Foredragene vil finne sted, dersom ikke annet er oppgitt, på
Many statistical procedures are based on conditional distributions given sufficient statistics. The clue is that such distributions do not depend on unknown parameters. In certain cases one is able to derive the conditional distributions analytically. In general, however, it is impossible to arrive at tractable explicit expressions. The obvious solution is then to try Monte Carlo simulations. This talk is about such a simulation approach for computing conditional expectations given sufficient statistics, and also for sampling from the conditional distributions. Some applications will be given, as well as a brief discussion of connections to Bayesian and fiducial statistics.
When a large oilfield is produced, several reservoirs often share the same processing facility. This facility is only capable of processing limited amounts of commodities per unit of time. In order to satisfy these processing limitations, the production needs to be choked according to some suitable production strategy. In this presentation we focus on optimization of oil production only. The production from every reservoir is modeled using multi-segmented production profiles and ordinary differential equations. If the production profiles can be characterized by linear differential equations, a specific priority strategy is proven to be optimal. More generally, if the production profiles can be characterized by convex differential equations, the fields are sorted according to a certain ordering criterion. A production strategy can then be derived by prioritizing the reservoirs according to this criterion. When the production profiles are characterized by concave differential equations, we focus on the problem of maximizing the length of the plateau phase of the production. We show how to solve this problem for two classes of concave differential equations. A backtracking algorithm is used to derive the optimal production strategy for concave differential equations. The performance of the proposed approaches is promising, and problems in high dimension may be analyzed with low execution times within the proposed framework.
For testing whether a distribution function is heavy tailed, we study the Kolmogorov-Smirnov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations.
Det er et betydelig engasjement og driv i dag i ulike industrier og i samfunnet generelt for å implementere risikostyring. Det synes å være store forventninger om at risikostyring er det som skal til for å unngå ulykker, skader og tap, og sikre høy avkastning. Dessverre er det ikke rett fram å implementere risikostyring i en praktisk situasjon - det er nødvendig med både teoretisk kunnskap og erfaring for å lykkes. Risikostyringsfaget er ungt, og fremdeles er det mange vanskelige og uavklarte spørsmål. I dette foredraget vil vi se nærmere på noen av disse. Spesielt vil vi se på de grunnleggende prinsipper og ideer som fagområdet hviler på. Min erfaring er at mange av problemene som oppstår i det praktisk risikostyringsarbeid har sin rot i manglende forståelse og innsikt i de fundamentale spørsmålene, for eksempel; hva er risiko? Hvordan beskrive og kommunisere risiko? Hvordan beskrive usikkerhet? Hvordan vektlegge usikkerhet? Hvordan forstå og bruke forsiktighetsprinsippet og føre-var? Hvordan balansere ulike hensyn, som sikkerhet og økonomi? Hvordan bruke forventningsverdier i risikostyringen? Påstander: ¥ Risiko er mer enn sannsynligheter og forventningsverdier ¥ Kost-nytteanalyser med basis i forventet nåverdi kan ikke alene brukes for å bestemme hva som er riktig sikkerhetsnivå ¥ Bruk av risikoakseptkriterier er prinsipielt feil <\UL>
n an ecological study outcome and exposure/confounder data are available on groups of individuals, rather than on the individuals themselves. Such studies are logistically appealing, since they may make use of routinely-available data and offer increased power and exposure contrasts, but suffer from a number of problems due to within-group variability in exposures and confounders, an umbrella term for which is ecological bias. Ecological bias can appear in very simple situations. For example, the Scottish lip cancer data has been analyzed by numerous authors, who have all used an incorrect mean model, when viewed from an individual-level perspective. Much of the methodological development with spatial count data has concentrated upon proposing models for residual spatial dependence, but here we emphasize the futility of this exercise if the mean function is incorrectly specified. The use of hierarchical models per se cannot correct for ecological bias; the only solution is to supplement ecological data with individual samples. In this talk, after detailing different sources of ecological bias, various study designs and estimation methods will be described and compared. In particular, the aggregate data design of Prentice and Sheppard (1995) and the ecological embedded case-control study of Haneuse and Wakefield (2005) will be outlined. Simulated data will be used to the compare various study designs.
We start by giving a gentle introduction to local stationarity in financial time series modelling. We then go on to propose a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise constant function with an unknown number and location of jumps, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that our model explains well the common stylised facts of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in our model, where Haar wavelets are combined with the variance-stabilizing Fisz transform. The resulting volatility estimator is mean-square consistent with a near-parametric rate, does not require any pre-estimates, is rapidly computable and easy to implement. We also discuss important variations on the choice of estimation parameters. We show that our modelling and estimation approach both gives a very good fit to selected currency exchange datasets, and achieves accurate long- and short-term volatility forecasts in comparison to the GARCH(1,1) and moving window techniques. Also, if time permits, we discuss a related technique, based on Unbalanced Haar wavelets and the Fisz transform, for segmenting financial log-return series into approximately stationary pieces.
A theory is developed for estimation and testing in time series that are both nonstationary and nonlinear. The emphasis is on nonparametric estimation and, in the absence of mixing, Markov chain regeneration theory is used. In particular we look at the nonlinear regression situation and point out the connection to the problem of nonlinear cointegration in econometrics. Examples will be discussed, and an alternative approach via local time for Brownian motion will be briefly mentioned.
