Integrated building performance simulation

This paper justifies the need for an integrated approach to building performance assessment and provides examples of the technical appraisals that may then be enabled. The contention is that the use of design tools which focus on a single domain will result in sub-optimum design solutions in terms of indoor air quality, occupant comfort, energy use and environmental impact

Large deviation asymptotics and control variates for simulating large functions

Consider the normalized partial sums of a real-valued function $F$ of a Markov chain, $$\phi_n:=n^{-1}\sum_{k=0}^{n-1}F(\Phi(k)),\qquad n\ge1.$$ The chain $\{\Phi(k):k\ge0\}$ takes values in a general state space $\mathsf {X}$, with transition kernel $P$, and it is assumed that the Lyapunov drift condition holds: $PV\le V-W+b\mathbb{I}_C$ where $V:\mathsf {X}\to(0,\infty)$, $W:\mathsf {X}\to[1,\infty)$, the set $C$ is small and $W$ dominates $F$. Under these assumptions, the following conclusions are obtained: 1. It is known that this drift condition is equivalent to the existence of a unique invariant distribution $\pi$ satisfying $\pi(W)<\infty$, and the law of large numbers holds for any function $F$ dominated by $W$: $$\phi_n\to\phi:=\pi(F),\qquad{a.s.}, n\to\infty.$$ 2. The lower error probability defined by $\mathsf {P}\{\phi_n\le c\}$, for $c<\phi$, $n\ge1$, satisfies a large deviation limit theorem when the function $F$ satisfies a monotonicity condition. Under additional minor conditions an exact large deviations expansion is obtained. 3. If $W$ is near-monotone, then control-variates are constructed based on the Lyapunov function $V$, providing a pair of estimators that together satisfy nontrivial large asymptotics for the lower and upper error probabilities. In an application to simulation of queues it is shown that exact large deviation asymptotics are possible even when the estimator does not satisfy a central limit theorem.Comment: Published at http://dx.doi.org/10.1214/105051605000000737 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A data driven equivariant approach to constrained Gaussian mixture modeling

Maximum likelihood estimation of Gaussian mixture models with different class-specific covariance matrices is known to be problematic. This is due to the unboundedness of the likelihood, together with the presence of spurious maximizers. Existing methods to bypass this obstacle are based on the fact that unboundedness is avoided if the eigenvalues of the covariance matrices are bounded away from zero. This can be done imposing some constraints on the covariance matrices, i.e. by incorporating a priori information on the covariance structure of the mixture components. The present work introduces a constrained equivariant approach, where the class conditional covariance matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of the matrix Psi, when a priori information is not available, and the optimal amount of shrinkage are investigated. The effectiveness of the proposal is evaluated on the basis of a simulation study and an empirical example

Variational Bayes with Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many interesting situations such as in state space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This paper extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions.Comment: 40 pages, 6 figure

Static Hedging of Multivariate Derivatives by Simulation

We propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The method uses simulated paths to estimate the weights of the hedging portfolio and is related to Monte Carlo control variates techniques. We report numerical results showing the performance of this static hedging procedure on bivariate options on the maximum of two assets and on 2- and 7-dimensional portfolio options. It is shown that, in the presence of transaction costs, Value at Risk and Expected Shortfall of the dynamically hedged positions can be higher than the ones obtained by a static hedge.Monte Carlo methods, option pricing, static and dynamic hedging

A Re-examination of the Link between Real Exchange Rates and Real Interest Rate Differentials

The real exchange rate - real interest rate (RERI) relationship is central to most open economy macroeconomic models. However, empirical support for the relationship, especially when cointegrationbased methods are used, is rather weak. In this paper we reinvestigate the RERI relationship using bilateral real exchange rate data spanning the period 1978 to 1997. We first clarify the logic of applying cointegration methods to the RERI and propose an alternative way of testing the relationship. We demonstrate that the failure of earlier analyses to detect a stationary real interest rate is largely due to the low power of the tests employed.real exchange rates, real interest rates, cointegration

Industrial development, agricultural growth, urbanization and environmental Kuznets curve in Pakistan

The debate of environmental issues and their analysis is of vital interest for economic policies. Institutions are engaged in identifying and estimating the extent of environmental impact of determinants controllable via policy measures. Annual data from the on Carbon Dioxide emission, economic growth, consumption of energy, openness for foreign trade, urbanization, industrial growth and agriculture growth on Pakistan is used for 1971 to 2007. Augmented Vector Autoregression technique and cointegration analysis is implemented to test Granger causality. Gross domestic product significantly Granger causes emission of Carbon Dioxide and energy consumption. On the other hand emissions of CO2 affect economic growth, agriculture and industrial growth in the long run. It is also evident that energy consumption unidirectional Granger causes emission of Carbon Dioxide. Industrialization and urbanization bidirectional Granger causes each other. The results indicate the more careful industrial and energy policies to reduce emissions and control global warming.Pakistan, Carbon Dioxide emission, Environment, Energy Consumption, Economic Growth, Foreign Trade