Bayesian recursive parameter estimation for hydrologic models

The uncertainty in a given hydrologic prediction is the compound effect of the parameter, data, and structural uncertainties associated with the underlying model. In general, therefore, the confidence in a hydrologic prediction can be improved by reducing the uncertainty associated with the parameter estimates. However, the classical approach to doing this via model calibration typically requires that considerable amounts of data be collected and assimilated before the model can be used. This limitation becomes immediately apparent when hydrologic predictions must be generated for a previously ungauged watershed that has only recently been instrumented. This paper presents the framework for a Bayesian recursive estimation approach to hydrologic prediction that can be used for simultaneous parameter estimation and prediction in an operational setting. The prediction is described in terms of the probabilities associated with different output values. The uncertainty associated with the parameter estimates is updated (reduced) recursively, resulting in smaller prediction uncertainties as measurement data are successively assimilated. The effectiveness and efficiency of the method are illustrated in the context of two models: a simple unit hydrograph model and the more complex Sacramento soil moisture accounting model, using data from the Leaf River basin in Mississippi

Improving forecast accuracy by combining recursive and rolling forecasts

This paper presents analytical, Monte Carlo, and empirical evidence on the effectiveness of combining recursive and rolling forecasts when linear predictive models are subject to structural change. We first provide a characterization of the bias-variance tradeoff faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two. From that, we derive pointwise optimal, time-varying and data-dependent observation windows and combining weights designed to minimize mean square forecast error. We then proceed to consider other methods of forecast combination, including Bayesian methods that shrink the rolling forecast to the recursive and Bayesian model averaging. Monte Carlo experiments and several empirical examples indicate that although the recursive scheme is often difficult to beat, when gains can be obtained, some form of shrinkage can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width.Forecasting

PReMo : An Analyzer for P robabilistic Re cursive Mo dels

This paper describes PReMo, a tool for analyzing Recursive Markov Chains, and their controlled/game extensions: (1-exit) Recursive Markov Decision Processes and Recursive Simple Stochastic Games

Multiscale likelihood analysis and complexity penalized estimation

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy to those underlying a standard multiresolution analysis for wavelets, and hence can be viewed as a multiresolution analysis for likelihoods. We then consider the use of these factorizations in the task of nonparametric, complexity penalized likelihood estimation. We study the risk properties of certain thresholding and partitioning estimators, and demonstrate their adaptivity and near-optimality, in a minimax sense over a broad range of function spaces, based on squared Hellinger distance as a loss function. In particular, our results provide an illustration of how properties of classical wavelet-based estimators can be obtained in a single, unified framework that includes models for continuous, count and categorical data types

Escaping Nash inflation

Mean dynamics govern convergence to rational expectations equilibria of self-referential systems under least squares learning. We highlight escape dynamics that propel away from a rational expectations equilibrium under fixed-gain recursive learning schemes. These learning schemes discount past observations. In a model with a unique self-confirming equilibrium, we show that the destination of the escape dynamics is an outcome associated with government discovery of too strong a version of the natural rate hypothesis. That destination is not sustainable as a self-confirming equilibrium but is visited recurrently. The escape route dynamics cause recurrent outcomes close to the Ramsey (commitment) inflation rate in a model with an adaptive government. JEL Classification: E3, E52, E58

Aversion to ambiguity and model misspecification in dynamic stochastic environments

Preferences that accommodate aversion to subjective uncertainty and its potential misspecification in dynamic settings are a valuable tool of analysis in many disciplines. By generalizing previous analyses, we propose a tractable approach to incorporating broadly conceived responses to uncertainty. We illustrate our approach on some stylized stochastic environments. By design, these discrete time environments have revealing continuous time limits. Drawing on these illustrations, we construct recursive representations of intertemporal preferences that allow for penalized and smooth ambiguity aversion to subjective uncertainty. These recursive representations imply continuous time limiting Hamilton–Jacobi–Bellman equations for solving control problems in the presence of uncertainty.Published versio

An empirical evaluation of four variants of a universal species-area relationship

The Maximum Entropy Theory of Ecology (METE) predicts a universal species-area relationship (SAR) that can be fully characterized using only the total abundance (N) and species richness (S) at a single spatial scale. This theory has shown promise for characterizing scale dependence in the SAR. However, there are currently four different approaches to applying METE to predict the SAR and it is unclear which approach should be used due to a lack of empirical evaluation. Specifically, METE can be applied recursively or a non-recursively and can use either a theoretical or observed species-abundance distribution (SAD). We compared the four different combinations of approaches using empirical data from 16 datasets containing over 1000 species and 300,000 individual trees and herbs. In general, METE accurately downscaled the SAR (R^2> 0.94), but the recursive approach consistently under-predicted richness, and METEs accuracy did not depend strongly on using the observed or predicted SAD. This suggests that best approach to scaling diversity using METE is to use a combination of non-recursive scaling and the theoretical abundance distribution, which allows predictions to be made across a broad range of spatial scales with only knowledge of the species richness and total abundance at a single scale.Comment: main text: 20 pages, 2 tables, 3 figure