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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.
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 approach
Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics by Kou, Zhou and Wong [math.ST/0507080]
Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference on aspect
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been s
We extend Hoeffdings lemma to general-state-space and not necessarily reversible Markov chains. Let ${X_i}_{i ge 1}$ be a stationary Markov chain with invariant measure $pi$ and absolute spectral gap $1-lambda$, where $lambda$ is defined as the opera