An exact predictive recursion for Bayesian nonparametric analysis of incomplete data

Exact solution of the (approximated) well-known Newton\u27s computational procedure to the bayesian nonparamertric approach to censored data

Evidence that Prefibrotic Myelofibrosis Is Aligned along a Clinical and Biological Continuum Featuring Primary Myelofibrosis

PURPOSE: In the WHO diagnostic classification, prefibrotic myelofibrosis (pre-MF) is included in the category of primary myelofibrosis (PMF). However, strong evidence for this position is lacking. PATIENTS AND METHODS: We investigated whether pre-MF may be aligned along a clinical and biological continuum in 683 consecutive patients who received a WHO diagnosis of PMF. RESULTS: As compared with PMF-fibrotic type, pre-MF (132 cases) showed female dominance, younger age, higher hemoglobin, higher platelet count, lower white blood cell count, smaller spleen index and higher incidence of splanchnic vein thrombosis. Female to male ratio and hemoglobin steadily decreased, while age increased from pre-MF to PMF- fibrotic type with early and to advanced bone marrow (BM) fibrosis. Likely, circulating CD34+ cells, LDH levels, and frequency of chromosomal abnormalities increased, while CXCR4 expression on CD34+ cells and serum cholesterol decreased along the continuum of BM fibrosis. Median survival of the entire cohort of PMF cases was 21 years. Ninety-eight, eighty-one and fifty-six percent of patients with pre-MF, PMF-fibrotic type with early and with advanced BM fibrosis, respectively, were alive at 10 years from diagnosis. CONCLUSION: Pre-MF is a presentation mode of PMF with a very indolent phenotype. The major consequences of this contention is a new clinical vision of PMF, and the need to improve prognosis prediction of the disease

Association between Frequency of Chromosomal Aberrations and Cancer Risk Is Not Influenced by Genetic Polymorphisms in GSTM1 and GSTT1

To evaluate the role of polymorphisms in glutathione S-transferase M1 (GSTM1) and theta 1 (GSTT1) as effect modifiers of the association between CA and cancer risk. A case-control study was performed pooling data from cytogenetic studies carried out in 1974-1995 in three laboratories in Italy, Norway, and Denmark. The subjects were classified as low, medium, and high by tertile of CA frequency. The data were analysed by setting up a Bayesian model which included prior information about cancer risk by CA frequency

Una generalizzazione del processo di Ehrenfest

The core of the method of Statistical Mechanics is that of studyingthe macroscopic properties at our human scale in terms of the properties of the microscopic constituents (Jancel 1969). A similar aim affects some new approaches to macroeconomic modeling (Aoki 1996), that have been developed in order to describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities (agents, price elements,...). These entities are supposed to change their state unceasingly, ruled by a probabilistic dynamics represented by jump Markov chains. Relationships among economic variables are statistical in an essential way, and are not made so by having additive disturbance or measurement errors superimposed on deterministic relationships.(Aoki 1996). In this work we want give an exact model able to unify a large extent of hypotheses introduced in this approach (Kelly 1979, Kirman 1993, Aoki 1999). Our treatise starts from the most known discrete model of Classical Statistical Physics (complementary to the continuous Brownian Motion), that is the celebrated stochastic process envisaged by Paul and Tatiana Ehrenfest at the beginning of this century. The main generalization we perform consists in introducing choice correlations between agents, that give raise to "herd behavior" if they are strong and positive

A stationary probabilistic mechanism for generating power laws distributions

Focusing on the evergreen problem of the size of firms, we discuss the incompatibility between empirical data and Ewens sampling formula. An alternative model is suggested, inspired to Simon's approaches to the firm size problem. It differs from the Ewens model both in destruction and in creation. In particular the probability of herding is independent on the size of the herd. This very simple assumption destroys the exchangeability of the random partitions, and forbids an analytical solution. Simple computational simulations look to confirm that actually the mean number of clusters of size i (the equilibrium distribution) follows the corresponding Yule distribution. Finally we introduce a Markov chain, that resembles the marginal dynamics of a cluster, which drives the cluster to the right-censored Yule distribution

An exact predictive recursion for Bayesian nonparametric analysis of incomplete data

This paper presents an original extension of the Bayesian predictive inferences to compound evidence. Does the idea that the predictive uncertainty can be encoded in a single measure, and that learning occurs by adding measure, holds also for missing data? The positive answer comes from the class of computationally efficient methods to approximate mixtures of Dirichlet processes, which involves order dependent recursive algorithms. In the present note, in the case where data are right-censored, we proof that there is a unique rational pattern which recursively produces the exact posterior predictive distributions for subsequent samples under a Dirichlet process prior. By "exact" we mean that our result coincides with the Susarla-Van Ryzin estimator under squared error loss

Herding and clustering: Ewens vs. Simon-Yule models

Our ambition is to bridge the gap between agent-based computational models (where there is a lack of probabilistic insight) and stochastic processes (which appear "phenomenological'' if they are non ''agent-based''). In order to obtain a power law for all sizes of firms in the present paper we shall explore the route inspired by Yule, Zipf and Simon. It differs from the Ewens model both for destruction and creation

A finitary characterization of the Ewens sampling formula

The clustering of agents i is subject to many economic interpretations, often described by the Ewens Sampling Formula (ESF). In contrast with the usual complex derivations, our approach is finitary in the sense that we provide a probabilistic description of a system of n individuals considered as a closed system, a population, where individuals can change attributes over time. The probability is understood as the fraction of time the system spends in the considered partition. As the ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way

Herd behavior in Artificial Stock Markets

Herd behavior in Economics can be fruitfully represented by a generalization of the well-known Ehrenfest urn model to correlated clustering. The strategies of an agent in a stock market (planning to buy, to sell or to be inactive) are represented by three urns, and the accommodation of each agent in one of them is ruled by a random mechanism that may depend strongly on the behavior of the other agents. This mechanism is introduced in the "Genoa Artificial Stock Market"