Life times of load sharing systems parallel have been considered in the statistical literature at least since Daniels (1945). The main characteristic of such a two component system is that after the failure of one component the surviving component has to shoulder extra load and hence is prone to failure at an earlier time than what is expected under the original model. Gross et al (1971) observed that similar considerations affect the functioning of a two organ system. In this paper we first consider several observations schemes and identifiability issues under them. Then we construct a general semiparametric bivariate family of distributions which explicitly models this phenomenon through propotional conditional hazards. McCool (2006) has suggested a test for the hypothesis that the failures take place according to the original model against the alternative hypothesis that the second failure takes place earlier than warranted within the Weibull model. We propose nonparametric tests for the same problem which may be used for any conitnuous bivariate continuous distribution for the component life times. We obtain estimates of the power of the test and observe that it is quite high even for moderately distant alternatives. The tests are applied to several real data sets to illustrate its use.
USIT opprettet for en tid tilbake en tjenestegruppe for statistikk. Vi vil presentere tankene bak dette initiativet, si litt om hvordan vi er organisert, hva vi kan tilby og hvilken kompetanse vi har (og ikke har), og hvilke programmer og verktøy som brukes, hvilke erfaringer vi har høstet til nå og hvordan vi tenker framover.
The Nobel Prize in literature 1965 was awarded Mikhail Sholokhov (1905--1984), for the epic novel "And Quiet Flows the Don" about Cossack life and the birth of a new Soviet society. In Russia alone his books have been published in more than a thousand editions, selling in total more than sixty million copies. But in the autumn of 1974 an article was published in Paris, claiming that The Quiet Don was not at all Sholokhov's work, but that it rather was written by Fiodor Kriukov. The article was given credibility and prestige by none other than Aleksandr Solzhenitsyn (a Nobel prize winner five years after Sholokhov), who wrote a preface giving full support to the article's conclusion. Are we in fact faced with one of the most flagrant cases of plagiarism in the history of literature? My contribution is to re-analyse some quantitative linguistic data collected by professor Geir Kjetsaa and colleagues, and in particular to squeeze out better statistical discrimination from their sentence length data.
Likelihood ideas have driven most of the progress in statistical modeling in the last 3 decades, in particular in the area of generalized linear models and survival analysis. I will describe the various extensions of the likelihood concept to deal with observation- and parameter-driven complexities, up to the idea of extended likelihood for random-effect parameters. While we can say with reasonable confidence that we have a general consensus about the utility of the likelihood function for modeling, the same cannot be said for statistical inference, where the direct use of likelihood is still controversial. I will discuss Fisher's idea of ladder of uncertainty to resolve this problem.
What is the genetic structure of a wild-life population, studied over an area, and how should it be mapped out? This is the theme of a new field, landscape genetics, which amalgamates population genetics and ecology, and which requires geo-statistical methods. For inference we use specifically tailored MCMC calculations to thematically color regions with respect to sub-population habitats The regions are constructed by tessellation from a random point pattern. The method is applied to a population of wolverines (jerv)
Mechanistic models are used in just about every area of science, technology, industry and, increasingly, policy-making. Models are used to understand, predict or control real-world phenomena. There is a growing demand for the uncertainties in the predictions of such models to be quantified. This talk concerns a suite of Bayesian techniques that have been developed over the last 15 years or so to tackle the quantification and management of uncertainty in model outputs. The talk will outline the basic technique of Gaussian process emulation, and will go on to show how the emulator is then used to address questions of uncertainty and sensitivity analysis. When we face models with real-world data, new questions of calibration, data assimilation and model validation arise, but before we can address those we must also try to understand how the model differs from reality. All these techniques are being further developed in a large research project in the UK, and the talk will end with a few words about this project.
An issue often encountered in statistical genetics is whether, or to what extent, it is possible to estimate the degree in which individuals sampled from a background population are related to each other, on the basis of the available diploid multi-locus genotype data and some information on the demography of that population. In this talk, this question is considered by using an explicit modelling and reconstruction of the pedigrees and gene flows at the marker loci. For computational reasons, the analysis is restricted to a relatively recent history of the population, currently extending, depending of the data, up to ten or twenty generations backwards in time. As a computational tool, we use Markov Chain Monte Carlo numerical integration on the state space of genealogies of the sample individuals. The main technical challenge has been in devising a variety of joint proposal distributions which would guarantee that the algorithm has reasonable mixing properties. As illustrations of the method, we consider the question of relatedness both in terms of individuals (pedigree based relatedness estimation) and at the level of genes/genomes (IBD-estimation), using both simulated and real data. This talk is based on joint work with Dario Gasbarra, Matti Pirinen and Mikko SillanpŠŠ.
As denoted in the title, this talk has two parts. We start out by describing some difficulties with traditional nonparametric smoothing methods. Thereafter, we point out the idea in scale-space methods and how they can be used to overcome the difficulties in traditional methods. A description of some existing scale-space methods will be given. The use of these methods in areas like climatology, medicine and fishery will also be illustrated. Important future research directions in the area of scale-space methods will be given. In the second part of the talk we focus on the use of statistical methods in telemedicine. This part gives a description of the statistical research to be performed in Troms¿ Telemedicine Laboratory (Centre for Research-Based Innovation).
