Bayesian inference and model choice in a hidden stochastic two-compartment model of hematopoietic stem cell fate decisions

Despite rapid advances in experimental cell biology, the in vivo behavior of hematopoietic stem cells (HSC) cannot be directly observed and measured. Previously we modeled feline hematopoiesis using a two-compartment hidden Markov process that had birth and emigration events in the first compartment. Here we perform Bayesian statistical inference on models which contain two additional events in the first compartment in order to determine if HSC fate decisions are linked to cell division or occur independently. Pareto Optimal Model Assessment approach is used to cross check the estimates from Bayesian inference. Our results show that HSC must divide symmetrically (i.e., produce two HSC daughter cells) in order to maintain hematopoiesis. We then demonstrate that the augmented model that adds asymmetric division events provides a better fit to the competitive transplantation data, and we thus provide evidence that HSC fate determination in vivo occurs both in association with cell division and at a separate point in time. Last we show that assuming each cat has a unique set of parameters leads to either a significant decrease or a nonsignificant increase in model fit, suggesting that the kinetic parameters for HSC are not unique attributes of individual animals, but shared within a species.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS269 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

New Challenges in Environmental Statistics

Quello delle statistiche ambientali è un campo in rapido sviluppo. Il presente lavoro apporta alcuni esempi dei principali problemi che possono sorgere e dei metodi utilizzati per analizzare i dati nel contesto della scienza ambientale. I dati ambientali spesso derivano dal monitoraggio dello spazio e del tempo. Di conseguenza, l'analisi di questi dati richiede l'uso di strumenti che tengano conto sia della dipendenza spaziale che di quella temporale. In questo lavoro vengono, quindi, mostrati alcuni di questi strumenti di analisi spazio-temporale, recentemente sviluppati per lo studio dei dati sull'inquinamento atmosferico e sul clima in generale

Asymptotic normality of quadratic forms of martingale differences

We establish the asymptotic normality of a quadratic form QnQn in martingale difference random variables ηtηt when the weight matrix A of the quadratic form has an asymptotically vanishing diagonal. Such a result has numerous potential applications in time series analysis. While for i.i.d. random variables ηtηt, asymptotic normality holds under condition ||A||sp=o(||A||)||A||sp=o(||A||), where ||A||sp||A||sp and ||A|| are the spectral and Euclidean norms of the matrix A, respectively, finding corresponding sufficient conditions in the case of martingale differences ηtηt has been an important open problem. We provide such sufficient conditions in this paper

Why distinguish between statistics and mathematical statistics - the case of Swedish academia

A separation between the academic subjects statistics and mathematical statistics has existed in Sweden almost as long as there have been statistics professors. The same distinction has not been maintained in other countries. Why is it kept in Sweden?In May 2015 it has been 100 years since Mathematical Statistics was formally established as an academic discipline at a Swedish university where Statistics had existed since the turn of the century. We give an account of the debate in Lund and elsewhere about this division during the first decades after 1900 and present two of its leading personalities. The Lund University astronomer (and mathematical statistician) C.V.L. Charlier was a leading proponent for a position in mathematical statistics at the university. Charlier's adversary in the debate was Pontus Fahlbeck, professor in political science and statistics, who reserved the word statistics for ``statistics as a social science''. Charlier not only secured the first academic position in Sweden in mathematical statistics for his former Ph.D. student Sven Wicksell, but he also demonstrated that a mathematical statistician can be influential in matters of state, finance, as well as in different natural sciences. Fahlbeck saw mathematical statistics as a set of tools that sometimes could be useful in his brand of statistics. After a summary of the organisational growth of the statistical sciences in Sweden that has taken place during the last 50 years, we discuss what effects the Charlier-Fahlbeck divergence might have had on this development

Hierarchical Bayesian auto-regressive models for large space time data with applications to ozone concentration modelling

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases temporal data are obtained by registering events, for example telecommunication or web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time auto-regressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method (Banerjee et al. [1]) is extended to include auto-regressive terms of latent space-time processes. Specifically, a space-time auto-regressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-hour average ground level ozone concentration data from 1997 to 2006 from a large study region in the eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of non-compliance with respect to the standard, are obtained and illustrated

Philosophy and the practice of Bayesian statistics

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3: Further typo fixes. v4: Revised in response to referee

Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure