Dynamic dependence networks: Financial time series forecasting and portfolio decisions (with discussion)

We discuss Bayesian forecasting of increasingly high-dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state-space models characterizing sparse patterns of dependence among multiple time series extend existing multivariate volatility models to enable scaling to higher numbers of individual time series. The theory of these "dynamic dependence network" models shows how the individual series can be "decoupled" for sequential analysis, and then "recoupled" for applied forecasting and decision analysis. Decoupling allows fast, efficient analysis of each of the series in individual univariate models that are linked-- for later recoupling-- through a theoretical multivariate volatility structure defined by a sparse underlying graphical model. Computational advances are especially significant in connection with model uncertainty about the sparsity patterns among series that define this graphical model; Bayesian model averaging using discounting of historical information builds substantially on this computational advance. An extensive, detailed case study showcases the use of these models, and the improvements in forecasting and financial portfolio investment decisions that are achievable. Using a long series of daily international currency, stock indices and commodity prices, the case study includes evaluations of multi-day forecasts and Bayesian portfolio analysis with a variety of practical utility functions, as well as comparisons against commodity trading advisor benchmarks.Comment: 31 pages, 9 figures, 3 table

Lower and Upper Conditioning in Quantum Bayesian Theory

Updating a probability distribution in the light of new evidence is a very basic operation in Bayesian probability theory. It is also known as state revision or simply as conditioning. This paper recalls how locally updating a joint state can equivalently be described via inference using the channel extracted from the state (via disintegration). This paper also investigates the quantum analogues of conditioning, and in particular the analogues of this equivalence between updating a joint state and inference. The main finding is that in order to obtain a similar equivalence, we have to distinguish two forms of quantum conditioning, which we call lower and upper conditioning. They are known from the literature, but the common framework in which we describe them and the equivalence result are new.Comment: In Proceedings QPL 2018, arXiv:1901.0947

Inference of Temporally Varying Bayesian Networks

When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data. Here we present a method that allows us to infer regulatory network structures that may vary between time points, utilising a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states we have applied the Hierarchical Dirichlet Process Hideen Markov Model, a nonparametric extension of the traditional Hidden Markov Model, that does not require us to fix the number of hidden states in advance. We apply our method to exisiting microarray expression data as well as demonstrating is efficacy on simulated test data

Potentials and Limits of Bayesian Networks to Deal with Uncertainty in the Assessment of Climate Change Adaptation Policies

Bayesian networks (BNs) have been increasingly applied to support management and decision-making processes under conditions of environmental variability and uncertainty, providing logical and holistic reasoning in complex systems since they succinctly and effectively translate causal assertions between variables into patterns of probabilistic dependence. Through a theoretical assessment of the features and the statistical rationale of BNs, and a review of specific applications to ecological modelling, natural resource management, and climate change policy issues, the present paper analyses the effectiveness of the BN model as a synthesis framework, which would allow the user to manage the uncertainty characterising the definition and implementation of climate change adaptation policies. The review will let emerge the potentials of the model to characterise, incorporate and communicate the uncertainty, with the aim to provide an efficient support to an informed and transparent decision making process. The possible drawbacks arising from the implementation of BNs are also analysed, providing potential solutions to overcome them.Adaptation to Climate Change, Bayesian Network, Uncertainty

Cutset Sampling for Bayesian Networks

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks