Scott A. Sisson

Sequential Monte Carlo without likelihoods.

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

Likelihood-Based Inference for Max-Stable Processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of United States precipitation extremes.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

In defence of model-based inference in phylogeography

Recent papers have promoted the view that model‐based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model‐based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model‐based inference in population genetics.

Transdimensional Markov Chains: A Decade of Progress and Future Perspectives

The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current state of the art and evaluate some of the most recent advances in this field. We also discuss future research perspectives in the context of the drive to develop sampling mechanisms with high degrees of both efficiency and automation.

The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis

The emergence of antibiotic resistance in Mycobacterium tuberculosis has raised the concern that pathogen strains that are virtually untreatable may become widespread. The acquisition of resistance to antibiotics results in a longer duration of infection in a host, but this resistance may come at a cost through a decreased transmission rate. This raises the question of whether the overall fitness of drug-resistant strains is higher than that of sensitive strains—essential information for predicting the spread of the disease. Here, we directly estimate the transmission cost of drug resistance, the rate at which resistance evolves, and the relative fitness of resistant strains. These estimates are made by using explicit models of the transmission and evolution of sensitive and resistant strains of M. tuberculosis, using approximate Bayesian computation, and molecular epidemiology data from Cuba, Estonia, and Venezuela. We find that the transmission cost of drug resistance relative to sensitivity can be as low as 10%, that resistance evolves at rates of ≈0.0025–0.02 per case per year, and that the overall fitness of resistant strains is comparable with that of sensitive strains. Furthermore, the contribution of transmission to the spread of drug resistance is very high compared with acquired resistance due to treatment failure (up to 99%). Estimating such parameters directly from in vivo data will be critical to understanding and responding to antibiotic resistance. For instance, projections using our estimates suggest that the prevalence of tuberculosis may decline with successful treatment, but the proportion of cases associated with resistance is likely to increase.

Using Approximate Bayesian Computation to Estimate Tuberculosis Transmission Parameters From Genotype Data

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.

Inference for Stereological Extremes

In the production of clean steels, the occurrence of imperfections—so-called “inclusions”—is unavoidable. The strength of a clean steel block is largely dependent on the size of the largest imperfection that it contains, so inference on extreme inclusion size forms an important part of quality control. Sampling is generally done by measuring imperfections on planar slices, leading to an extreme value version of a standard stereological problem: how to make inference on large inclusions using only the sliced observations. Under the assumption that inclusions are spherical, this problem has been tackled previously using a combination of extreme value models, stereological calculations, a Bayesian hierarchical model, and standard Markov chain Monte Carlo (MCMC) techniques. Our objectives in this article are twofold: (1) to assess the robustness of such inferences with respect to the assumption of spherical inclusions, and (2) to develop an inference procedure that is valid for nonspherical inclusions. We investigate both of these aspects by extending the spherical family for inclusion shapes to a family of ellipsoids. We then address the issue of robustness by assessing the performance of the spherical model when fitted to measurements obtained from a simulation of ellipsoidal inclusions. The issue of inference is more difficult, because likelihood calculation is not feasible for the ellipsoidal model. To handle this aspect, we propose a modification to a recently developed likelihood-free MCMC algorithm. After verifying the viability and accuracy of the proposed algorithm through a simulation study, we analyze a real inclusion dataset, comparing the inference obtained under the ellipsoidal inclusion model with that previously obtained assuming spherical inclusions.

Rapid shifts in dispersal behavior on an expanding range edge

Dispersal biology at an invasion front differs from that of populations within the range core, because novel evolutionary and ecological processes come into play in the nonequilibrium conditions at expanding range edges. In a world where species’ range limits are changing rapidly, we need to understand how individuals disperse at an invasion front. We analyzed an extensive dataset from radio-tracking invasive cane toads (Rhinella marina) over the first 8 y since they arrived at a site in tropical Australia. Movement patterns of toads in the invasion vanguard differed from those of individuals in the same area postcolonization. Our model discriminated encamped versus dispersive phases within each toad’s movements and demonstrated that pioneer toads spent longer periods in dispersive mode and displayed longer, more directed movements while they were in dispersive mode. These analyses predict that overall displacement per year is more than twice as far for toads at the invasion front compared with those tracked a few years later at the same site. Studies on established populations (or even those a few years postestablishment) thus may massively underestimate dispersal rates at the leading edge of an expanding population. This, in turn, will cause us to underpredict the rates at which invasive organisms move into new territory and at which native taxa can expand into newly available habitat under climate change.

Bayesian Inference, Monte Carlo Sampling and Operational Risk.

Operational risk is an important quantitative topic as a result of the Basel II regulatory requirements. Operational risk models need to incorporate internal and external loss data observations in combination with expert opinion surveyed from business specialists. Following the Loss Distributional Approach, this article considers three aspects of the Bayesian approach to the modelling of operational risk. Firstly we provide an overview of the Bayesian approach to operational risk, before expanding on the current literature through consideration of general families of non-conjugate severity distributions, g-and-h and GB2 distributions. Bayesian model selection is presented as an alternative to popular frequentist tests, such as Kolmogorov-Smirnov or Anderson-Darling. We present a number of examples and develop techniques for parameter estimation for general severity and frequency distribution models from a Bayesian perspective. Finally we introduce and evaluate recently developed stochastic sampling techniques and highlight their application to operational risk through the models developed.