Inference for SDE models via Approximate Bayesian Computation

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a MATLAB package implementing our ABC-MCMC algorithm is provided.Comment: Version accepted for publication in Journal of Computational & Graphical Statistic

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential

Theories of schizophrenia: a genetic-inflammatory-vascular synthesis

BACKGROUND: Schizophrenia, a relatively common psychiatric syndrome, affects virtually all brain functions yet has eluded explanation for more than 100 years. Whether by developmental and/or degenerative processes, abnormalities of neurons and their synaptic connections have been the recent focus of attention. However, our inability to fathom the pathophysiology of schizophrenia forces us to challenge our theoretical models and beliefs. A search for a more satisfying model to explain aspects of schizophrenia uncovers clues pointing to genetically mediated CNS microvascular inflammatory disease. DISCUSSION: A vascular component to a theory of schizophrenia posits that the physiologic abnormalities leading to illness involve disruption of the exquisitely precise regulation of the delivery of energy and oxygen required for normal brain function. The theory further proposes that abnormalities of CNS metabolism arise because genetically modulated inflammatory reactions damage the microvascular system of the brain in reaction to environmental agents, including infections, hypoxia, and physical trauma. Damage may accumulate with repeated exposure to triggering agents resulting in exacerbation and deterioration, or healing with their removal. There are clear examples of genetic polymorphisms in inflammatory regulators leading to exaggerated inflammatory responses. There is also ample evidence that inflammatory vascular disease of the brain can lead to psychosis, often waxing and waning, and exhibiting a fluctuating course, as seen in schizophrenia. Disturbances of CNS blood flow have repeatedly been observed in people with schizophrenia using old and new technologies. To account for the myriad of behavioral and other curious findings in schizophrenia such as minor physical anomalies, or reported decreased rates of rheumatoid arthritis and highly visible nail fold capillaries, we would have to evoke a process that is systemic such as the vascular and immune/inflammatory systems. SUMMARY: A vascular-inflammatory theory of schizophrenia brings together environmental and genetic factors in a way that can explain the diversity of symptoms and outcomes observed. If these ideas are confirmed, they would lead in new directions for treatments or preventions by avoiding inducers of inflammation or by way of inflammatory modulating agents, thus preventing exaggerated inflammation and consequent triggering of a psychotic episode in genetically predisposed persons

To the Cloud! A Grassroots Proposal to Accelerate Brain Science Discovery

The revolution in neuroscientific data acquisition is creating an analysis challenge. We propose leveraging cloud-computing technologies to enable large-scale neurodata storing, exploring, analyzing, and modeling. This utility will empower scientists globally to generate and test theories of brain function and dysfunctio

Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations

The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity. In the present study, 16 subjects with BMI between 18.5 and 63.6 kg/m(2) have been studied with a long-duration (5 hours) EHC. In order to explain the oscillations of glycemia occurring in response to the hyperinsulinization and to the continuous glucose infusion at varying speeds, we first hypothesized a system of ordinary differential equations (ODEs), with limited success. We then extended the model and represented the experiment using a system of stochastic differential equations (SDEs). The latter allow for distinction between (i) random variation imputable to observation error and (ii) system noise (intrinsic variability of the metabolic system), due to a variety of influences which change over time. The stochastic model of the EHC was fitted to data and the system noise was estimated by means of a (simulated) maximum likelihood procedure, for a series of different hypothetical measurement error values. We showed that, for the whole range of reasonable measurement error values: (i) the system noise estimates are non-negligible; and (ii) these estimates are robust to changes in the likely value of the measurement error. Explicit expression of system noise is physiologically relevant in this case, since glucose uptake rate is known to be affected by a host of additive influences, usually neglected when modeling metabolism. While in some of the studied subjects system noise appeared to only marginally affect the dynamics, in others the system appeared to be driven more by the erratic oscillations in tissue glucose transport rather than by the overall glucose-insulin control system. It is possible that the quantitative relevance of the unexpressed effects (system noise) should be considered in other physiological situations, represented so far only with deterministic models