv array. Genetic Epidemiology 35(6 - Cardin, Holmes, et al. - 2011 |

2 |
Random probability measures via Polya sequences: revisiting the Blackwell-MacQueen urn scheme
- Ishwaran, Zarepour
- 2003
(Show Context)
Citation Context ...ee et al., 2008, for more details). The most notable example of exchangeable SS-sequences is the Blackwell MacQueen sampling rule, which defines a Dirichlet Process (see Blackwell and MacQueen, 1973; =-=Ishwaran and Zarepour, 2003-=-). Let p be a DP with mass parameter γ and base measure G0(·), denoted as p ∼ DP(γ,G0). Then, the corresponding sequence of predictive probability function is the well-known Blackwell MacQueen samplin... |

2 | A Nonparametric Bayesian Model for Local Clustering - Lee, Müller, et al. - 2013 |

2 |
On the complexity of explicit duration hmm’s. Speech and Audio Processing
- Mitchell, Harper, et al.
- 1995
(Show Context)
Citation Context ...ometric state occupancy distribution characterizes ordinary hidden Markov models. Therefore, hidden semi-Markov process have also been referred to as “hidden Markov 12 Models with explicit duration” (=-=Mitchell et al., 1995-=-; Dewar et al., 2012) or “variable-duration hidden Markov Models” (Rabiner, 1989). We generate 1,000 datasets (1000 observations each) using a hidden semi-Markov process with four states and a negativ... |

1 | Betensky (2009). A latent class model with hidden markov dependence for array cgh data - DeSantis, Houseman, et al. |

1 | Willsky (2013). Bayesian nonparametric hidden semi-markov models - Johnson, S |