Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Performance analysis of near-far resistant CDMA detectors-influence of system parameter estimation errors

Little has been reported on the performance of near-far resistant CDMA detectors in the presence of system parameter estimation errors (SPEEs). Starting with the general mathematical model of matched filters, the paper examines the effects of three classes of SPEEs, i.e., time-delay, carrier phase, and carrier frequency errors, on the performance (BER) of an emerging type of near-far resistant coherent DS/SSMA detector, i.e., the linear decorrelating detector. For comparison, the corresponding results for the conventional detector are also presented. It is shown that the linear decorrelating detector can still maintain a considerable performance advantage over the conventional detector even when some SPEEs exist.

A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

A simple, coherent framework for partitioning uncertainty in climate predictions

A simple and coherent framework for partitioning uncertainty in multi-model climate ensembles is presented. The analysis of variance (ANOVA) is used to decompose a measure of total variation additively into scenario uncertainty, model uncertainty and internal variability. This approach requires fewer assumptions than existing methods and can be easily used to quantify uncertainty related to model-scenario interaction - the contribution to model uncertainty arising from the variation across scenarios of model deviations from the ensemble mean. Uncertainty in global mean surface air temperature is quantified as a function of lead time for a subset of the Coupled Model Intercomparison Project phase 3 ensemble and results largely agree with those published by other authors: scenario uncertainty dominates beyond 2050 and internal variability remains approximately constant over the 21st century. Both elements of model uncertainty, due to scenario-independent and scenario-dependent deviations from the ensemble mean, are found to increase with time. Estimates of model deviations that arise as by-products of the framework reveal significant differences between models that could lead to a deeper understanding of the sources of uncertainty in multi-model ensembles. For example, three models are shown diverging pattern over the 21st century, while another model exhibits an unusually large variation among its scenario-dependent deviations.

Uncertainty in the relationship between climate forcing and hydrological response in UK catchments

This paper assesses the relationship between amount of climate forcing – as indexed by global mean temperature change – and hydrological response in a sample of UK catchments. It constructs climate scenarios representing different changes in global mean temperature from an ensemble of 21 climate models assessed in the IPCC AR4. The results show a considerable range in impact between the 21 climate models, with – for example - change in summer runoff at a 2oC increase in global mean temperature varying between -40% and +20%. There is evidence of clustering in the results, particularly in projected changes in summer runoff and indicators of low flows, implying that the ensemble mean is not an appropriate generalised indicator of impact, and that the standard deviation of responses does not adequately characterise uncertainty. The uncertainty in hydrological impact is therefore best characterised by considering the shape of the distribution of responses across multiple climate scenarios. For some climate model patterns, and some catchments, there is also evidence that linear climate change forcings produce non-linear hydrological impacts. For most variables and catchments, the effects of climate change are apparent above the effects of natural multi-decadal variability with an increase in global mean temperature above 1oC, but there are differences between catchments. Based on the scenarios represented in the ensemble, the effect of climate change in northern upland catchments will be seen soonest in indicators of high flows, but in southern catchments effects will be apparent soonest in measures of summer and low flows. The uncertainty in response between different climate model patterns is considerably greater than the range due to uncertainty in hydrological model parameterisation.

Uncertainty in climate change impacts on basin-scale freshwater resources – preface to the special issue: the QUEST-GSI methodology and synthesis of results

This paper presents a preface to this Special Issue on the results of the QUEST-GSI (Global Scale Impacts) project on climate change impacts on catchment-scale water resources. A detailed description of the unified methodology, subsequently used in all studies in this issue, is provided. The project method involved running simulations of catchment-scale hydrology using a unified set of past and future climate scenarios, to enable a consistent analysis of the climate impacts around the globe. These scenarios include "policy-relevant" prescribed warming scenarios. This is followed by a synthesis of the key findings. Overall, the studies indicate that in most basins the models project substantial changes to river flow, beyond that observed in the historical record, but that in many cases there is considerable uncertainty in the magnitude and sign of the projected changes. The implications of this for adaptation activities are discussed.

