Markowitz theory of asset allocation is one of very few research ideas that made it into practical finance. Yet, its investment recommendations exhibit incredible sensitivity to even smallest variations in the estimation horizon or estimation techniques. Scientists as well as practitioners have put enormous effort into stabilizing the estimators of portfolios (with moderate success, according to some). However, there seems to be no simple quantitative method to measure the portfolio stability. In this talk, I will derive
analytical formulas that relate the mean and the covariance matrix of asset returns with the stability of portfolio composition. These formulas allow for the indentification of main culprits of worse-than-expected performance of the Markowitz framework. In particular, I will question the common wisdom that puts the main responsibility on estimation errors of the mean.

This research is a spin-off of a consultancy project at the University of Warsaw regarding the allocation of the foreign reserves of Polish Central Bank.

Alexander Schied (Mannheim)
Mathematical aspects of market impact modeling
Abstract: In this talk, we discuss the problem of executing large orders in illiquid markets so as to optimize the resulting liquidity costs. There are several reasons why this problem is relevant. On the mathematical side, it leads to interesting  nonlinearity effects that arise from the price feedback of  strategies. On the economical side, it helps  understanding which market impact models are viable, because the analysis of order execution provides a test for the existence of undesirable properties of a model. In the first part of the talk, we present market impact models with transient price impact, modeling the resilience of electronic limit order books. In the second part of the talk, we consider the Almgren-Chriss market impact model and analyze the effects of risk aversion on optimal strategies by using stochastic control methods. In the final part, we discuss effects that occur in a multi-player equilibrium.

Theo Kypraios (Nottingham)
A novel class of semi-parametric time series models: Construction and Bayesian Inference
Abstract
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In this talk a novel class of semi-parametric time series models will be presented, for which we can specify in advance the marginal distribution of the observations and then build the dependence structure of the observations around them by introducing an underlying stochastic process termed as 'latent branching tree'. It will be demonstrated how can we draw Bayesian inference for the model parameters using Markov Chain Monte Carlo methods as well as Approximate Bayesian Computation methodology. Finally a real dataset on genome scheme data will be fitted to these models and we will also discuss how this kind of models can be used in modelling Internet traffic.

Vincent Macaulay, Dept of Statistics, University of Glasgow
Inference of migration episodes from modern DNA sequence variation
One view of human prehistory is of a set of punctuated migration events across space and time, associated with settlement, resettlement and discrete phases of immigration. It is pertinent to ask whether the variability that exists in the DNA sequences of samples of people living now, something which can be relatively easily measured, can be used to fit and test such models. Population genetics theory already makes predictions of patterns of genetic variation under certain very simple models of prehistoric demography. In this presentation I will describe an alternative, but still quite simple, model designed to capture more aspects of human prehistory of interest to the archaeologist, show how it can be rephrased as a mixture model, and illustrate the kinds of inferences that can be made on a real data set, taking a Bayesian approach.

Prakash Patil (University of Birmingham)
Smoothing based Lack-of-Fit (or Goodness-of-Fit) Tests

To construct a nonparametric (smoothing-based) test of lack-of-fit, one measures one way or other, the discrepancy between a smooth estimator of the unknown curve and the hypothesised curve. Although there are many possible choices for measuring this discrepancy, for being technically most easy to deal with, the lack-of-fit tests based on the ISE seem to have received the most(?) attention. But since a test based on the ISE requires the estimation of the unknown curve, its ability to distinguish between the null model and the departures from the null model is linked to the smoothing parameter that one chooses to estimate the curve. Whereas, if one takes a local view and then constructs a test, one can show that the test has better power properties. And although the performance of the test is still linked to the smoothing parameter, the choice of smoothing parameter will now be dictated by the `testing’ aspect of the problem rather than be driven by the estimation of the unknown curve. In this talk, we will mainly use regression quantile curves to illustrate the above points but will show that this procedure could be used for density and hazard rate curves.

David Findley (US Census Bureau)

Two improved Diebold-Mariano test statistics for comparing the forecasting ability of incorrect time series models

We present and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h -step-ahead forecasts than another, as measured by the difference of approximations to their asymptotic mean square forecast errors. The two statistics differ in the variance estimate whose square root is the statistic's denominator. Both variance estimates are consistent even when the ARMA components of the models considered are incorrect. Our principal statistic's variance estimate accounts for parameter estimation. Our simpler statistic's variance estimate treats parameters as fixed. The broad consistency properties of these estimates yield improvements to what are known as tests of Diebold and Mariano (1995) type. These are tests whose variance estimates treat parameters as fixed and are generally not consistent in our context.

