# The LiU Seminar Series in Statistics and Mathematical Statistics

Fall 2011

### Thursday, September 29, 10.15 am, 2011. Seminar in Mathematical Statistics

**Market Implied Valuation of Equity Derivatives**

Magnus Ekdahl, Carnegie Investment Bank AB

Magnus Ekdahl

*Abstract*: An important characteristic of any financial pricing model is the ability to replicate traded market prices. One way of doing this is to choose a process model with relatively small amount of parameters, and try to verify that one's guess is correct. Another is to choose a large enough parameter set so that traded market instruments can be priced very accurately by the model. This seminar is about the practicalities of the latter approach.

Location: Kompakta rummet, MAI.

### Tuesday, October 11, 3.15 pm, 2011. Seminar in Statistics

**Efficient Bayesian Multivariate Surface Regression**

Feng Li, Department of Statistics, Stockholm University

Feng Li

*Abstract*: Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they are likely to be less successful in that setting because of the curse of dimensionality, especially when there are more than a couple of covariates. We propose a regression model for a multivariate Gaussian response that combines both additive splines and interactive splines, and a highly efficient MCMC algorithm that updates all the knot locations jointly. We use shrinkage priors to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. This makes it possible for the model to adapt to varying degrees of nonlinearity in different parts of the data in a parsimonious way. Simulated data and an application to firm leverage data show that the approach is computationally efficient, and that allowing for freely estimated knot locations can offer a substantial improvement in out-of-sample predictive performance.

*Keywords*: Bayesian inference, Markov chain Monte Carlo, Surface regression, Splines, Free knots.

[ Paper | Slides ]

Location: John von Neumann

### Tuesday, October 25, 3.15 pm, 2011. Seminar in Mathematical Statistics

**Generalized Smooth Finite Mixtures**

Mattias Villani, Statistics, LiU

Mattias Villani

*Abstract*: We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates though a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model's parameterization and variable selection prior are chosen to prevent overfitting. We use simulated and real data sets to illustrate the methodology.

*Keywords*: Bayesian inference, Conditional distribution, GLM, Markov Chain Monte Carlo, Mixture of Experts, Variable selection.

[ Paper ]

Location: Kompakta rummet, MAI.

### Tuesday, November 8, 3.15 pm, 2011. Seminar in Mathematical Statistics

**Tractability of some high dimensional problems**

Mikhail Lifshits, MAI, LiU and S:t Petersburg State University

Mikhail Lifshits

*Abstract*: We study finite rank L_2-approximation of tensor product random fields with covariance K^{(d)}(s,t)=\prod_{j=1}^d K_j(s_j,t_j) depending on many parameters (d is very large). We first give some general criteria for various bounds on approximation errors (tractability of approximation problem). Then, as an example, we consider tensor products of r_j-times integrated Wiener process and investigate the interplay between tractability and smoothness of the field. Surprisingly, the type of integration (Euler or classical) influences the results significantly.

Location: Kompakta rummet, MAI.

### Tuesday, November 22, 3.15 pm, 2011. Seminar in Statistics

**Chain graphs: Expressiveness and learning**

Jose M. Peña, Database and Information Techniques (IDA/ADIT), LiU

Jose M. Peña

*Abstract*: Probabilistic graphical models (PGMs) are an increasingly popular formalism for representing probability distributions efficiently. A PGM consists of a graph and a set of factors or potentials. The PGM represents the probability distribution resulting from the product of the factors. The graph encodes the independencies in the probability distribution represented, which enables reasoning with the distribution efficiently. When the graph is a directed and acyclic graph, PGMs are also called Bayesian networks. When the graph is an undirected graph, PGMs are typically called Markov networks. When the graph contains (possibly) both directed and undirected edges, PGMs are called chain graphs. In this talk, I will focus on the latter models. In particular, I will address the following three questions. Of course, chain graphs are more expressive than Bayesian and Markov networks. But how much more ? The answer is significantly more. Does every chain graph represent a probability distribution ? The answer is yes. Can we efficiently learn the chain graph that represents a probability distribution if we only have access to a finite sample of the distribution ? The answer is yes under mild assumptions.

Location: John von Neumann

### Tuesday, December 6, 3.15 pm, 2011. Seminar in Mathematical Statistics

**On the Inference of Ranked Set Sampling Using the Bootstrap Method**

Saeid Amiri, Department of Mathematics, Uppsala University

Saeid Amiri

*Abstract*: We consider the bootstrap approach to infer the ranked set sampling (RSS) method. Here a sequential bootstrap approach is used to shift the analysis from an unbalanced RSS sample to the analysis of a balanced RSS sample. The balanced RSS is also discussed. Consequences of using different algorithms for carrying out resampling are discussed. The proposed methods are studied using Monte Carlo investigations. Furthermore, the theoretical side of the approach is considered.

Location: Kompakta rummet, MAI.

### Tuesday, December 20, 3.15 pm, 2011. Docent Lecture in Statistics

**Ordinal scales for Bayes factors - communicating evidentiary strength in court**

Anders, Nordgaard, SKL and Statistics, LiU

Anders, Nordgaard

*Abstract*: Forensic findings, i.e. results from the examination of technical evidence, must be evaluated with respect to different competing propositions (hypotheses) each providing an explanation to its emergence. The logical approach to evidence evaluation makes use of Bayesian hypothesis testing, in particular the calculation of the Bayes factor, which measures the evidentiary strength. However, in the absence of knowledge about the exact probability distributions that govern the forensic findings under each of the competing hypothesis the Bayes factor can only be approximated. Very often it simplifies to a likelihood ratio, which in turn may sometimes be estimated from explicit data from historical cases. When such data is lacking the estimation must be made on a cruder scale, but such a scale may also be useful when the evidentiary strength should be communicated further, i.e. to end-users not familiar with statistical models and language. In this talk we give an overview of Bayesian hypothesis testing and its application within forensic science and we further show how an ordinal scale can be constructed on which the evidence value may be reported.

Location: Alan Turing

Page responsible: Mattias Villani

Last updated: 2012-02-19