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Michael Evans

Publications and source records attributed to Michael Evans.

At least 37 records · Page 2Linked to original sources
arXiv2020

Scheduling of energy storage

The increasing reliance on renewable energy generation means that storage may well play a much greater role in the balancing of future electricity systems. We show how heterogeneous stores, differing in capacity and rate constraints, may be optimally, or nearly optimally, scheduled to assist in such balancing, with the aim of minimising the total imbalance (unserved energy) over any given period of time. It further turns out that in many cases the optimal policies are such that the optimal decision at each point in time is independent of the future evolution of the supply-demand balance in the system, so that these policies remain optimal in a stochastic environment.

math.OC↗
arXiv2020

Detecting conflicting summary statistics in likelihood-free inference

Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary statistic before performing Bayesian inference, and the choice of this statistic is often difficult. The summary statistic should be low-dimensional for computational reasons, while retaining as much information as possible about the parameter. Using a recent idea from the interpretable machine learning literature, we develop some regression-based diagnostic methods which are useful for detecting when different parts of a summary statistic vector contain conflicting information about the model parameters. Conflicts of this kind complicate summary statistic choice, and detecting them can be insightful about model deficiencies and guide model improvement. The diagnostic methods developed are based on regression approaches to likelihood-free inference, in which the regression model estimates the posterior density using summary statistics as features. Deletion and imputation of part of the summary statistic vector within the regression model can remove conflicts and approximate posterior distributions for summary statistic subsets. A larger than expected change in the estimated posterior density following deletion and imputation can indicate a conflict in which inferences of interest are affected. The usefulness of the new methods is demonstrated in a number of real examples.

stat.ME↗
arXiv2020

Using prior expansions for prior-data conflict checking

Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesian models by expanding the prior used for the analysis into a larger family of priors, and considering a marginal likelihood score statistic for the expansion parameter. Consideration of different expansions can be informative about the nature of any conflict, and extensions to hierarchically specified priors and connections with other approaches to prior-data conflict checking are discussed. Implementation in complex situations is illustrated with two applications. The first concerns testing for the appropriateness of a LASSO penalty in shrinkage estimation of coefficients in linear regression. Our method is compared with a recent suggestion in the literature designed to be powerful against alternatives in the exponential power family, and we use this family as the prior expansion for constructing our check. A second application concerns a problem in quantum state estimation, where a multinomial model is considered with physical constraints on the model parameters. In this example, the usefulness of different prior expansions is demonstrated for obtaining checks which are sensitive to different aspects of the prior.

stat.ME↗
arXiv2019

The Measurement of Statistical Evidence as the Basis for Statistical Reasoning

There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that all approaches make reference to the evidence in the data concerning questions of interest as a justification for the methodology employed. It is fair to say, however, that none of the most commonly used methodologies is absolutely explicit about how statistical evidence is to be characterized and measured. We will discuss the general problem of statistical reasoning and the development of a theory for this that is based on being precise about statistical evidence. This will be shown to lead to the resolution of a number of problems.

math.ST↗
arXiv2019

Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist properties that hold for any proper prior. This leads to a possible resolution to an apparent conflict between these approaches to statistical reasoning. Frequentism is seen as establishing a figure of merit for a statistical study, while Bayesianism plays the key role in determining inferences based upon statistical evidence.

math.ST↗
arXiv2019

Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis

The data of four recent experiments --- conducted in Delft, Vienna, Boulder, and Munich with the aim of refuting nonquantum hidden-variables alternatives to the quantum-mechanical description --- are evaluated from a Bayesian perspective of what constitutes evidence in statistical data. We find that each of the experiments provides strong, or very strong, evidence in favor of quantum mechanics and against the nonquantum alternatives. This Bayesian analysis supplements the previous non-Bayesian ones, which refuted the alternatives on the basis of small p-values, but could not support quantum mechanics.

quant-ph↗
arXiv2018

Checking the Model and the Prior for the Constrained Multinomial

The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data conflict is considered here for such models. A theorem is proved that establishes the consistency of the check on the prior. Applications are presented to models that arise in quantum state estimation as well as the Bayesian analysis of models for ordered probabilities.

math.ST↗
arXiv2018

Robustly Maximal Utilisation of Energy-Constrained Distributed Resources

We consider the problem of dispatching a fleet of distributed energy reserve devices to collectively meet a sequence of power requests over time. Under the restriction that reserves cannot be replenished, we aim to maximise the survival time of an energy-constrained islanded electrical system; and we discuss realistic scenarios in which this might be the ultimate goal of the grid operator. We present a policy that achieves this optimality, and generalise this into a set-theoretic result that implies there is no better policy available, regardless of the realised energy requirement scenario.

eess.SY↗
arXiv2018

Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm.

math.ST↗
arXiv2017

Using history matching for prior choice

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will be limited due to constraints of time, cost and other factors. This paper develops effective numerical methods for exploring reasonable choices of a prior distribution from a parametric class, when prior information is specified in the form of some limited constraints on prior predictive distributions, and where these prior predictive distributions are analytically intractable. The methods developed may be thought of as a novel application of the ideas of history matching, a technique developed in the literature on assessment of computer models. We illustrate the approach in the context of logistic regression and sparse signal shrinkage prior distributions for high-dimensional linear models.

stat.AP↗
arXiv2017

Elicitation, measuring bias, checking for prior-data conflict and inference with a Dirichlet prior

Methods are developed for eliciting a Dirichlet prior based upon bounds on the individual probabilities that hold with virtual certainty. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated how to assess the bias in the prior as well as how to check for prior-data conflict. It is shown that the assessment of a hypothesis via relative belief can easily take into account what it means for the falsity of the hypothesis to correspond to a difference of practical importance and provide evidence in favor of a hypothesis.

stat.ME↗
arXiv2016

Checking for prior-data conflict using prior to posterior divergences

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models based on comparing the observed value of a prior to posterior divergence to its distribution under the prior predictive distribution for the data. The divergence measure used in our model check is a measure of how much beliefs have changed from prior to posterior, and can be thought of as a measure of the overall size of a relative belief function. It is shown that the proposed method is intuitive, has desirable properties, can be extended to hierarchical settings, and is related asymptotically to Jeffreys' and reference prior distributions. In the case where calculations are difficult, the use of variational approximations as a way of relieving the computational burden is suggested. The methods are compared in a number of examples with an alternative but closely related approach in the literature based on the prior predictive distribution of a minimal sufficient statistic.

stat.ME↗
arXiv2016

Multiple testing via relative belief ratios

Some large scale inference problems are considered based on using the relative belief ratio as a measure of statistical evidence. This approach is applied to the multiple testing problem. A particular application of this is concerned with assessing sparsity. The approach taken to sparsity has several advantages as it is based on a measure of evidence and does not require that the prior be restricted in any way.

math.ST↗
arXiv2016

Prior based model checking

Model checking procedures are considered based on the use of the Dirichlet process and relative belief. This combination is seen to lead to some unique advantages for this problem. In particular, it avoids double use of the data and prior-data conflict. Several examples have been incorporated, in which the proposed approach exhibits excellent performance.

stat.ME↗
arXiv2015

Optimal Robustness Results for Some Bayesian Procedures and the Relationship to Prior-Data Conflict

The robustness to the prior of Bayesian inference procedures based on a measure of statistical evidence are considered. These inferences are shown to have optimal properties with respect to robustness. Furthermore, a connection between robustness and prior-data conflict is established. In particular, the inferences are shown to be effectively robust when the choice of prior does not lead to prior-data conflict. When there is prior-data conflict, however, robustness may fail to hold.

math.ST↗
arXiv2014

Bayesian Hypothesis Assessment in Two-arm Trials Using Relative Belief Ratios

This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either for or against a hypothesis. In addition to the relative belief ratio, we also compute a measure of the strength of this evidence as a calibration of the relative belief ratio. Furthermore, we make use of the relative belief ratio as a measure of evidence, to assess whether a given prior induces bias either for or against a hypothesis. Prior elicitation, model checking and checking for prior-data conflict procedures are developed to ensure that the choices of model and prior made are relevant to the specific application. We highlight the applicability of the approach and illustrate the proposed method by applying it to a data set obtained from a two-arm clinical trial.

stat.AP↗
arXiv2013

What does the proof of Birnbaum's theorem prove?

Birnbaum's theorem, that the sufficiency and conditionality principles entail the likelihood principle, has engendered a great deal of controversy and discussion since the publication of the result in 1962. In particular, many have raised doubts as to the validity of this result. Typically these doubts are concerned with the validity of the principles of sufficiency and conditionality as expressed by Birnbaum. Technically it would seem, however, that the proof itself is sound. In this paper we use set theory to formalize the context in which the result is proved and show that in fact Birnbaum's theorem is incorrectly stated as a key hypothesis is left out of the statement. When this hypothesis is added, we see that sufficiency is irrelevant, and that the result is dependent on a well-known flaw in conditionality that renders the result almost vacuous.

math.ST↗