# The LiU Seminar Series in Statistics and Mathematical Statistics

Fall 2013

### Wednesday, September 11, 4.15 pm, 2013. Seminar in Mathematical Statistics

**Simulation of conditional diffusions via forward-reverse stochastic representations**

Christian Bayer, Weierstrass Institute, Berlin, Germany.

Christian Bayer

*Abstract*: In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein et al. [Bernoulli 10(2):281-312, 2004] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset.

Location: Hopningspunkten

### Tuesday, September 24, 3.15 pm, 2013. Seminar in Statistics

**Recent developments on non-Gaussian stochastic processes and fields - spectral representation, Slepian model, extreme behavior and applications**

Krzysztof Podgorski, Department of Statistics, Lund University.

Krzysztof Podgorski

*Abstract*: I will present account of recent results on non-Gaussian stochastic models involving the generalized Laplace distribution. The focus will be on moving average processes driven by Laplace motion. As oppose to models based on the Gaussian distribution, these ones account explicitly for transients, asymmetries, and heavy tails. The model is characterized by a low number of parameters accounting for fundamental characteristics of multivariate signals: the covariance matrix representing size of the signals and their mutual dependence, the excess kurtosis that in the model is related to relative size of transients, and the time scale. I will start with a presentation of an application to modeling multivariate road and vehicle data. Then two methodological problems will be discussed. The first one is dealing with the spectral representation of the Laplace moving average and its application to efficient simulations. The second discusses the Slepian model, i.e. the model that represents biased sampling distribution of a stochastic process when it is observed at the crossings of a level. The Slepian model for the Gaussian case has particularly simple form and we look at its extension to our non-Gaussian case. A method of effective simulating from the developed Slepian model will be also presented together with some discussion of the behavior at the extreme level crossings.

Location: Alan Turing

### Tuesday, October 8, 3.15 pm, 2013. Seminar in Mathematical Statistics

**Iterated random functions**

**Örjan Stenflo**

Mathematical Statistics, Uppsala University

Mathematical Statistics, Uppsala University

*Abstract*: This talk will be a brief introduction to the theory of iterated random functions and its applications in the theory of fractals, Markov chains and simulations.

Location: Hopningspunkten

### Tuesday, October 22, 3.15 pm, 2013. Seminar in Statistics

**Impact of covariates on low-template DNA analysis results**

**Ronny Hedell**, SKL and Chalmers

*Abstract*:Crime scene samples containing DNA are routinely analysed at the Swedish National Laboratory of Forensic Science (SKL). When the amount of DNA is scarce only partial results may be obtained. In order to optimize the analysis and the interpretation of results the impact of different covariates on the DNA analysis results has to be assessed. In this talk I'll present some results from such a study performed at SKL. We use Bayesian hierarchical modelling and Bayesian inference to learn how the output parameters (e.g. drop-out, peak heights and heterozygote balance) depend on the different covariates (e.g. PCR cycle number, CE injection time and marker type). We utilize the joint posterior distributions and the Deviance Information Criterion for model selections. Possible discrepancies between the experimental data and real casework data are analysed via the predictive distributions of the final models. Via reference to available literature I'll mention how findings from studies like this may enhance the interpretation of results from DNA analysis.

Location: Alan Turing

### Tuesday, November 5, 3.15 pm, 2013. Seminar in Mathematical Statistics

**Hierarchical modeling of spatial structure of epidermal nerve fibers**

Aila Särkkä, Mathematical Statistics, Chalmers University.

Aila Särkkä

*Abstract*: Epidermal nerve fiber (ENF) density and morphology are used to diagnose small fiber involvement in diabetic and other small fiber neuropathies. ENF density and summed length of ENFs per epidermal surface area are reduced, and based on mainly visual inspection, ENFs seem to appear more clustered within the epidermis (the outmost living layer of the skin) in subjects with small fiber neuropathy compared to healthy subjects. We have investigated the spatial structure of ENF entry points, which are the locations where the nerves enter the epidermis, and ENF end points, which are the terminal nodes of ENFs. The study is based on suction skin blister specimens from two body locations of 32 healthy subjects and 15 subjects with diabetic neuropathy. The ENF entry (end) points are regarded as a realization of a spatial point process and Ripley's K function is used to summarize the spatial structure. A hierarchical Bayesian approach is then used to model the relationship between this summary characteristic and the disease status and some other covariates (gender, age, body mass index).

Location: Hopningspunkten

### Tuesday, November 19, 3.15 pm, 2013. Seminar in Mathematical Statistics

**Stochastic Approximation Methods for American Type Options**

Dmitrii Silvestrov, Mathematical Statistics, Stockholm University.

Dmitrii Silvestrov

*Abstract*: This lecture presents a survey of results from my new book, which is devoted to stochastic approximation methods for rewards of American type options for multivariate modulated Markov log-price processes. The classes of discrete and continuous time log-price processes (LPP) under consideration include multivariate modulated Markov chains, modulated random walks, and various autoregressive models, multivariate modulated Markov log-price processes, diffusion and Levy processes. General convergence results are presented, as well as their applications to space skeleton approximations, tree approximations, and Monte Carlo based approximation algorithms for option rewards. Also, results related to studies of structure for optimal stopping domains are presented as well as results related to option reselling problem. Theoretical results are illustrated by results of experimental studies. The book contains two parts and the lecture will be mainly concentrated on the results related to discrete time processes. These results included in the first part of the book, which is expected to appear in 2013.

Location: Hopningspunkten

### Tuesday, December 3, 3.15 pm, 2013. Seminar in Statistics

**Balance and sampling**

Anton Grafström, Section of Forest Resource Analysis, SLU Umeå.

Anton Grafström

*Abstract*: When sampling from a finite population there is often auxiliary information available on unit level. By using such information wisely and select samples that are balanced in different ways (e.g. spatially balanced) we can significantly reduce the variance of estimators. Different methods to select balanced samples will be presented as well as some properties of balanced samples.

Location: Alan Turing

Page responsible: Mattias Villani

Last updated: 2013-11-18