A Hierarchical Bayesian meta-analysis model developed by Dumouchel is derived by implementing the General Bayesian Linear model (GBLM) theorem. The aim is to obtain the joint posterior distribution of all parameters in the model. Simulation study is conducted to confirm the estimation of all parameters of interest. Results show parameter estimates as close to the true values indicating paramete...

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can exten...

Human learners routinely make inductive inferences, or inferences that go beyond the data they have observed. Inferences like these must be supported by constraints, some of which are innate, although others are almost certainly learned. This thesis presents a hierarchical Bayesian framework that helps to explain the nature, use and acquisition of inductive constraints. Hierarchical Bayesian mo...

20.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.1 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.2 Latent Dirichlet Allocation . . . . . . . . . . . ...

In this paper we present a simple hierarchical Bayesian treatment of the sparse kernel logistic regression (KLR) model based MacKay’s evidence approximation. The model is re-parameterised such that an isotropic Gaussian prior over parameters in the kernel induced feature space is replaced by an isotropic Gaussian prior over the transformed parameters, facilitating a Bayesian analysis using stan...

It is unquestionably true that hierarchical models represent an order of magnitude increase in the scope and complexity of models for ecological data. The past decade has seen a tremendous expansion of applications of hierarchical models in ecology. The expansion was primarily due to the advent of the Bayesian computational methods. We congratulate the authors for writing a clear summary of hie...

Health care utilization and outcome studies call for hierarchical approaches. The objectives were to predict major complications following percutaneous coronary interventions by health providers, and to compare Bayesian and non-Bayesian sample size calculation methods. The hierarchical data structure consisted of: (1) Strata: PGY4, PGY7, and physician assistant as providers with varied experien...

Model-based diagnosis reasons backwards from a functional schematic of a system to isolate faults given observations of anoma­ lous behavior. We develop a fully proba­ bilistic approach to model based diagno­ sis and extend it to support hierarchical models. Our scheme translates the func­ tional schematic into a Bayesian network and diagnostic inference takes place in the Bayesian network. A B...

We demonstrate the potential of using a Bayesian hierarchical mixture approach to model individual differences in cognition. Mixture components can be used to identify latent groups of subjects who use different cognitive processes, while hierarchical distributions can be used to capture more minor variation within each group. We apply Bayesian hierarchical mixture methods in two illustrative a...

Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as inference for a set of parameters that are shared across tasks. Here, we reformulate the model-agnostic meta-learning algorithm (MAML) of Finn et al. (2017) as ...