I explain quantum nonlocality experiments and discuss how to optimize them. Statistical tools from missing data maximum likelihood are crucial. New results are given on Bell, CGLMP, CH and ladder inequalities. Open problems are also discussed. Prior knowledge of quantum theory or indeed physics is not needed to follow the talk; indeed its lack could even be an advantage ;-) It may be difficult to resist discussion of the philosophical implications of Bell's inequality. Slides for a previous version of this talk, and reference to a paper http://www.math.leidenuniv.nl/~gill/betterbelltalk.pdf http://arxiv.org/abs/math.ST/0610115 [to appear in IMS Monograph volume for conference on occasion of Piet Groeneboom's 65th birthday]
My talk will report on work that by definition is very recent in that it is inspired by the two last Tuesday seminars. The two modi of large-sample approximations for statistics of spatial models in the literature have been "infill asymptotics" and "expansion asymptotics". I will discuss an attempt at creating "middle ground asymptotics", where the sampling region increases while the neighbour interdistance becomes smaller. This leads to new approximations for the behaviour of estimators of parameters of spatial models. Douglas Wiens (University of Alberta) discussed robust prediction and design in spatial studies. Among his examples were methods for estimating the variance and range parameters in spatial models with exponential correlation functions. I show that in a certain sense this is impossible -- even with a multiplujillion data points. S¿ren Johansen (University of K¿benhavn) outlined a representation theory for fractional autoregressive processes, where one of the basis theorems gives the limit distribution of n(\hat\rho-1) for the special case of a unit root process. My methods lead to different large-sample approximations, and hence to modified tests and confidence intervals.
Based on an idea of Granger (1986), we analyse a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients of the model for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X_{t} of order d, for which there are vectors § so that §'X_{t} is fractional of order d-b. We find a representation of the solution which demonstrates the fractional properties. Finally we suggest a model that allows for a polynomial fractional vector, that is, the process X_{t} is fractional of order d, §'X_{t} is fractional of order d-b and a linear combinaton of §'X_{t} and Delta^{b}X_{t} is fractional of order d-2b. The representations and conditions are analogous to the well known conditions for I(0), I(1) and I(2) variables.
I consider robust methods for the construction of sampling designs in spatial studies.The designs are robust against misspecified regression responses, and are tailored for possible use with predictors which are minimax robust against misspecified variance/covariance structures. The loss function is based on the mean square error of the predicted values. This is maximized, analytically, over a neighbourhood quantifying the departure from the fitted linear regression response. This maximum is then minimized numerically - by simulated annealing, or sequentially - in order to obtain the optimal designs.
We will discuss the use of differential equation models to consider the analysis of two types of space-time data. In one case we look at soil moisture observed at a collection of locations in two our increment over the course of several months. Soil moisture levels are a complex process that is driven by inputs of precipitation along with transpiration and drainage. Infinitesimal change in soil moisture can be expressed using a differential equation involving forms for transpiration and drainage as a function of soil moisture. In a second case we consider space time point patterns driven by a latent space time intensity surface which is a realization of a stochastic process, that is, our model is an example of a Cox process. The intensity surface is formulated as a growth process characterized through a stochastic differential equation. Our motivating example is to understand annual urban growth through single family home construction. We show how both of these examples can be handled using hierarchical modelling specification. In each case, we discretize time, replacing integrals by sums. However, each introduces further computational wrinkles. The former works with empirically specified transpiration and drainage functions while the latter treats a very large number of points (roughly 12.000 houses). Results or the analyses will be presented.
Survival prediction from high-dimensional genomic data (e.g gene expression, SNP or CGH data) is subject to much research effort in today's medicine. When dealing with these kinds of data, one has to take into account the problem of both censored observations and that the number of genetic variables p usually by far exceeds the number of patients n (p>> n). Most of the proposed methods handle this by combining the Cox proportional hazards model with some regularization techniques for estimation. In our socalled "Microsurv" project we investigate the performance of six such methods; two subset selection methods, principal components regression (PCR), supervised PCR, ridge regression, and our own modified partial least squares (PLS) Cox regression method. In the talk we will describe the estimation techniques and criteria for evaluating the performance of the methods. Results from applications to three different published datasets will be shown and discussed.
People are able to recognize their own handwriting or signature at a glance, and manuscript experts can usually determine genuineness with almost scientific exactitude, or so they claim. The analysis of variations in handwriting style is useful, for example, in forensic investigations, biometric identification, and in the dating of ancient manuscripts. This talk introduces a statistical approach to off-line signature analysis and verification based on an observation model in which white noise is superimposed on an underlying curvature function. The technique is applied to a collection of documented instances of Shakespeare's signature.
The subject of stochastic partial differential equations has undergone a breathtaking development in the last three decades. These equations occur as stochastic models in the investigation of problems that arise in a variety of disciplines such as neurophysiology, environmental pollution, chemical reaction diffusion, infinite particle systems and turbulence. More recently such equations have also been applied to finance. In this talk I want to give some examples where stochastic partial differential equations as an important mathematical tool come on the scene.
The question of interest is whether a particular model appears to provide an adequate fit in Bayesian hierarchical models. In complicated hierarchical models it is easy to loose track of the different layers, and standard and existing methods may not work very well in such cases. The focus of present work is on an extension of the posterior predictive p-value for checking hierarchical models in applications where we especially are interested in the dynamic of the 2nd stage process. These processes are not necessary (conditionally) exchangeable exemplified in the dynamics of an AR(p) process. The posterior predictive p-values are typically non-uniform under the null-model. However, a post-processing of the p-values, generally computed by a double simulation scheme, makes the resulting calibrated p-values uniform on the unit interval under model conditions. We illustrate how these calibrated p-values may be used to assess and compare across different priors and models where we pay particular attention of checking a couple of fairly simply hierarchical models. This is a joint work with Geir Storvik and Nils Lid Hjort as a part of my Phd.
Some times spatial and spatio-temporal data contain a large amount of zeros. Then the probability mass at point zero exceeds that allowed under a standard parametric family of distributions. Using a traditional modelling approach without taking the zeros carefully into account might lead to biased estimates and erroneous results. We model zero-inflated Pollock egg counts from the western Gulf of Alaska according to a zero-inflated Bayesian hierarchical space-time model. This data set contains samples of the number of eggs per m2, collected within (52 - 61 degrees N, 139-168 degrees W), over the years 1978,1979,1981,...,2000. For each year a different number of boats sampled at different locations within the given area, and at different Julian days. We are interested in examining if there are any changes over the years regarding preferences of spawning regions. Analyzing these temporal changes could give valuable information about possible major shifts in spawning habits, and a contribution in explaining environmental changes within the area.
