Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Turbulent passive scalar field of a small prandtl number

The statistical-mechanics theory of the passive scalar field convected by turbulence, developed in an earlier paper [Phys. Fluids 28, 1299 (1985)], is extended to the case of a small molecular Prandtl number. The set of governing integral equations is solved by the equation-error method. The resultant scalar-variance spectrum for the inertial range is F(k)~x−5/3/[1+1.21x1.67(1+0.353x2.32)], where x is the wavenumber scaled by Corrsin's dissipation wavenumber. This result reduces to the − (5)/(3) law in the inertial-convective range. It also approximately reduces to the − (17)/(3) law in the inertial-diffusive range, but the proportionality constant differs from Batchelor's by a factor of 3.6.

A passive scalar field convected by turbulence

Classical statistical mechanics is applied to the study of a passive scalar field convected by isotropic turbulence. A complete set of independent real parameters and dynamic equations are worked out to describe the dynamic state of the passive scalar field. The corresponding Liouville equation is solved by a perturbation method based upon a Langevin–Fokker–Planck model. The closure problem is treated by a variational approach reported in earlier papers. Two integral equations are obtained for two unknown functions: the scalar variance spectrum F(k) and the effective damping coefficient (k). The appearance of the energy spectrum of the velocity field in the two integral equations represents the coupling of the scalar field with the velocity field. As an application of the theory, the two integral equations are solved to derive the inertial-convective-range spectrum, obtaining F(k)=0.61 −1/3 k−5/3. Here is the dissipation rate of the scalar variance and is the dissipation rate of the energy of the velocity field. This theoretical value of the scalar Kolmogorov constant, 0.61, is in good agreement with experiments.

Optimal Correction for Guessing in Multiple-Choice Tests

Building on Item Response Theory we introduce students’ optimal behavior in multiple-choice tests. Our simulations indicate that the optimal penalty is relatively high, because although correction for guessing discriminates against risk-averse subjects, this effect is small compared with the measurement error that the penalty prevents. This result obtains when knowledge is binary or partial, under different normalizations of the score, when risk aversion is related to knowledge and when there is a pass-fail break point. We also find that the mean degree of difficulty should be close to the mean level of knowledge and that the variance of difficulty should be high.

The Relationship between Risk and Expected Return in Europe

Revised: 2006-07

Habilidades sociales y contextos de la conducta social

[Es] Las habilidades sociales, o habilidades interpersonales, han sido objeto de creciente interés durante los últimos años en psicología social, clínica y educativa; y, sin embargo, tanto su evaluación como la intervención psicológica para su mejora se topan con una desconcertante proliferación de clasificaciones o categorías divergentes de las mismas. En este trabajo, y como resultado de sucesivos análisis factoriales, se proponen cinco grandes categorías de habilidades sociales (Interacción con personas desconocidas en situaciones de consumo, Interacción con personas que atraen, Interacción con amigos y compañeros, Interacción con familiares, y Hacer y rechazar peticiones a los amigos/as) que responden a distintos contextos de interacción social. Las cinco escalas, correspondientes a tales categorías, de un nuevo instrumento de medida, el Cuestionario de Dificultades Interpersonales (CDI), con alta consistencia interna (·= 0,896), explican el 47,47% de la varianza total. Los análisis correlacionales entre el CDI y el Test de Autoverbalizaciones en la Interacción Social (SISST) de Glass, Merluzzi, Biever y Larsen (1982) revelan diferencias cognitivas significativas entre los sujetos de alta y baja habilidad social, dándose una mayor frecuencia de autoverbalizaciones positivas y una menor frecuencia de autoverbalizaciones negativas en los sujetos de alta habilidad social que en los sujetos de baja habilidad social.

Efectos tamaño y sector sobre la rentabilidad, endeudamiento y coste de la deuda de las empresas familiares riojanas

Ponencia presentada y defendida en las XIV jornadas Hispano Lusas de Gestión Científica celebradas en Azores en febrero de 2004.

Use of aerial survey and aerophotogrammetry methods in monitoring manatee populations

We evaluated the use of strip-transect survey methods for manatees through a series of replicate aerial surveys in the Banana River, Brevard County, Florida, during summer 1993 and summer 1994. Transect methods sample a representative portion of the total study area, thus allowing for statistical extrapolation to the total area. Other advantages of transect methods are less flight time and less cost than total coverage, ease of navigation, and reduced likelihood of double-counting. Our objectives were: (1) to identify visibility biases associated with the transect survey method and to adjust the counts accordingly; (2) to derive a population estimate with known variance for the Banana River during summer; and (3) to evaluate the potential value of this survey method for monitoring trends in manatee population size over time. (51 page document)

Los dominios social y personal del autoconcepto

[Es] El estudio del autoconcepto continúa siendo uno de los grandes retos de la investigación psicológica. Se trata de un campo de investigación muy amplio en el que tanto la dimensión física como la académica han sido objeto de numerosas investigaciones; por el contrario son pocas las investigaciones llevadas a cabo tanto sobre el autoconcepto social como sobre el autoconcepto personal. En este trabajo se informa de dos estudios llevados a cabo con el fin de verificar si los análisis factoriales confirman una estructura multidimensional de tres componentes en el caso del social (la responsabilidad social, la aceptación social y la competencia social) y de cuatro componentes en la del personal: la autorrealización, la honradez, la autonomía, y el ajuste emocional. Los resultados obtenidos a partir de la aplicación de dos cuestionarios elaborados específicamente para medir ambos dominios (APE y AUSO) confirman en buena medida esta estructura; los factores identificados explican un 52,56% y un 41,43%, respectivamente, de la varianza. Por otro lado, los índices de consistencia interna son aceptables en ambos casos: alpha 0.85 en el APE y alpha 0.76 en el AUSO. Se proponen algunos cambios a incorporar en la versión definitiva de ambos cuestionarios.

