Many and long were the conversations between Lord Byron and Shelley to which I was a devout and silent listener. During one of these, various philosophical doctrines were discussed, and among others the nature of the principle of life, and whether there was any probability of its ever being discovered and communicated. They talked of the experiments of Dr. Darwin (I speak not of what the doctor really did or said that he did, but, as more to my purpose, of what was then spoken of as having been done by him), who preserved a piece of vermicelli in a glass case till by some extraordinary means it began to move with a voluntary motion. Not thus, after all, would life be given. Perhaps a corpse would be reanimated; galvanism had given token of such things: perhaps the component parts of a creature might be manufactured, brought together, and endued with vital warmth (Butler 1998).

This page contains some information on research by David Poole and students on probabilistic reasoning and decision making. It is not intended to be an introduction to the vast literature on these topics, but only the incremental work done by me. For more different perspectives, see the pointers from the Uncertainty in AI (UAI) home page. Maybe someday I will write an online introduction. Probabilistic Horn abduction is a pragmatic combination of logic and probability.

You may skip most of these readings if you have prior programming experience in Java.

You happen to know that Tim and Harry have recently had a terrible row that ended their friendship. Now someone tells you that she just saw Tim and Harry jogging together. The best explanation for this that you can think of is that they made up. You conclude that they are friends again. One morning you enter the kitchen to find a plate and cup on the table, with breadcrumbs and a pat of butter on it, and surrounded by a jar of jam, a pack of sugar, and an empty carton of milk. You conclude that one of your house-mates got up at night to make him- or herself a midnight snack and was too tired to clear the table. This, you think, best explains the scene you are facing. To be sure, it might be that someone burgled the house and took the time to have a bite while on the job, or a house-mate might have arranged the things on the table without having a midnight snack but just to make you believe that someone had a midnight snack. But these hypotheses strike you as providing much more contrived explanations of the data than the one you infer to. Walking along the beach, you see what looks like a picture of Winston Churchill in the sand. It could be that, as in the opening pages of Hilary Putnam's (1981), what you see is actually the trace of an ant crawling on the beach. The much simpler, and therefore (you think) much better, explanation is that someone intentionally drew a picture of Churchill in the sand. That, in any case, is what you come away believing. In these examples, the conclusions do not follow logically from the premises.

Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full quantification of both probabilistic uncertainties and utility values. For problems where all random variables and decision spaces are finite and discrete, here we develop a symbolic way to calculate the expected utilities of influence diagrams that does not require a full numerical representation. Within this approach expected utilities correspond to families of polynomials. After characterizing their polynomial structure, we develop an efficient symbolic algorithm for the propagation of expected utilities through the diagram and provide an implementation of this algorithm using a computer algebra system. We then characterize many of the standard manipulations of influence diagrams as transformations of polynomials. We also generalize the decision analytic framework of these diagrams by defining asymmetries as operations over the expected utility polynomials.

Over the last two years I've occasionally been giving a very basic tutorial to Bayesian statistics using R and Stan. At the end of the tutorial I hand out an exercise for those that want to flex their newly acquired skills. I call this exercise Bayesian computation with Stan and Farmer Jöns and it's pretty cool! Now, it's not cool because of me, but because the expressiveness of Stan allowed me to write a small number of data analytic questions that quickly takes you from running a simple binomial model up to running a linear regression. Throughout the exercise you work with the same model code and each question just requires you to make a minimal change to this code, yet you will cover most models taught in a basic statistics course!

An important problem for HCI researchers is to estimate the parameter values of a cognitive model from behavioral data. This is a difficult problem, because of the substantial complexity and variety in human behavioral strategies. We report an investigation into a new approach using approximate Bayesian computation (ABC) to condition model parameters to data and prior knowledge. As the case study we examine menu interaction, where we have click time data only to infer a cognitive model that implements a search behaviour with parameters such as fixation duration and recall probability. Our results demonstrate that ABC (i) improves estimates of model parameter values, (ii) enables meaningful comparisons between model variants, and (iii) supports fitting models to individual users. ABC provides ample opportunities for theoretical HCI research by allowing principled inference of model parameter values and their uncertainty.

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameters. The effective dimension for the Gibbs sampling is low because iterative sampling is done from only three conditional posterior PDFs that correspond to three parameter groups, along with sampling of the equation-error precision parameter from another conditional posterior PDF in one of the algorithms where it is not integrated out as a "nuisance" parameter. A nice feature from a computational perspective is that it is not necessary to solve a nonlinear eigenvalue problem of a structural model. The effectiveness and robustness of the proposed algorithms are illustrated by applying them to the IASE-ASCE Phase II simulated and experimental benchmark studies. The goal is to use incomplete modal data identified before and after possible damage to detect and assess spatially-sparse stiffness reductions induced by any damage. Our past and current focus on meeting challenges arising from Bayesian inference of structural stiffness serve to strengthen the capability of vibration-based structural system identification but our methods also have much broader applicability for inverse problems in science and technology where system matrices are to be inferred from noisy partial information about their eigenquantities.