The notions of direct and indirect effects are often used informally to describe phenomena where mediating variables play an important role. Examples can be found in many disciplines. In order to get a more formal grasp of direct/indirect effects, I will introduce some basic concepts of causal reasoning, including counterfactuals, Pearl's "do"-operator and (causal) graphical models. The formal definitions of direct/indirect effect as they have been given by Pearl (2001) and Robins (2003) and their collaborators will be reviewed and discussed. Particular attention will be paid to parametric model assumptions that allow interpreting individual parameters as direct/effect. Finally, the identifiability of the direct/indirect effect will be addressed. Graphical models can help to make explicit the prior knowledge, and then to characterise a sufficient set of "confounders" that, if observed, will allow the identification.
A crime has been committed, no suspects are directly avaiable, but a search through a database of DNA profiles gives exactly one match. This person is put to trial. There has been a considerable controversy on how to report the evidence. The bayesian approach, reporting Bayes factors, ha sbeen challanged by the lack of taking the multiple testing setting properly into account. The frequentist approach has been criticized for not considering the proper hypotheses. The controversy appears because the different approaches to th problem give dramatic differences in quantitative evidence. In this talk we show that the main reason for the difference is not due to the use of frequentistic versus bayesian methology or whether the multiple testing setting is taken properly into account. Rather, the question is about differences in conditioning. We further challenge the use of Bayes factors and likelihood ratios as quantities of evidence. This is a joint work with Thore Egeland, Ullevål University Hospital.
The Aalen additive hazards model (Aalen, 1980) is a useful alternative to the Cox model (Cox, 1972) when analysing survival data. A particular useful aspect of the Aalen model is that it allows for time-varying covariate effects. It will often be of interest to investigate whether a covariate is constant with time, however. In this talk we describe how such hypothesis may be investigated and how do it in practise using the R-package timereg. An interesting model in between the constant effects model and the full Aalen model is the change-point model where the effect of a given covariate is constant up to an unknown point in time and changed thereafter to a new value. For instance, a given new drug may have an initial effect only; or the other way around, there may an initial phase without effect. We will also describe how to do estimation and inference within such a change-point model. The methods will be illustrated on real datasets.
Missing values are problematic for the analysis of microarray data. Imputation methods have been compared in terms of the similarity between imputed and true values in simulation experiments and not of their influence on the final analysis. The focus has been on missing at random, while entries are missing also not at random. We investigate the influence of imputation on the detection of differentially expressed genes from cDNA microarray data. We apply ANOVA for microarrays and SAM and look to the differentially expressed genes that are lost because of imputation. We show that this new measure provides useful information that the traditional root mean squared error cannot capture. We also show that the type of missingness matters: imputing 5% missing not at random has the same effect as imputing 10-30% missing at random. We propose a new method for imputation (LinImp), fitting a simple linear model for each channel separately, and compare it with the widely used KNNimpute method. For 10% missing at random, KNNimpute leads to twice as many lost differentially expressed genes as LinImp. This is joint work with Magne Aldrin, Ingrid K. Glad, Ragnhild Sørum, Heidi Lyng and Arnoldo Frigessi.
O'Hagan (2003) introduces some tools for criticism of Bayesian hierarchical models that can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. His method relies on computing the posterior median of a conflict index, typically through MCMC simulations. We investigate a Gaussian model of two-way analysis of variance, and show that O'Hagan's approach gives unreliable false warning probabilities. We extend and refine the method, especially avoiding double use of data by a data splitting approach, accompanied by theoretical justifications from a non trivial special case. Through extensive numerical experiments we show that our method detects model misspecification about as well as O'Hagan's method does, while retaining the desired false warning probability for data generated from the assumed model. This also holds for a Student-t version of the model.
I foredraget vil jeg vise hvordan en kan bruke en versjon av Aalen's additive hazard modell til å analysere longitudinelle binære data. Som motivasjon og illustrasjon vil jeg bruke en studie av insidens og prevalens av diare blant brasilianske barn. I denne studien ble nesten tusen barn under 3 år fulgt opp over vel ett år, og tilfeller av diare ble registrert. Viktige utfordringer i analysen er å ta hensyn til heterogeniteten mellom barna og at en god del observasjoner mangler. Foredraget er basert på et fellesarbeid med Rosemeire L. Fiaccone, Robin Henderson og Mauricio L. Barreto. Det er tilgjengelig som e-print fra Matematisk institutt: www.math.uio.no/eprint/stat_report/2005/09-05.html
When estimating the prevalence of a rare trait such as human immunodeficiency virus (HIV), the use of pooled testing can confer substantial benefits when compared to individual testing. In addition to screening experiments for infectious diseases, pooled testing has also been exploited in other biomedical applications such as drug discovery, epidemiology, risk assessment, plant pathology, and genetics. Pooled testing is not a new idea, but, until recently, nearly all biomedical studies using pooled testing have treated individuals as homogeneous. In most real problems, researchers have access to covariate information on each individual subject. Thus, a major thrust becomes understanding how this information can be used efficiently. In this talk, I will introduce a new approach called "informative group screening," whereby covariates are used to determine how pooled information can be efficiently converted into individual information. I will also present some new approaches to modeling the prevalence of multiple traits with pooled data. The methodology will be discussed in the context of a real HIV study conducted in rural Kenya.
