Jan 23rd 2023. Adam Sanborn (Psychology, Warwick). Bayesian brains without probabilities.

Over the past two decades, a wave of Bayesian explanations has swept through cognitive science, explaining behavior in domains from intuitive physics and causal learning, to perception, motor control and language. Yet people produce stunningly incorrect answers in response to even the simplest questions about probabilities. How can a supposedly Bayesian brain paradoxically reason so poorly with probabilities? Perhaps Bayesian brains do not represent or calculate probabilities at all and are, indeed, poorly adapted to do so. Instead, the brain could be approximating Bayesian inference through sampling: drawing samples from its distribution of likely hypotheses over time. Only with infinite samples does a Bayesian sampler conform to the laws of probability, and in this talk I show how using a finite number of samples systematically generates classic probabilistic reasoning errors in individuals, upending the longstanding consensus on these effects, and show how an extended model explains estimates, choices, response times, and confidence judgments.

Jan 30th 2023. Bruno Martins (SLS, Warwick). Round the clock: circadian gene expression, growth and division in cyanobacteria.

Circadian clocks are regulatory networks that generate 24-h rhythms of gene expression in anticipation to daily cycles of sunlight. Substantial progress has been made in understanding how cells generate and sustain these rhythms in response to stereotypical environmental cues. However, our knowledge of how the clock is coupled to other circuits and cellular processes inside the cell, as well as to the environment, what types of dynamics arise from this coupling, and what biological functions it serves is still incomplete. I will discuss how we are using cyanobacteria as a model system to address those questions through an interplay of theory and experiment. Our main focus is on developing a quantitative understanding of how and why the clock regulates the cell division cycle and cellular growth. Through a combination of single-cell microscopy data and statistical inference, we estimated a phenomenological time-dependent coupling function between the clock and cell division. Using mathematical models and fluorescence live imaging, we are now aiming to reveal the molecular mechanisms underpinning clock-cell cycle coupling. This approach provides a template towards understanding the complex interdependency between the clock, the environment and cellular physiology. 

Feb 6th 2023. Mafalda Viana.

Feb 13th 2023. Trevor Graham (Institute of cancer Research, London). Measuring cancer evolutionary dynamics using maths and genomics.

Cancers evolve. But rarely can we directly observe this dynamic process, because our data derives from single samples that capture only snapshots in time. I will discuss how we can construct simple mathematical models of tumour evolution and fit them to these "snapshots" (the data are cancer genome sequencing) to learn the unobservable evolutionary dynamics of cancer development.

Feb 20th 2023. Randolf Altmeyer (Mathematics, Cambridge UK). Modelling and Statistical inference with Stochastic partial differential equations.

In this talk we will discuss how stochastic partial differential equations (SPDEs) can be used in modelling non-linear dynamics relevant to biological processes, usually described by deterministic PDEs. The observable data depend on dynamic noise and differ qualitatively from the deterministic PDE model corrupted by independent measurement errors. To demonstrate the usefulness of this approach we will see a concrete extension of a classical reaction-diffusion model for cell repolarisation. The dynamic noise has interesting effects on the repolarisation behaviour without destroying the pattern formation we are after. In the second part of the talk we will focus on statistical theory for estimating the model parameters from data. We show that estimators for diffusivity, transport and reaction coefficients in the linear part of the SPDE are minimax rate optimal in an asymptotic regime where the solution is observed continuously in time over a shrinking spatial windows (e.g., by a microscope). The proof for optimality relies on an explicit analysis of the reproducing kernel Hilbert space of the underlying Gaussian process, which may be of independent interest.

Mar 6th 2023. Theodore Kypraios (School of Mathematical Sciences, Nottingham). Bayesian nonparametric inference for stochastic infectious disease models

Infectious disease transmission models require assumptions about how the pathogen spreads between individuals. These assumptions may be somewhat arbitrary, particularly when it comes to describing how transmission varies between individuals of different types or in different locations and may in turn lead to incorrect conclusions or policy decisions.

In this talk, we will present a novel and general Bayesian nonparametric framework for transmission modelling which removes the need to make such specific assumptions with regards to the infection process. We use multi-output Gaussian process prior distributions to model different infection rates in populations containing multiple types of individuals. Further challenges arise because the transmission process itself is unobserved, and large outbreaks can be computationally demanding to analyse. We address these issues by data augmentation and a suitable efficient approximation method. Simulation studies using synthetic data demonstrate that our framework gives accurate results. Finally, we use our methods to enhance our understanding of the transmission mechanisms of the 2001 UK Foot and Mouth Disease outbreak.