Statistics and Operations Research Seminars 2009-2010,
Department of Economics, Pompeu Fabra University
Schedule.
Friday, September 4, 12:00, room 23.S03.
Miguel Belmonte, University of Warwick
Sequential Monte Carlo Methods for Time Series Analysis.
Abstract:
Econometrics and Statistics fit time series using models of different
nature, classified as observation driven and parameter driven. Depending
on the type, modelling and inference techniques differ. I offer a quick
comparison between both methodologies. Usually parameter-driven or
state-space models require simulation methods, since unobserved states
cannot be integrated out, required to have an analytical likelihood. I
offer an overview of recent methods and algorithms to implement online
filtering and offline parameter estimation.
Thursday, October 1, 12:00,
room 20.237.
Dietmar Maringer (Univ. Basel)
Heuristic Optimization for Portfolio Management: Concepts and Applications
Abstract:
A crucial question in financial management is how to combine risky assets into portfolios. Stating the problem is rather simple: investors want high rewards, but low risk. Solving this problem, however, is much less straightforward. Individual investors can differ in their attitudes toward risk and, hence, what they consider a suitable risk-reward trade-off; future asset returns are likely to follow non-standard distributions and exhibit non-linear dependencies; institutional and regulatory requirements have to be met. Furthermore, practical issues such as transaction costs or lot size restrictions can cause further complications to the selection process. From an optimization point of view, these aspects will make the search space rough and discontinuous, and traditional numerical methods can no longer provide reliable solutions. However, simplifying the (formal) optimization problem until traditional methods can be used is not recommendable either, since crucial aspects might be excluded.
One way out of this dilemma is the use of alternative methods. Heuristic methods are non-deterministic approaches that serve this purpose well: For one, they are much more flexible in incorporating constraints and are not limited to specific types of objective functions. Furthermore, they include features that allow the evasion of local optima and prevent premature convergence. Therefore, they can deal with the inherent complexity of real world financial optimization problems.
This talk presents how heuristics methods can be used for financial portfolio optimization. Discussing different problem settings, the underlying concepts of different heuristics and their application will be outlined.
Thursday, October 8, 12:00,
room 20.287.
Nikos Demiris (Athens)
On the Epidemic of Financial Crises
Abstract:
The frequency and intensity of financial crises is of growing concern to policymakers. Questions are increasingly raised about the nature of these crises, and the policies needed both to prevent them from occurring in the first place and, once occurred, to limit their severity and contagious spread to other countries. Naturally, any discussion of the appropriate policy response must be based on an analytical understanding of contagion, as given by a model of that phenomenon. The contagion literature does not directly model the inherent dependencies involved in the spread of crises. We argue that a transmission model may be more appropriate, and we propose a stochastic model from epidemic theory where the population of countries is explicitly structured and the crisis may be transmitted both locally and globally. The approach is illustrated using historical data. The likelihood for such data is numerically intractable and we surmount the problem by augmenting the parameter space using a random graph that effectively describes the underlying contact process. The results indicate an increasing trend for global transmission over time. Policy implications are also addressed. This is joint work with L.V. Smith, Cambridge
Tuesday, October 20, 12:00, room 20.237.
Ab Mooijaart (Leiden University)
Testing for nonlinear relationship in Structural Equation Modeling
Abstract: In this paper we first show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. This may lead to the wrong conclusion that a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, while the underlying model may in fact be severely nonlinear. This phenomenon has been explained by Mooijaart & Satorra, Psychometrika (2009). Secondly, we show that introduction of cross-product terms beyond the second-order allows to analyze interaction, i.e. nonlinear terms. The issue is whether a specific set of added higher order moments has enough power to detect the presence of interaction terms given the data. Here we show how this power analysis can be carried out using a simple procedure. So we elaborate the power as criterion for selection of the third order moments. This paper gives the statistical theory and some small Monte Carlo study will be presented.
Wednesday, October 21, 12:00,
room 20.287.
Juan Antonio Cuesta Albertos (Universidad de Cantabria)
Applications of random projections in the analysis of functional data
Abstract:
Practical applications of random projections have been based on the
Johnson-Lindenstrauss lemma that describes metric properties of the method.
However, there were no results explaining the relationship between
a probability distribution and its randomly selected marginals.
In this talk we present a theorem that establishes that if P is a probability
distribution that satisfies certain moment conditions, then one randomly
selected marginal is sufficient to determine P.
We also present some applications of this result in statistics of functional
data, in goodness-of-fit problems, general linear models,...
Thursday, October 22, 12:00,
room 20.237.
