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The intent of a statistically-based phylogenetic method is to estimate tree topologies and values of possibly relevant parameters, as well as the uncertainty inherent in those estimations. A method that could do that with reasonable accuracy would be attractive indeed. It is often claimed that it is advantageous for a method to be based on a specific evolutionary model, because that allows incorporating into the analysis the ‘knowledge’ of the real world embodied in the model. Bayesian methods have become very prominent among model-based methods, in part because of computational advantages, and in part because they estimate the probability that a given hypothesis is true, given the observations and model assumptions. Through simulation studies, this chapter finds that even if there is the potential for Bayesian estimations of monophyly to provide correct topological estimations for infinite numbers of characters, the resulting claims to measure degrees of support for conclusions — in a statistical sense — are unfounded. Additionally, for large numbers of terminals, it is argued to be extremely unlikely that a search via Markov Monte Carlo techniques would ever pass through the optimal tree(s), let alone pass through the optimal tree(s) enough times to estimate their posterior probability with any accuracy.

In this chapter, Corey J. A. Bradshaw and Barry W. Brook, discuss measures of biodiversity patterns followed by an overview of experimental design and associated statistical paradigms. Conservation biology is a highly multidisciplinary science employing methods from ecology, Earth systems science, genetics, physiology, veterinary science, medicine, mathematics, climatology, anthropology, psychology, sociology, environmental policy, geography, political science, and resource management. Here we focus primarily on ecological methods and experimental design. It is impossible to census all species in an ecosystem, so many different measures exist to compare biodiversity: these include indices such as species richness, Simpson's diversity, Shannon's index and Brouillin's index. Many variants of these indices exist. The scale of biodiversity patterns is important to consider for biodiversity comparisons: α (local), β (between‐site), and γ (regional or continental) diversity. Often surrogate species ‐ the number, distribution or pattern of species in a particular taxon in a particular area thought to indicate a much wider array of taxa ‐ are required to simplify biodiversity assessments. Many similarity, dissimilarity, clustering, and multivariate techniques are available to compare biodiversity indices among sites. Conservation biology rarely uses completely manipulative experimental designs (although there are exceptions), with mensurative (based on existing environmental gradients) and observational studies dominating. Two main statistical paradigms exist for comparing biodiversity: null hypothesis testing and multiple working hypotheses – the latter paradigm is more consistent with the constraints typical of conservation data and so should be invoked when possible. Bayesian inferential methods generally provide more certainty when prior data exist. Large sample sizes, appropriate replication and randomization are cornerstone concepts in all conservation experiments. Simple relative abundance time series (sequential counts of individuals) can be used to infer more complex ecological mechanisms that permit the estimation of extinction risk, population trends, and intrinsic feedbacks. The risk of a species going extinct or becoming invasive can be predicted using cross‐taxonomic comparisons of life history traits. Population viability analyses are essential tools to estimate extinction risk over defined periods and under particular management interventions. Many methods exist to implement these, including count‐based, demographic, metapopulation, and genetic. Many tools exist to examine how genetics affects extinction risk, of which perhaps the measurement of inbreeding depression, gene flow among populations, and the loss of genetic diversity with habitat degradation are the most important.

This chapter presents a case study mapping mortality rates for Hodgkin's disease in French departments. It illustrates and compares various methods for estimating rates for rare diseases. Some practical issues for implementing the fully Bayesian approach are discussed.

Adaptive procedures are developed to reduce the burden of data collection in psychophysics by creating more efficient experimental test designs and methods of estimating either statistics or parameters. In some cases, these adaptive procedures may reduce the amount of testing by as much as 80% to 90%. This chapter begins with a description of classical staircase procedures for estimating the threshold and/or slope of the psychometric function, followed by a description of modern Bayesian adaptive methods for optimizing psychophysical tests. We introduce applications of Bayesian adaptive procedures for the estimation of psychophysically measured functions and surfaces. The bias, precision and efficiency of estimates is considered. Each method is accompanied by an illustrative example and sample results and a discussion of the practical requirements of the procedure.

This chapter examines the underlying assumptions of Bayesian methods for disease mapping and discusses mathematical details. The chapter proceeds as follows. Section 7.2 describes a three-state hierarchical model within which disease mapping data may be viewed. Section 7.3 considers implementation and simulation-based techniques. Section 7.4 provides two illustrative examples of the use of Bayesian disease mapping models. Section 7.5 considers some extensions and alternative approaches to the models presented. Section 7.6 provides a concluding discussion.

This chapter begins with a discussion of the difficulties posed by interactive learning. It then identifies two competing schools of thought in game theory. One school points optimistically to particular classes of games that can in fact be learned by simple updating procedures, such as learning minimax equilibria by fictitious. This school also points to the fact that any game can be learned by Bayesian methods provided that the priors are sufficiently aligned to begin with. The other school views the situation more pessimistically. Its adherents point out that simple learning procedures tend to work only in special cases, such as zero-sum games, potential games, and so forth. Moreover, they are unimpressed by the fact that Bayesian methods lead to learning if the priors are sufficiently aligned to begin with. An overview of the subsequent chapters is also presented.

This chapter surveys applications of Bayesian theory in biostatistics. It begins by discussing hierarchical models. Arguably the most tightly regulated and well controlled applications of statistical inference in biomedical research are the design and analysis of clinical trials. While far from being an accepted standard, Bayesian methods can contribute significantly to improving trial designs and to constructing designs for complex experimental layouts. Another example of how the Bayesian paradigm can provide coherent and principled answers to complex inference problems can be found in problems related to the control of multiplicities and massive multiple comparisons. The chapter concludes with a brief review of related research.