We describe how the new test statistics can be calculated algebraically for any pair of ARIMA models with the same differencing operator. Our size and power studies demonstrate their superiority over the Diebold-Mariano statistic. The power study and the empirical study also reveal that, in comparison to treating estimated parameters as fixed, accounting for parameter estimation can increase power and can yield more plausible model selections for some time series in standard textbooks.

(Joint work with Tucker McElroy)

Ann Nicholson (Monash)

Incorporating expert knowledge when learning Bayesian network structure: Heart failure as a case study

Bayesian networks (BNs) are rapidly becoming a leading technology in applied Artificial Intelligence (AI), with medicine one of its most popular application area.  Both automated learning of BNs and expert elicitation have been used to build these networks, but the potentially more useful combination of these two methods remain underexplored. In this seminar, I will present a case study of this combination using public-domain data for heart failure. We run an automated causal discovery system (CaMML), which allows the incorporation of multiple kinds of prior expert knowledge into its search, to test and compare unbiased discovery with discovery biased with different kinds of expert opinion. We use adjacency matrices enhanced with numerical and colour labels to assist with the interpretation of the results.  These techniques are presented within a wider context of knowledge engineering with Bayesian networks (KEBN). 

David White (Warwick)

Informal Group Meeting

Applications of Bayesian Networks

Informal Group Meeting

Petros Dellaportas (Athens University of Economics and Business)
Control variates for reversible MCMC samplers
A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive, consistent MCMC estimators are derived for these optimal coefficients. All methodological and asymptotic arguments are rigorously justified. Numerous MCMC simulation examples from Bayesian inference applications demonstrate that the resulting variance reduction can be quite dramatic.

Omiros Papaspiliopoulos (Universitat Pompeu Fabra)

Ann Nicholson (Monash University)
Bayesian Networks for Biosecurity Risk Assessment

Bayesian networks (BNs) are rapidly becoming a tool of choice for ecological and environmental modelling and decision making. By combining a graphical representation of the dependencies between variables with probability theory and efficient inference algorithms, BNs provide a powerful and flexible tool for reasoning under uncertainty.  The popularity of BNs is based on their ability to reason both diagnostically and predictively, and to explicitly model causal interventions and cost-benefit trade-offs.

In Australia, current biosecurity risk assessments are typically qualitative, combining assessment across the stages of importatation, distribution, entry, establishment and spread. In this seminar, I will show a BN that directly models the current qualitative method.  I'll then adapt the BN to explicitly model the volume of infestation, adding clarity and precision.  I will demonstrate how more complex BNs can explicitly model the factors influencing each stage, and can be extended with management decisions and cost functions for decision making.

William Astle (Imperial)

A Bayesian model of NMR spectra for the deconvolution and quantification of metabolites in complex biological mixtures

Mahadevan Ganesh (Edinburgh)

Idris Eckley (Lancaster)
Wavelets - the secret to great looking hair?

Texture is the visual character of an image region whose structure is, in some sense, regular, for example the appearance of a woven material. The perceived texture of an image depends on the scale at which it is observed. In this talk we show how wavelet processes can be used to model and analyse texture structure. Our wavelet texture models permit the classification of images based on texture and reveal important information on differences between subtly different texture types. We provide examples, taken from industry, where wavelet methods have enhanced the classification of images of hair and fabrics.

Informal Group Meeting

John Aston (Warwick)

Prof Adrian Bowman, University of Glasgow

  

Informal Group Meeting

Sujit Sahu (Southampton)

High Resolution Bayesian Space-Time Modelling for Ozone Concentration Levels

This talk will first discuss the two air quality standards for ozone levels and then will develop high resolution Bayesian space-time models which can be used to assess compliance. Predictive inference properties of several rival modelling strategies for both spatial interpolation and temporal forecasting will be compared and illustrated with simulation and real data examples. A number of large real life ozone concentration data sets observed over the eastern United States will also be used to illustrate the Bayesian space-time models. Several prediction maps from these models for the eastern US, published and used by the USEPA, will be discussed. 

Jim Nolen (Duke)

Andrew Gelman (Columbia University)

Nothing is Linear, Nothing is Additive: Bayesian Models for Interactions in Social Science

Tim Johnson

Tim Johnson