Felix Reed-Tsochas (Oxford)
Title: Modelling the structure and dynamics of organisational networks from real-world data
Abstract: In my talk I will cover three related pieces of research, all grounded in the same empirical dataset recording the evolution of an organisational network. The dataset tracks payments between manufacturers and suppliers in the New York garment industry from 1985 to 2003, and provides an unusually complete picture of the structure of relationships that underpin manufacturing in a specific sector. The first piece of research explores the dynamics of network contraction, both in terms of the empirically observed behaviour, and with respect to a stochastic model based on the empirical findings that can be generalised to other contexts. Here, I will argue that the key findings relate to the mechanisms that generate topological robustness in a network that is shrinking. The second piece of research starts from the two distinct classes of organisations that are embedded in the network, manufacturers and suppliers, and examines the bipartite network structure that is created if members of the two different classes need to cooperate with each other. Here I consider what assembly rules, in terms of an appropriate stochastic model, can generate some of the key structural features observed in our organisational network. Beyond the specific focus of the NewYork garment industry, I will argue that plant-pollination networks can be modelled in the same way, which raises the more general question of the extent to which the proposed bipartite cooperation model may be applied to different contexts. Finally, for the third and more preliminary piece of research I consider the propagation of errors in the New York garment industry supplier network, where in this case errors correspond to refund payments. Here I examine whether these errors appear to propagate through the network, and what mechanisms may enable of inhibit contagion.
References:
(1) S. Saavedra, F. Reed-Tsochas and B. Uzzi, “Asymmetric disassembly and robustness in declining networks”, Proceedings of the National Academy of Sciences of the USA, 105, 16466-16471 (2008).
(2) S. Saavedra, F. Reed-Tsochas and B. Uzzi, “A simple model of bipartite cooperation for ecological and organizational networks”, Nature, 457, 463-466 (2009).
Thursday, October 29, 12:00,
room 20.237.
Daniel Corsten (IE)
Mitigating the Deleterious Effects of Supplier Punishment - The Role of Information Exchange and Buyer Reputation
Abstract:
Tuesday, November 17, 12:00,
room 20.237.
Patrick Mair (WU Wirtschaftsuniversität Wien)
Gifi Methods for Optimal Scaling in R: The Package homals
Abstract:
Homogeneity analysis combines the idea of maximizing the correlations between vari-
ables of a multivariate data set with that of optimal scaling. In this article we present
methodological and practical issues of the R package homals which performs homogeneity
analysis and various extensions. By setting rank constraints nonlinear principal compo-
nent analysis can be performed. The variables can be partitioned into sets such that
homogeneity analysis is extended to nonlinear canonical correlation analysis or to predic-
tive models which emulate discriminant analysis and regression models. For each model
the scale level of the variables can be taken into account by setting level constraints. All
algorithms allow for missing values.
Friday, November 20, 12:00,
room 20.287.
Francis de Vericourt
Diagnostic Accuracy Under Congestion
Abstract:
In diagnostic services, agents typically need to weigh the benefit of running an additional test and improve the diagnosis accuracy against the cost of delaying the provision of service to others. Our paper analyzes how to dynamically manage this accuracy/congestion tradeoff. To that end, we study an elementary congested service facing an arriving stream of customers. The diagnostic process consists of a search problem in which the agent conducts a sequence of imperfect tests to
determine whether a customer is of a given type. Our analysis yields counter-intuitive insights into managing diagnostic services. First, we find that the maximum number of customers allowed in the system should initially increase with the number of performed tests. This result is in sharp contrast with the established literature on value/congestion tradeoffs, which consistently asserts that congestion levels should decrease with service times. In our diagnosis system, only after the agent has run enough tests without identifying the customer type should the maximum number of customers in the system decrease. Second, we find that the agent should sometimes diagnose the customer with the searched type, even when all tests are negative. This surprising result disappears when controlling for congestion, i.e. in a single diagnostic task. Finally, our numerical study shows that our counter-intuitive findings have a significant impact on the system performance.
Thursday, November 26, 12:00,
room 20.237.
Richard Steinberg (LSE)
Pricing of Media Service Provision
Abstract:
Thursday, December 3, 17:00,
room 40.047A.
Fabrizio Leisen (Universidad de Navarra)
Vectors of dependent Poisson Dirichlet processes
Abstract: The definition of vectors of dependent random
probability measures is a topic of interest in applications to
Bayesian statistics. They, indeed, define dependent nonparametric
prior distributions that are useful for modelling observables whose
values depend on covariates. In this work we propose a vector of
two-parameter Poisson-Dirichlet processes. It is well-known that each
component can be obtained by resorting to a change of measure of a
$\sigma$-stable process. Thus dependence is achieved by applying a
Lévy copula to the marginal intensities. In a two-sample problem, we
evaluate the corresponding partition probability function which turns
out to be partially exchangeable. Moreover, we evaluate predictive and
posterior distributions. This is a work in collaboration with Antonio
Lijoi (University of Pavia).
Thursday, December 10, 12:00,
room 20.237.
Catalina Stefanescu (LBS-ESMT)
Upgrades, Upsells and Pricing in Revenue Management
Abstract:
Capacity providers often experience a mismatch between supply and demand that can be partially alleviated while improving revenues by allowing for product upgrades. When prices are fixed and demands are independent, the problem is to decide which customer demands to upgrade to which products and when. We show that a fairness constraint can be imposed without loss of optimality under mild conditions. We also investigate a model that limits upgrades to the next higher quality product, and we provide necessary and sufficient conditions for its revenues to be as high as that of any less restricted upgrade model. Resellers of capacity also have an incentive to use upgrades as a mechanism to entice customers to higher quality products with higher commission margins. We show that this practice can be very profitable and that the profits can be much larger than direct commissions from sales would indicate. We then investigate the case where sellers have pricing flexibility and customer demand is driven by a choice model. We derive pricing formulas under the assumption that demand for products follows a multinomial logit model, and we develop an algorithm for finding a global optimal solution to the capacity constrained profit function. For this model we show that neither upgrades nor upsells improve profits when margins are homogenous and there is complete freedom in selecting prices. However, upgrades can improve revenues significantly when sensible business constraints on prices are imposed and when margins are heterogenous.
Friday, December 11, 12:00,
room 20.137.
Ery Arias-Castro (University of California, San Diego)
Detection of an Abnormal Cluster in a Network
Abstract: We consider the model problem of detecting whether or not in a given sensor network, there is a cluster of sensors which exhibit an ``unusual behavior''. Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses. Under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with positive mean and unit variance, while the rest are i.i.d. standard normal. The cluster is a subset of the nodes only known to satisfy some constraints, e.g. shape or size.
We also address surveillance settings where each sensor in the network transmits information over time. The resulting model is similar, now with a time series is attached to each node. We again observe the process over time and want to decide between the null, where all the variables are i.i.d. standard normal; and the alternative, where there is an emerging cluster of i.i.d. normal variables with positive mean and unit variance. The class of growth models we use to represent the emerging cluster is quite general, and includes cellular automata used in modelling epidemics.
In both settings, we study minimax detection rates for a variety of cluster classes and show that the scan statistic, by far the most popular method in practice, is near-optimal in a wide array of situations.
Joint work with Emmanuel Candes (Stanford) and Arnaud Durand (Université Paris XI)
Marathon runners' double feature special seminar!!
Thursday, March 4, 15:00,
room 20.233.
Bernard Bercu (Université Bordeaux 1)
Exponential inequalities for self-normalized martingales
Abstract:
We shall propose several exponential inequalities for self-normalized martingales similar to those recently established by De la Pena.
The keystone is the introduction of a new concept of random variables
heavy on left or right. Several statistical applications associated with
linear regressions, autoregressive and branching processes
will be also presented.
Fabrice Gamboa (IMT Université Paul Sabatier)
Random moments and random matrices models.
We will first recall some asymptotic results (mainly in large deviations) for measures that are solution of random moment problems. Further, these random measures will be interpreted as spectral measures supported by the eigenvalues of random matrices. Asymptotic behavior in large deviations of these random spectral measures will be discussed.
Friday, March 19, 15:30,
room 20.287.
Krzysztof Latuszynski (Warwick)
Making black boxes out of black boxes - the Bernoulli Factory problem
and its applications
Abstract:
Assume that a black box generating p-coins is available and 0< p< 1 is unknown.
Is it possible to use these p-coins and generate a min(1,2p)-coin?
Given a known function f, is it possible to obtain an f(p)-coin?
The problem, in a simplified form, originates from John von Neumann
and naturally arises in several problems in stochastic simulation.
I will present a reverse time martingale approach that offers a constructive solution.
This is joint work with Ioannis Kosmidis, Omiros Papaspiliopoulos,
Gareth O. Roberts and Dario Spano.
Friday, March 26, 12:00,
room 20.237.
J.H.L. Oud (Behavioural Science Institute, Radboud University Nijmegen, The Netherlands) First and second-order stochastic differential equation modeling as an alternative to the LGC and ALT model of panel data Abstract: In the structural equation modeling (SEM) literature, two models for the analysis of longitudinal data became very popular in the past: autoregressive (AR) cross-lagged model and latent growth curve (LGC) or latent trajectory (LT) model. Curran and Bollen (2001) and Bollen and Curran (2004), however, argued that, theoretically, there are many instances when both the processes described by the AR model and the processes described by the LT model are plausible. They proposed the autoregressive latent trajectory (ALT) model, which captures features of both. The discrete-time approach in the ALT model has been criticized by Delsing and Oud (2008), who proposed a continuous time version of the ALT model, using stochastic differential equations, called “continuous time autoregressive latent trajectory” (CALT) model. Next, serious problems related to the linear components in the LGC, ALT and CALT models are dealt with. As an alternative for the linear component the first-order derivative in a second-order stochastic differential equation model is proposed. This is applied to Marital Satisfaction data, collected in four consecutive years (2002-2005). It is pointed out that the first-order derivative as explanatory variable has none of the problems associated with the linear component.