相对论力学中普遍定律的实用判别法和协变集的实用构造法

给出相对论力学中普遍定律的衫和判别法和协变集的衫和构造法，还给出实现非普遍定律的“可导出性”的一种实用方法。

Data Revisions in the Estimation of DSGE Models

Revisions of US macroeconomic data are not white-noise. They are persistent, correlated with real-time data, and with high variability (around 80% of volatility observed in US real-time data). Their business cycle effects are examined in an estimated DSGE model extended with both real-time and final data. After implementing a Bayesian estimation approach, the role of both habit formation and price indexation fall significantly in the extended model. The results show how revision shocks of both output and inflation are expansionary because they occur when real-time published data are too low and the Fed reacts by cutting interest rates. Consumption revisions, by contrast, are countercyclical as consumption habits mirror the observed reduction in real-time consumption. In turn, revisions of the three variables explain 9.3% of changes of output in its long-run variance decomposition.

Analysis of volatility transmissions in integrated and interconnected markets: The case of the Iberian and French markets

This paper models the mean and volatility spillovers of prices within the integrated Iberian and the interconnected Spanish and French electricity markets. Using the constant (CCC) and dynamic conditional correlation (DCC) bivariate models with three different specifications of the univariate variance processes, we study the extent to which increasing interconnection and harmonization in regulation have favoured price convergence. The data consist of daily prices calculated as the arithmetic mean of the hourly prices over a span from July 1st 2007 until February 29th 2012. The DCC model in which the variances of the univariate processes are specified with a VARMA(1,1) fits the data best for the integrated MIBEL whereas a CCC model with a GARCH(1,1) specification for the univariate variance processes is selected to model the price series in Spain and France. Results show that there are significant mean and volatility spillovers in the MIBEL, indicating strong interdependence between the two markets, while there is a weaker evidence of integration between the Spanish and French markets. We provide new evidence that the EU target of achieving a single electricity market largely depends on increasing trade between countries and homogeneous rules of market functioning.

Assessment of cobia, Rachycentron canadum, in the waters of the U.S. Gulf of Mexico

This assessment applies to cobia (Rachycentron canadum) located in the territorial waters of the U.S. Gulf of Mexico. Separation of the Gulf of Mexico and Atlantic Ocean is defined by the seaward extension of the Dade/Monroe county line in south Florida. Mixing of fish between the Atlantic and Gulf of Mexico occurs in the Florida Keys during winter months. Cobia annually migrate north in early spring in the Gulf to spawning grounds in the northern Gulf of Mexico, returning to the Florida Keys by winter. Catches of cobia in the Gulf of Mexico are dominated by recreational landings, accounting for nearly 90% of the total. Since 1980, the landings of cobia in the recreational fishery have remained fairly stable at around 400-600 mt with a slight peak of 1,014 mt in 1997. The recreational fishery was estimated to have landed 471 mt in 2000. The landings from the commercial fishery have shown a steady increase from 45 mt in 1980 to a peak of 120 mt in 1994, followed by a decline to 62 mt in 2000. The previous assessment of cobia occurred in 1996 using a virtual population analysis (VPA) model. For this analysis a surplus-production model (ASPIC) and a forward-projecting, age-structured population model programmed in the AD Model Builder (ADMB) software were applied to cobia data from the Gulf of Mexico. The primary data consisted of four catch-per-unit-effort (CPUE) indices derived from the Marine Recreational Fisheries Statistics Survey (MRFSS) (1981-1999), Southeast region headboat survey (1986-1999), Texas creel survey (1983-1999), and shrimp bycatch estimates (1980-1999). Length samples were available from the commercial (1983-2000) and recreational (1981-2000) fisheries. The ASPIC model applied to the cobia data provided unsatisfactory results. The ADMB model fit described the observed length composition data and fishery landings fairly well based on graphical examination of model residuals. The CPUE indices indicated some disagreement for various years, but the model fit an overall increasing trend from 1992-1997 for the MRFSS, headboat, and Texas creel indices. The shrimp bycatch CPUE was treated as a recruitment index in the model. The fit to these data followed an upward trend in recruitment from 1988-1997, but did not fit the 1994-1997 data points very well. This was likely the result of conflicting information from other data sources. Natural mortality (M) for cobia is unknown. As a result, a range of values for M from 0.2-0.4, based on longevity and growth parameters, were selected for use in the age-structured model. The choice of natural mortality appears to greatly influence the perceived status of the population. Population status as measured by spawning stock biomass in the last year relative to the value at maximum sustainable yield (SSB2000/SSBMSY), spawning stock biomass in the last year relative to virgin spawning stock biomass (SSB2000/S0), and static spawning stock biomass per recruit (SSBR) all indicate the population is either depleted, near MSY, or well above MSY depending on the choice of M. The variance estimates for these benchmarks are very large and in most cases ranges from depleted to very healthy status. The only statement that can be made with any degree of certainty about cobia in the Gulf of Mexico is that the population has increased since the 1980s. (PDF contains 61 pages)

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.