Likelihoods har vært en sentral og selvfølgelig del av statistisk metodikk siden Fishers arbeider på 1920-tallet, men har primært og nødvendigvis vært av parametrisk natur, selv om visse varianter har vært i bruk også i semi- og ikkeparametriske modeller. Men for tyve år siden laget Art Owen en genuint ikkeparametrisk likelihood. Siden da har feltet vokst seg stort & bredt ("empirical likelihood" gir 44000 google-treff), og finner anvendelser i en lang rekke statistiske modeller. Mitt foredrag skal gi en kort introduksjon til empirisk likelihood (EL), for så å albue frem utvidelser av teorien i tre nye retninger: (i) EL med ikkeparametrisk plugg-inn for plageparametre; (ii) EL med langsommere-enn-vanlig konvergens; og (iii) EL med flere og flere parametre som funksjon av sample-størrelse. Anvendelser vil bli pekt på. Foredraget er basert på en Annals of Statistics-artikkel jeg har skrevet sammen med Ian McKeague og Ingrid Van Keilegom.
Copulas er en raskt voksende metode for avhengighetsmodellering, både innen forskning og i praksis, og spesielt innen finans og forsikring. Problemet med copulas har vært å finne en god måte å finne den copulan som best tilpasser et datasett. Vi introduserer en ny goodness-of-fit test, basert på Rosenblatt (1952) sin transformasjon. Testen gjør det mulig å vekte visse områder av copulan og resultater fra simuleringer viser at testen gjør det bra og at vektings funksjonaliteten er veldig kraftig. Vi anvender så testen på porteføljer med aksjer og resultatene viser at Student-t copulan passer mye bedre til dataene enn både den Gaussiske- og Clayton copulan. Jeg vil anbefale de som har tid å ta en titt på følgende notat før seminaret da visse kunnskaper om copulas vil være en stor fordel: http://www.nr.no/files/samba/bff/SAMBA2204b.pdf
In survival analysis, regression models are most often specified for the hazard function. This is in contrast to classical linear models for the mean of quantitative data. For a survival time, T, the mean E(T) is rarely well-determined due to right-censoring and it has been suggested to study instead the t-restricted mean E(min(T,t)). We shall study regression models for the t-restricted mean based on so-called pseudo-observations. The methods will be illustrated by two real examples and some Monte Carlo simulations. The seminar is based on joint work with John Klein, Milwaukee, and Mette Harhoff, Copenhagen (LIDA, 2004, 335-350).
Bonferronikorreksjon av P-verdier er en utbredt prosedyre for å kontrollere risikoen for falske positive når man tester mange hypoteser samtidig. Denne er dog svært konservativ dersom hypotesene er positivt korrelert. Simes har introdusert en modifisert prosedyre som håndterer positivt korrelerte hypoteser effektivt. Siden Simes' prosedyre i likhet med Bonferronis prosedyre er enkel å gjennomføre og kun baserer seg på P-verdiene for de enkelte hypotesene, er det en svært anvendelig prosedyre. Mange tilfeller av multippel hypotesetesting, f.eks. innen bioinformatikk og maskinlæring, innebærer testing av et stort antall tildels sterkt korrelerte hypoteser; Simes' prosedyre er da en klar forbedring i forhold til Bonferronikorreksjon. Simes' prosedyre er bevist gyldig i noen sammenhenger og i henhold til simuleringer synes den å fungere svært bra i mange sammenhenger, men det finnes eksempler der prosedyren fungerer dårlig og blir altfor liberal. Det er blitt påpekt at disse moteksemplene er svært konstruerte, men dette er i seg selv et svakt argument. Jeg styrker dette argumentet ved å vise at Simes' prosedyre, selv om den i bestemte tilfeller kan bli liberal for enkelte signifikansnivåer, ikke kan være gjennomgående liberal: at den er "gyldig i gjennomsnitt" i en viss forstand.
I en rekke anvendelser er det ønske om å estimere familierelasjoner mellom individer (mennesker, andre dyr og planter). Jeg vil diskutere en bayesiansk tilnærming som generaliserer Egeland, Mostad et al. (2000). Denne modellen består av tre trinn: (i) en apriorifordeling etableres på utfallsrommet av mulige stamtrær (ii) likelihood for DNA data beregnes og (iii) aposteriorifordeling finnes ved Bayes teorem. I foredraget vektlegges trinn (i). Ofte må DNA data suppleres med annen informasjon slik som aldersdata. Videre vil visse familerelasjoner, slik som eksempelvis 'bestefar-barnebarn', 'onkel-nevø' få samme likelihood basert på de DNA markører som vanligvis brukes i rettsgenetiske anvendelser. Jeg vil illustrere metoden på et mye diskutert generelt problem i rettsgenetikken: Hva gjør man hvis DNA er i konflikt med annen informasjon? Et eksempel med reelle data er en sak der man har informasjon om at en kvinne er mor til et barn (eller ihvertfall at hun har født barnet), men der DNA markørene peker i en annen retning. Jeg vil argumentere for at det er naturlig å diskutere dette og tilsvarende eksempler innenfor den nevnte bayesianske rammen.
In my talk I will present two applications of complex Bayesian Hierarchical models. The first one involves binary transport mode decisions in Munich, Germany, while the second considers high frequency financial time series of price changes. In the first application a new approach to incorporate individual cluster effects and a new proper prior distribution for spatial agregated data based on Markov random fields is presented. In the the second application I will show how ordinal valued time series models with more than three categories can be fitted by MCMC efficiently using grouped move multigrid Monte Carlo sampler suggested by Liu and Sabatti (2000).
Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored (independent or dependent) failure times and in the joint modeling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite-dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. In this work, we present several classes of semiparametric regression models, which unify and extend the existing models. We construct appropriate nonparametric likelihoods, which involve both finite-dimensional and infinite-dimensional parameters. We establish that the resultant nonparametric maximum likelihood estimators are consistent and asymptotically Gaussian with limiting covariance matrices which achieve the semiparametric efficiency bounds and which can be consistently estimated. We develop simple and efficient numerical algorithms to implement the corresponding inference procedures. Simulation studies demonstrate that the proposed inferential and numerical methods perform well in practical settings. Applications to several medical studies are provided. Areas in need of further development are discussed.
The topography of spatial surfaces is often of interest to investigate. In particular, assuming sufficient smoothness, one can investigate gradients to a spatial surface. When the surface is a random realization of a spatial process, under suitable conditions for the process covariance function, we can, in fact, consider the ensemble of gradients $\{D_{\mathbf{u}}Y(\mathbf{s})\}$ where $\mathbf{s}$ indexes locations in some spatial region and $\mathbf{u}$ indexes directions. Banerjee, Gelfand and Sirmans (2003) developed the necessary distribution theory and inference in the case of a Gaussian process for $Y(\mathbf{s})$. In this talk we will go beyond this work, looking at the following cases: (i) the random surface arises as a realization of a mean process which is, itself, a linear transformation of a multivariate spatial process, (ii) the random surface arises through nonparametric specification such as the spacial Dirichlet process, introduced in Gelfad, Kottas, and MacEachern (2005), (iii) the random surface evolves in time say with time discretized so that we have a dynamic spatial process model with the ensemble of variables $\{D_{\mathbf{u}}Y(\mathbf{s},t)\}$. Here we can work with evolving Gaussian processes or spatial Dirichlet processes. Theoretical results involving local convergence and formal distribution theory will be offered as well as applications to problems involving exposure surfaces, land value surfaces and returns on land value investments.
Det argumenteres først for at det aller meste av statistisk konsultasjon har referanse til enkle statistiske modeller og metoder. En kan komme ganske langt ved å bruke disse enkle modellene på en fleksibel måte. Det er imidlertid viktig å unngå feil som kan ha alvorlige konsekvenser. Når modellen første er valgt, gir denne et språk som kan brukes til å stille spørsmål om naturen. I siste del tas opp problemet om hvordan kandidater til enkle modeller kan velges, og det argumenters gjennom en rekke eksempler for at kravet til invarians under en naturlig gruppe er et rimelig kriterium. Ett eksempel er regresjon der en i utgangspunktet har mange forklaringsvariable som har samme enhet. Til slutt nevnes komplementære modeller, et viktig begrep om en vil se på sammenhengen mellom statistikk og moderne fysikk.
I 1930 presenterte Fisher sine fidusfordelinger som et alternativ til Bayesianske apriorifordelinger med flat prior - for å få slutt på 150 år med tåke og forvirring, som han sa. Andre har ment at dette var "Fisher's biggest blunder". Konfidensfordelinger spenner ut konfidensintervaller ved sine kvantiler, og er identiske med fidusfordelinger når de er eksakte. Det trengs ikke noen apriorifordeling for å lage en konfidensfordeling, men eksakte konfidensfordelinger er bare tilgjengelige i enkle modeller. Konfidensfordelinger for flerdimensjonale parametere lar seg ofte ikke karakterisere fullstendig. Konfidensnett er nøstede familier av konfidensområder indeksert med konfidensgrad, og kan gi en delvis karakterisering av konfidensfordelingen. Efrons abc-metode kan ofte brukes for å konstruere skalare konfidensnett for (et endelig antall) punkter på en kurve, og det samme bootstraputvalget kan brukes til å konstruere et konfidensnett for kurven (en familie konfidensbånd indeksert ved simultan konfidensgrad). Disse konfidensnettene kan være balanserte eller ubalanserte (Beran 1988), og de kan pålegges å være monotone eller ha andre egenskaper. Som illustrasjon vil jeg se på grønlandshval utenfor Alaska og kapitalinntekt i Norge.
Vi sammenligner flere regnskapsbaserte modeller for å predikere konkurs. Modellene er utviklet og testet på regnskapene til alle norske små- og mellom-store bedrifter i perioden 1995-2000. 'Out-of-sample' og 'Out-of-time' validering viser at generaliserte additive modeller utkonkurrerer andre modeller som lineær diskriminantanalyse, generaliserte lineære modeller og nevrale nettverk, for alle risikonivå. Videre undersøker vi viktige tema som tidshorisonten for prediksjon og forringelsesraten av modellens ytelse. Til slutt ser vi på en fler-års modell, utviklet på alle data fra tre etterfølgende år. Denne sammenlignes med en modell utviklet på data fra kun det seneste år. Fler-års modellen viser en ønsket robusthet overfor årlige svingninger som ikke er tilstede i ett-års modellen.
Sensorisk analyse og forbrukerundersøkelser spiller i dag en svært viktig rolle for moderne mat- og drikkevareindustri. Dette gjelder både for produktutvikling og for kvalitetskontroll. Slike analyser resulterer i store datamengder som det er svært vanskelig å tolke. I alle tilfeller er det mange faktorer som påvirker sluttresultatet og det er alltid mange egenskaper i sluttprodukt som er av interesse for forbrukeren. Dette betyr at multivariat statistisk forsøksdesign og multivariat statistikk spiller en avgjørende rolle for effektiv utnyttelse av slike analyser. I dette foredraget vil det fokuseres på anvendelser av denne typen innen studier av vinkvalitet.
Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for Object Oriented Data Analysis create several potentially large new interfaces between mathematics and statistics. Even in situations where Euclidean analysis makes sense, there are statistical challenges because of the High Dimension Low Sample Size problem, which motivates a new type of asymptotics leading to non-standard mathematical statistics. vv
Given a set of microarray data, the problem is to detect differentially expressed genes, using a False Discovery Rate (FDR) criterion to correct for multiple testing. As opposed to common procedures in literature, we do not base the selection criterion on statistical significance only, but also on biological significance. Therefore, we would like to select only those genes which are significantly more differentially expressed than some fold $f$ (e.g. $f=2$). This corresponds to interval hypothesis testing (which uses inequality instead of equality in the null-hypothesis). We adopt the Bayesian interpretation of FDR: the probability that the parameter of interest lies in the null domain (e.g. $\mu < 2$) given that the test criterion exceeds a threshold. Based on a simple error model, we discuss a naive estimator of FDR. We show how to improve the simple estimator by using deconvolution. That is, we recover the density of the parameter of interest from the data and the (known) noise process. We study the performance of the estimators using simulations. Joint work with Kyung In Kim
A semiparametric version of the competing risks model is given. It is based on an assumption of proportionality between the cause specific intensity functions. The maximum likelihood estimator for the aggregated intensity function and the cause specific factors of proportionality is obtained, leading to a multiplicative semiparametric estimator. Corresponding Bayesian treatment has been proceeded by using a Beta process and a Dirichlet random vector. Large sample properties have been investigated, together with goodness-of fit for the assumption of the model. Illustration via a malignant melanoma data set will be provided. Joint work with Nils Lid Hjort
Se sammendrag for mer informasjon
In GÃ¥semyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).
I will present "functional importance sampling," a technique for producing efficient and smooth simulation estimates of functions containing integrals. In particular, I will present the special case "Laplace importance sampling", with Gaussian importance samplers based on expansions about the mode of the integrand. I will discuss how these methods relate to other methods for simulating or approximating likelihood functions, and I will present some applications to simulated maximum likelihood estimation of generalized linear mixed models. In the selected applications, the method works well even for small importance samples, and the method provides precise and computationally cheap estimates of exact maximum likelihood estimates.
Faglige institusjoner som NVE har behov for analyse av data i mange ulike deler av sine store produksjons-system. Data samles inn i store mengder, foredles i flere trinn, kvalitetstestes og brukes i flere uavhengige beslutnings-prosesser. Statistisk analyse trengs som verktøy i alle disse prosessene. Bortsett fra i spesifikke slutt-analyser blir ikke statistikerens rolle å være eneforvalter av analysen. I stedet er statistikeren sammen med programmeren en verktøybygger for fagpersonene, i dette tilfelle hydrologene. Det blir en kort presentasjon av ulik statistisk analyse som foretas i et slikt stort fagmiljø, både de deler som er knyttet til systemet og til slutt-analysen. Analyse som slutt-produkt er kjent stoff, så de to eksemplene som får fokus er fra koblingen mellom statistikk og faglig datasystem. Her blir statistikk brukt til å videre-foredle data, i tildels store volum, for så å inngå i systemet igjen. Eksempel 1 er vannføringskurve-problematikken, altså sammenheng vannføring og vannstand i en elveprofil. Slike metadata er uhyre viktig å generere korrekt for den videre hydrologiske analyse. Her ligger det en god del system- og kvalitets-føringer som gjør dette ikke-lineære regresjonsproblemet ekstra interessant. Eksempel 2 er en kvalitets-undersøkelse av tidsserier basert på Bayesiansk modellvalg. Erfaringene fra dette tyder på at slik statistisk analyse kan gjøres brukervennlig.
Subjektiv likelihood introduseres som modell for menneskelig usikkerhet. Med dette menes at en person anslår den relative sannsynligheten for den observasjonen han gjør under forskjellige forutsetninger. Denne tilnærmingen sammenliknes med etablerte metoder for modellering av usikkerhet innen ekspertsystemer (sikkerhetsfaktorer, fuzzy logic, Dempster Schaeffer-teori, lower previsions, subjektiv sannsynlighet og Bayesianske nett). Det vises en anvendelse av metoden i et ekspertsystem for artsbestemmelse av sopper. Systemet stiller en sekvens av spørsmål om egenskaper ved soppen som brukeren har plukket i skogen (f eks om undersiden av hatten har skiver, rør eller porer). Usikkerhet i svarene blir tolket gjennom subjektive likelihood-verdier. Ekspertsystemet vil bli demonstrert, bl.a. for at undertegnede skal få anledning til å vise sine flotte soppbilder.
Etter foredraget blir det anledning til aa vaere med til Songsvann og plukke sopp, under kyndig veiledning av Fredrik, som har soppkontrolloer-sertifikat og vet alt som er verdt aa vite om sopp-plukking. Etterpaa tilbereder og spiser vi fangsten sammen (hvor avhenger av hvor mange vi blir). Paamelding til fadahl@math.uio.no innen mandag 6. september, spesifiser om du du vil vaere med paa bare tur eller baade tur og spising (foredraget har ikke paamelding!).