Curran, P.J. and K.A. Bollen (2001), The best of both worlds: Combining autoregressive and latent curve models. In A. Sayer and L. Collins (Eds.), New methods for the analysis of change (pp. 107-135). Washington, DC: American Psychological Association.
Bollen, K.A. and P.J. Curran (2004), Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.
Delsing, M.J.M.H., & Oud, J.H.L. (2008). Analyzing reciprocal relationships by means of the continuous-time autoregressive latent trajectory model. Statistica Neerlandica, 62, 58- 82.
Friday, April 9, 12:00,
room 20.237.
Jitka Bartosova (University of Economics, Prague)
and Nick Longford (SNTL and UPF)
A research agenda for studying poverty in Europe using EU-SILC
Abstract: The European Union Statistics on Income and Living Conditions (EU-SILC)
is the principal source of data about income of households in European
countries. It has an annual cross-sectional and a rotating panel component
that started in 2004/05. The seminar will describe a general agenda for
exploring various alternative definitions of poverty and using them to
compare various aspects of poverty in the countries and their regions;
these aspects include the poverty gap, the functioning of the social
transfer system, persistence of poverty over time and concentration of the
poverty in subpopulations. The role of sensitivity analysis will be
highlighted. Some preliminary results will be presented.
Thursday, April 29, 16:00,
room 23.S05.
Rein Taagepera (University of California-Irvine and University of Tartu-Estonia)
Interconnected Knowledge Requires Symmetric Regression
Abstract:
Physics uses algebraic equations, while OLS regression equations are directional and intransitive. Symmetric regression does yield algebraic equations. This is what social scientists should use, to advance toward interconnected knowledge.
Longer Abstract:
Physics would be unthinkable if it did not use algebraic equations, oblivious to causal direction. These equations are reversible, so that F=am also means m=F/a and a=F/m, and transitive, so that z calculated from y, itself calculated from x is the same as z calculated from x directly. As a result, interlocking relationships among variables are possible.
This is not so with OLS, so widely used in social sciences. Regressing y on x yields a line (y<--a+bx) different from regressing x on y (x<--a'+b'y). Writing them as y=a+bx and x=a'+b'x, as if they were reversible, confuses them with algebraic equations. OLS regression is not transitive either:
z<--y<--x and z<--x do not yield the same results. Thus, interlocking relationships are not possible.
Scale-independent symmetric linear regression (with slope dy/dx=SIGMAy^2/SIGMAx^2) does yield algebraic equations, reversible and transitive. It minimizes the rectangular areas formed by vertical and horizontal distances from data points to line. R-squared reflects lack of scatter around this symmetric regression line, not around either OLS slope. This is the linear regression social scientists should use, if they wish ever to advance toward interconnected knowledge. However, both OLS and symmetric regressions are overly sensitive to outliers.
This presentation expands on the corresponding chapter in Taagepera, Making Social Sciences More Scientific (2008, Oxford UP).
Friday, May 7, 12:00,
room 20.287.
Yohji Akama (Tokohu University, Japan)
Consistency of eigenvalues for
principal component analysis.
Abstract: When the number n of data and the dimension d of data tend
simultaneously to infinity, the eigenvalues and eigenvectors of the data
covariance matrix S do not necessarily converge to those of the covariance
matrix, according to Bai and Johnstone. By Vapnik--Chervonenkis theory
and measure concentration inequalities, we provide a sufficient
condition on n and d for the sum of the first eigenvalues of S to be
consistent.
Thursday, May 13, 12:00,
room 40.047C.
Sorana Froda (Université du Québec à Montréal)
Statistical inference for the parameters of planar ODEs
Abstract:
Many phenomena in nature and society display oscillatory behaviour,
and simple ODE (ordinary differential equations) models can explain
it. Such systems do depend on parameters, which are typically unknown.
Moreover, the solutions cannot be expressed explicitly in terms of
these parameters, which, nonetheless, determine the ODE's properties.
We propose simple stochastic models which allow to estimate these
parameters, and give also some tests. We point to possible extensions
and certain limitations of our procedures.
Friday, May 21, 12:00,
room 20.137.
José R. León (Universidad Central de Venezuela)
Anisotropy rest for Gaussian fields
Abstract.