Tobias Rydén

Stylized facts of daily return series and the hidden Markov model

In two recent papers, Granger and Ding (1995a,b) considered long return series that are first differences of logarithmed price series or price indices. They established a set of temporal and distributional properties for such series and suggested that the returns are well characterized by the double exponential distribution. The present paper shows that a mixture of normal variables with zero mean can generate series with most of the properties Granger and Ding singled out. In that case, the temporal higher-order dependence observed in return series may be described by a hidden Markov model. Such a model is estimated for ten subseries of the well-known S&P 500 return series of about 17,000 daily observations. It reproduces the stylized facts of Granger and Ding quite well, but the parameter estimates of the model sometimes vary considerably from one subseries to the next. The implications of these results are discussed.

Persistent malignant stem cells in del(5q) myelodysplasia in remission.

BACKGROUND The in vivo clinical significance of malignant stem cells remains unclear. METHODS Patients who have the 5q deletion (del[5q]) myelodysplastic syndrome (interstitial deletions involving the long arm of chromosome 5) have complete clinical and cytogenetic remissions in response to lenalidomide treatment, but they often have relapse. To determine whether the persistence of rare but distinct malignant stem cells accounts for such relapses, we examined bone marrow specimens obtained from seven patients with the del(5q) myelodysplastic syndrome who became transfusion-independent while receiving lenalidomide treatment and entered cytogenetic remission. RESULTS Virtually all CD34+, CD38+ progenitor cells and stem cells that were positive for CD34 and CD90, with undetectable or low CD38 (CD38−/low), had the 5q deletion before treatment. Although lenalidomide efficiently reduced these progenitors in patients in complete remission, a larger fraction of the minor, quiescent, CD34+,CD38-/low, CD90+ del(5q) stem cells as well as functionally defined del(5q) stem cells remained distinctly resistant to lenalidomide. Over time, lenalidomide resistance developed in most of the patients in partial and complete remission, with recurrence or expansion of the del(5q) clone and clinical and cytogenetic progression. CONCLUSIONS In these patients with the del(5q) myelodysplastic syndrome, we identified rare and phenotypically distinct del(5q) myelodysplastic syndrome stem cells that were also selectively resistant to therapeutic targeting at the time of complete clinical and cytogenetic remission. (Funded by the EuroCancerStemCell Consortium and others.)

Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method

Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism.

Combined Gene Expression and Genomic Profiling Define Two Intrinsic Molecular Subtypes of Urothelial Carcinoma and Gene Signatures for Molecular Grading and Outcome

In the present investigation, we sought to refine the classification of urothelial carcinoma by combining information on gene expression, genomic, and gene mutation levels. For these purposes, we performed gene expression analysis of 144 carcinomas, and whole genome array-CGH analysis and mutation analyses of FGFR3, PIK3CA, KRAS, HRAS, NRAS, TP53, CDKN2A, and TSC1 in 103 of these cases. Hierarchical cluster analysis identified two intrinsic molecular subtypes, MS1 and MS2, which were validated and defined by the same set of genes in three independent bladder cancer data sets. The two subtypes differed with respect to gene expression and mutation profiles, as well as with the level of genomic instability. The data show that genomic instability was the most distinguishing genomic feature of MS2 tumors, and that this trait was not dependent on TP53/MDM2 alterations. By combining molecular and pathologic data, it was possible to distinguish two molecular subtypes of T(a) and T(1) tumors, respectively. In addition, we define gene signatures validated in two independent data sets that classify urothelial carcinoma into low-grade (G(1)/G(2)) and high-grade (G(3)) tumors as well as non-muscle and muscle-invasive tumors with high precisions and sensitivities, suggesting molecular grading as a relevant complement to standard pathologic grading. We also present a gene expression signature with independent prognostic effect on metastasis and disease-specific survival. We conclude that the combination of molecular and histopathologic classification systems might provide a strong improvement for bladder cancer classification and produce new insights into the development of this tumor type.

Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.

An EM algorithm for estimation in Markov-modulated Poisson processes

It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. In this paper we present an EM algorithm for computing such estimates and discuss how it may be implemented. We also compare it to the Nelder-Mead downhill simplex algorithm for some numerical examples, and the results show that the number of iterations the EM algorithm requires to converge is in general smaller than the number of likelihood evaluations required by the downhill simplex algorithm. An EM iteration is more complicated than a likelihood evaluation, though, and thus also implementation aspects must be taken into account to determine the efficiencies of the algorithms.

Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers

Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions. We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-combine moves in the spirit of Richardson and Green. We illustrate these extensions both for mixtures of distributions and for hidden Markov models. We demonstrate the strong similarity of reversible jump and continuous time methodologies by showing that, on appropriate rescaling of time, the reversible jump chain converges to a limiting continuous time birth-and-death process. A numerical comparison in the setting of mixtures of distributions highlights this similarity.

On recursive estimation for hidden Markov models

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modelling sequences of dependent random variables. In this paper we consider a recursive estimator for HMMs based on the m-dimensional distribution of the process and show that this estimator converges to the set of stationary points of the corresponding Kullback-Leibler information. We also investigate averaging in this recursive scheme and show that conditional on convergence to the true parameter, and provided m is chosen large enough, the averaged estimator is close to optimal.

Estimation in the Cox-Ingersoll-Ross Model

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are discussed, and we also compare their performance in a simulation study.

Parameter Estimation for Markov Modulated Poisson Processes

A Markov modulated Poisson process (MMPP) is a doubly stochastic Poisson process whose intensity is controlled by a finite state continuous-time Markov chain. MMPPs have during the last decade been used to model traffic flows in communication networks as well as environmental data. We give a brief survey of methods, most of which are based on moment matching, that have earlier been proposed for estimating the parameters of MMPPs. Then we turn to likelihood based methods, prove a strong consistency property of the maximum likelihood estimator, and discuss some practical methods for calculating MLEs for two-state MMPPs