Store bedrifter og institusjoner budsjetterer og styrer økonomisk ved å stille krav til de enkelte enhetene og avdelingene. Samtidig vil det finnes en buffer for bedriften som helhet, fordi det med svært liten sannsynlighet vil intreffe store tap for alle enhetene samtidig. Vi vil se på denne problemstillingen ved å ta utgangspunkt i totalrisikomodellering for DnBNOR konsernet. Konsernet er eksponert for kreditt-, markeds- og operasjonell risiko, samt risiko fra eierskapet i Vital forsikring. Vi er interessert i kvantiler i tapsfordelingene (Value-at-Risk) og a finne tilsvarende størrelse for totalrisikoen fra disse, gitt en bestemt korrelasjonsstruktur. Vi vil diskutere ulike måter å gjøre dette på, men spesielt fokusere på copulas.
Vi analyserer et datamateriale over årlige gjennomsnittlige personellkostnader i Forsvaret i perioden 1994-2002. Fordi datamaterialet er så begrenset, benytter vi "puristisk" Bayesiansk analyse, ved at vi forsøker å representere reell forhåndskunnskap gjennom priorfordelinger på parametrene. Modelleringen bygger på en antagelse om en driftskostnadsvekst (dkv) som representerer en årlig fordyringsfaktor pr årsverk utover konsumprisindeksen. Dette leder til en tilstandsmodell på formen x_i = x_{i-1} + c + e_i hvor x_i er logaritmen av kostnaden i år i, og e_i er en normalfordelt støy. Observasjonslikningen er gitt ved y_i = x_i + f_i hvor y_i er logaritmen av observert kostnad for år i, og f_i er normalfordelt støy. For estimering av aposteriorifordelingen benyttes MCMC-simuleringer sammen med Kalmanfilterberegninger. Modellens brukbarhet undersøkes med "posterior predictive p-values", og vår nyutviklede "calibrated posterior predictive p-value" (cppp).
I Aalen's additive modeller uttrykkes hazardfunksjonene lineært i regresjonsfunksjoner og kovariater. Jeg vil i dette foredraget presentere estimatorer for de kumulative regresjonfunksjonene med data fra kasus-kohort og nøstede kasus-kontroll studier. For estimatorene benyttes vektingsteknikker der vektene er inverse av inklusjonsandeler blant kasus (syke) og kontroller (friske). Spesielt utvikles variansestimatorer. Jeg ser deretter på hvordan estimatorene av regresjonsfunksjonene og deres variansestimatorer oppfører seg på simulerte og ekte data.
Multivariate models are of great importance in theoretical and applied quantitative genetics. We extend quantitative genetic theory to accommodate situations in which there is linear feedback or recursiveness between the phenotypes involved in a multivariate system, assuming an infinitesimal, additive, model of inheritance. It is shown that structural parameters defining a simultaneous or recursive system have a bearing on the interpretation of quantitative genetic parameter estimates (e.g., heritability, offspring-parent regression, genetic correlation) when such features are ignored. Matrix representations are given for treating a plethora of feedback-recursive situations. The likelihood function is derived, assuming multivariate normality, and results from econometric theory for parameter identification are adapted to a quantitative genetic setting. A Bayesian treatment with a Markov chain Monte Carlo implementation is suggested for inference and developed. When the system is fully recursive, all conditional posterior distributions are in closed form, so Gibbs sampling is straightforward. If there is feedback, a Metropolis step may be embedded for sampling the structural parameters, since their conditional distributions are unknown. Extensions of the model to discrete random variables and to non-linear relationships between phenotypes are discussed.
Tradisjonelt har statistikere vært svært skeptiske til alt snakk om kausalitet. Likevel, i statistisk praksis er det ofte årsakssammenhenger man egentlig er interessert i. Innsikt i årsakssammenhenger er interessant bl.a. når det gjelder å forstå mekanismer og forutsi effekter av intervensjoner. I dette foredraget vil jeg kort presentere ulike innfallvinkler til kausal inferens.
Consider the additive regression model $E(y|\mathbf{x})=\beta_0+s_1(x_1)+ \cdots + s_p(x_p)$, where $y$ is a response variable, the $x_j$'s are predictor variables and the $s_j$'s are smooth functions. They are often estimated by penalized least squares, penalizing the curvatures of the $s$-functions. In this paper I suggest controlling the slopes as well, penalizing the first derivatives in addition to the second derivatives. This is the penalization used in ridge regression for linear models. Estimation is based on double penalized B-splines. Tuning (or smoothing) parameters are estimated by permuted leave-k-out cross-validation. The prediction performance of various methods is compared by a simulation experiment: penalizing both slope and curvature is either better than or as good as penalizing curvature only.
Sammendrag: Vi studerer prising av forward/futures i elektrisitets og værmarkedet, og opsjoner skrevet på disse. Empiriske studier motiverer introduksjonen av Levy prosesser og sesongvarierende varians for temperatur og spot elektrisitet. basert på slike modeller, utleder vi forward/futures priser som er basert på gjennomsnittlig temperatur eller spot elektrisitet. Hvis vi tar tilnærmingen til Heath-Jarrow-Morton, som modellerer forwards/futures direkte, får vi inn komplekse krav for arbitrasje når produktenes leveringstid kan overlappe. Vi benytter data fra den nordiske elbørsen Nordpool i våre studier.
NB! Bemata-prosjektet 'Evaluation of Bayesian hierarchical models' starter opp sine seminarer med
Foredraget er basert på de to artiklene "Frequentist model average estimators" og "The focussed information criterion", av Nils Lid Hjort og Gerda Claeskens. Foredragsholderen er ydmykt stolt over at disse to arbeidene er "papers of the year" i Theory and Methods -delen i Journal of the American Statistical Association; med diskusjonsbidrag og rejoinder tar dette 67 sider i JASA, noe han håper er verdensrekord. Artiklene og rejoinderen kan lastes ned fra Gerda Claeskens' hjemmeside.
I hoestsemesteret 2003 hadde vi følgende på programmet: