Bayesian experimental design for models with intractable likelihoods

Neurophysiological and imaging biomarkers of lower motor neuron dysfunction in motor neuron diseases/amyotrophic lateral sclerosis: IFCN handbook chapter

This chapter discusses comprehensive neurophysiological biomarkers utilised in motor neuron disease (MND) and, in particular, its commonest form, amyotrophic lateral sclerosis (ALS). These encompass the conventional techniques including nerve conduction studies (NCS), needle and high-density surface electromyography (EMG) and H-reflex studies as well as novel techniques. In the last two decades, new methods of assessing the loss of motor units in a muscle have been developed, that are more convenient than earlier methods of motor unit number estimation (MUNE),and may use either electrical stimulation (e.g. MScanFit MUNE) or voluntary activation (MUNIX). Electrical impedance myography (EIM) is another novel approach for the evaluation that relies upon the application and measurement of high-frequency, low-intensity electrical current. Nerve excitability techniques (NET) also provide insights into the function of an axon and reflect the changes in resting membrane potential, ion channel dysfunction and the structural integrity of the axon and myelin sheath. Furthermore, imaging ultrasound techniques as well as magnetic resonance imaging are capable of detecting the constituents of morphological changes in the nerve and muscle. The chapter provides a critical description of the ability of each technique to provide neurophysiological insight into the complex pathophysiology of MND/ALS. However, it is important to recognise the strengths and limitations of each approach in order to clarify utility. These neurophysiological biomarkers have demonstrated reliability, specificity and provide additional information to validate and assess lower motor neuron dysfunction. Their use has expanded the knowledge about MND/ALS and enhanced our understanding of the relationship between motor units, axons, reflexes and other neural circuits in relation to clinical features of patients with MND/ALS at different stages of the disease. Taken together, the ultimate goal is to aid early diagnosis, distinguish potential disease mimics, monitor and stage disease progression, quantify response to treatment and develop potential therapeutic interventions.

Adaptive Bayesian inference of Markov transition rates

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations.

Designing group dose-response studies in the presence of transmission

Dose-response studies are used throughout pharmacology, toxicology and in clinical research to determine safe, effective, or hazardous doses of a substance. When involving animals, the subjects are often housed in groups; this is in fact mandatory in many countries for social animals, on ethical grounds. An issue that may consequently arise is that of unregulated between-subject dosing (transmission), where a subject may transmit the substance to another subject. Transmission will obviously impact the assessment of the dose-response relationship, and will lead to biases if not properly modelled. Here we present a method for determining the optimal design - pertaining to the size of groups, the doses, and the killing times - for such group dose-response experiments, in a Bayesian framework. Our results are of importance to minimising the number of animals required in order to accurately determine dose-response relationships. Furthermore, we additionally consider scenarios in which the estimation of the amount of transmission is also of interest. A particular motivating example is that of Campylobacter jejuni in chickens. Code is provided so that practitioners may determine the optimal design for their own studies.

Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach

Kinetic models are essential to quantitatively understand and predict the behaviour of metabolic networks. Detailed and thermodynamically feasible kinetic models of metabolism are inherently difficult to formulate and fit. They have a large number of heterogeneous parameters, are non-linear and have complex interactions. Many powerful fitting strategies are ruled out by the intractability of the likelihood function. Here, we have developed a computational framework capable of fitting feasible and accurate kinetic models using Approximate Bayesian Computation. This framework readily supports advanced modelling features such as model selection and model-based experimental design. We illustrate this approach on the tightly-regulated mammalian methionine cycle. Sampling from the posterior distribution, the proposed framework generated thermodynamically feasible parameter samples that converged on the true values, and displayed remarkable prediction accuracy in several validation tests. Furthermore, a posteriori analysis of the parameter distributions enabled appraisal of the systems properties of the network (e.g., control structure) and key metabolic regulations. Finally, the framework was used to predict missing allosteric interactions.

Likelihood-free simulation-based optimal design with an application to spatial extremes

In this paper we employ a novel method to find the optimal design for problems where the likelihood is not available analytically, but simulation from the likelihood is feasible. To approximate the expected utility we make use of approximate Bayesian computation methods. We detail the approach for a model on spatial extremes, where the goal is to find the optimal design for efficiently estimating the parameters determining the dependence structure. The method is applied to determine the optimal design of weather stations for modeling maximum annual summer temperatures.

Approximate Bayesian inference for complex ecosystems

Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists.

Modelling proteasome and proteasome regulator activities

Proteasomes are key proteases involved in a variety of processes ranging from the clearance of damaged proteins to the presentation of antigens to CD8+ T-lymphocytes. Which cleavage sites are used within the target proteins and how fast these proteins are degraded have a profound impact on immune system function and many cellular metabolic processes. The regulation of proteasome activity involves different mechanisms, such as the substitution of the catalytic subunits, the binding of regulatory complexes to proteasome gates and the proteasome conformational modifications triggered by the target protein itself. Mathematical models are invaluable in the analysis; and potentially allow us to predict the complex interactions of proteasome regulatory mechanisms and the final outcomes of the protein degradation rate and MHC class I epitope generation. The pioneering attempts that have been made to mathematically model proteasome activity, cleavage preference variation and their modification by one of the regulatory mechanisms are reviewed here.