Measuring the response of macroeconomic uncertainty to shocks

Recent research documents the importance of uncertainty in determining macroeconomic outcomes, but little is known about the transmission of uncertainty across such outcomes. This paper examines the response of uncertainty about inflation and output growth to shocks documenting statistically significant size and sign bias and spillover effects. Uncertainty about inflation is a determinant of output uncertainty, whereas higher growth volatility tends to raise inflation volatility. Both inflation and growth volatility respond asymmetrically to positive and negative shocks. Negative growth and inflation shocks lead to higher and more persistent uncertainty than shocks of equal magnitude but opposite sign.

Decision theory and real estate development: a note on uncertainty

Real estate development appraisal is a quantification of future expectations. The appraisal model relies upon the valuer/developer having an understanding of the future in terms of the future marketability of the completed development and the future cost of development. In some cases the developer has some degree of control over the possible variation in the variables, as with the cost of construction through the choice of specification. However, other variables, such as the sale price of the final product, are totally dependent upon the vagaries of the market at the completion date. To try to address the risk of a different outcome to the one expected (modelled) the developer will often carry out a sensitivity analysis on the development. However, traditional sensitivity analysis has generally only looked at the best and worst scenarios and has focused on the anticipated or expected outcomes. This does not take into account uncertainty and the range of outcomes that can happen. A fuller analysis should include examination of the uncertainties in each of the components of the appraisal and account for the appropriate distributions of the variables. Similarly, as many of the variables in the model are not independent, the variables need to be correlated. This requires a standardised approach and we suggest that the use of a generic forecasting software package, in this case Crystal Ball, allows the analyst to work with an existing development appraisal model set up in Excel (or other spreadsheet) and to work with a predetermined set of probability distributions. Without a full knowledge of risk, developers are unable to determine the anticipated level of return that should be sought to compensate for the risk. This model allows the user a better understanding of the possible outcomes for the development. Ultimately the final decision will be made relative to current expectations and current business constraints, but by assessing the upside and downside risks more appropriately, the decision maker should be better placed to make a more informed and “better”.

The uncertainty of valuation

Valuation is often said to be “an art not a science” but this relates to the techniques employed to calculate value not to the underlying concept itself. Valuation is the process of estimating price in the market place. Yet, such an estimation will be affected by uncertainties. Uncertainty in the comparable information available; uncertainty in the current and future market conditions and uncertainty in the specific inputs for the subject property. These input uncertainties will translate into an uncertainty with the output figure, the valuation. The degree of the uncertainties will vary according to the level of market activity; the more active a market, the more credence will be given to the input information. In the UK at the moment the Royal Institution of Chartered Surveyors (RICS) is considering ways in which the uncertainty of the output figure, the valuation, can be conveyed to the use of the valuation, but as yet no definitive view has been taken apart from a single Guidance Note (GN5, RICS 2003) stressing the importance of recognising uncertainty in valuation but not proffering any particular solution. One of the major problems is that Valuation models (in the UK) are based upon comparable information and rely upon single inputs. They are not probability based, yet uncertainty is probability driven. In this paper, we discuss the issues underlying uncertainty in valuations and suggest a probability-based model (using Crystal Ball) to address the shortcomings of the current model.

Uncertainty and feasibility studies: an Italian case study

Uncertainty affects all aspects of the property market but one area where the impact of uncertainty is particularly significant is within feasibility analyses. Any development is impacted by differences between market conditions at the conception of the project and the market realities at the time of completion. The feasibility study needs to address the possible outcomes based on an understanding of the current market. This requires the appraiser to forecast the most likely outcome relating to the sale price of the completed development, the construction costs and the timing of both. It also requires the appraiser to understand the impact of finance on the project. All these issues are time sensitive and analysis needs to be undertaken to show the impact of time to the viability of the project. The future is uncertain and a full feasibility analysis should be able to model the upside and downside risk pertaining to a range of possible outcomes. Feasibility studies are extensively used in Italy to determine land value but they tend to be single point analysis based upon a single set of “likely” inputs. In this paper we look at the practical impact of uncertainty in variables using a simulation model (Crystal Ball ©) with an actual case study of an urban redevelopment plan for an Italian Municipality. This allows the appraiser to address the issues of uncertainty involved and thus provide the decision maker with a better understanding of the risk of development. This technique is then refined using a “two-dimensional technique” to distinguish between “uncertainty” and “variability” and thus create a more robust model.