This chapter examines variation in the mitochondrial cytochrome b gene for 30 of the approximately 40 species of South American grass mice, genus Akodon. It observes that phylogenetic analyses encompassing both maximum parsimony and Bayesian methods consistently identified four clades, but each with varying levels of support: (1) the “varius group” from eastern Bolivia, western Paraguay, and Argentina; (2) the “boliviensis group,” a set of seven species from the high Andean and Sub-Andean grasslands that form a common phylogenetic order; (3) the “aerosus group,” an assemblage of eight species, including A. aerosus, A. affinis, A. cf. budini, A. mollis, A. orphilus, A. siberiae, and A. torques from the forested Andean slopes, plus A. albiventer from the Altiplano from southern Peru south to northern Argentina; and (4) the “cursor group,” from the coastal regions of Brazil south to Argentina.

In this chapter I concentrate on continuous inferential problems: problems where the dependent variable is continuous, such as classical regression problems. As in the previous chapter, using duality theory, I show that the info-metrics framework is general enough to include the class of information-theoretic methods as a special case. The formulation is developed for the classical regression problem, but the results apply to many other problems. A detailed discussion of the benefits and costs of using the info-metrics framework is provided and contrasted with other approaches. I use theoretical examples and policy-relevant applications to demonstrate the method. The common problem of misspecification is also discussed and studied within the info-metrics framework. I show that a misspecified model and a correctly specified one can yield similar answers. The appendices provide detailed discussions of the generalized method of moments and the Bayesian method of moments. Both are connected to info-metrics.

This chapter discusses optimal Bayesian model specification. It examines three methods that may be helpful in moving toward an optimal-model-specification goal. These methods are: an approach called Calibration Cross-Validation (CCV) that helps one pay the right price for data-peeking and Bayesian non-parametric methods for specifying sampling distributions and prior distributions.

This chapter discusses the hypothesis of the molecular clock and its use to date species divergences. It introduces various tests of the molecular clock as well as strategies to relax the clock in divergence time estimation. Bayesian methods of divergence time estimation are discussed in detail, including different prior models of rate drift such as the correlated-rate model based on the geometric Brownian motion process, and specification of the prior on divergence times incorporating uncertainties in fossil calibrations. The chapter describes the infinite-site and finite-site theories, which characterize the uncertainties in posterior divergence time estimates.

This chapter reviews the statistical approaches for simultaneous alignment and phylogeny reconstruction. It focuses on the modeling of insertion and deletion events in a phylogenetic framework, and on how recent advances in likelihood maximization and Bayesian methods enable these advanced statistical procedures to be used to align sequences. The chapter begins by discussing sequence evolution models used to model insertions and deletions (indels), and then describes the Markov-chain Monte Carlo methods for sampling multiple alignments and phylogenetic trees to their posterior distribution for given sequence data.

We consider the problem of short-term time series forecasting (nowcasting) when there are more possible predictors than observations. The motivating example is the use of Google Trends search engine query data as a contemporaneous predictor of economic indicators. Our preferred approach combines three Bayesian techniques: Kalman filtering, spike-and-slab regression, and model averaging. The Kalman filter can be used to control for time series feature, such as seasonality and trend; the regression can be used to incorporate predictors such as search engine queries; and model averaging can be used to reduce the danger of overfitting. Overall the Bayesian approach allows a flexible way to incorporate prior knowledge, both subjective and objective, into the estimation procedure. We illustrate this approach using search engine query data as predictors for consumer sentiment and gun sales.

This chapter surveys previous attempts to classify the genetic relationships among the Tungusic languages. The set of sound correspondences that can be employed in this classification is examined and it is argued that, if one assumes binary branching for a cladistic classification, there are three plausible classifications that result from the application of the classical comparative method. Next, a Bayesian phylogenetic analysis of basic vocabulary is undertaken to determine whether that analysis provides any further evidence for which of the three classifications is preferred. The conclusion is that it does and that one of the best classifications of Tungusic places Manchu, Xibe, and Jurchen in a Southern Branch together with Udihe and Nanai complexes, and the Even-Evenki complex in a Northern Branch. Though our analysis does not exclude the most common classification in which the Manchuric branch separated first from all other Tungusic languages.

Subgroup analysis involves the comparison of treatment efficacies in a clinical trial among subgroups defined by baseline patient characteristics, such as gender and age. Better subgroup analysis techniques can improve the extraction of information from clinical trials and lead to improved clinical trial designs. This chapter presents methods that cast subgroup analysis as a model selection procedure that can also be seen as a decision problem. Bayesian thinking allows one readily to formulate the probability model and to implement inference and decision making. The material presented here can be seen as a framework in which to carry out subgroup analysis rather than a specific instance of it.

Machine learning is a highly influential field that has made major contributions to the increased effectiveness of artificial intelligence. Machine learning utilizes different methods, four of which have been particularly effective. The Analogizers classify patterns based on their similarity to other patterns. Multidimensional scaling provides support. The Bayesians revise the probability of hypotheses based on new evidence. The Connectionists adjust the strength between layers of “neurons.” Deep leaning based on many layers of connections has proven particularly successful. The Symbolists use rules that combine pieces of pre-existing knowledge. Hybrid systems combine these methods to create systems that are more effective than individual methods.

A major effort of the Village Ecodynamics Project involved translating the archaeological record of the central Mesa Verde region into quantitative summaries of the actual ancestral Pueblo settlement history, using explicit and repeatable criteria. This chapter introduces the study area, explains how we translated the archaeological record into a quantitative database using Bayesian statistical methods, and presents the basic outlines of the resulting settlement history derived from these data. These analyses provide an introduction to the basic issues surrounding ancestral Pueblo historical ecology, whichthe remaining chapters of this book address in various ways. They also provide the “pattern of resistance” against which models of climate change; agricultural potential; water availability; wood, stone, and game resources; exchange; warfare; and settlement decisions are evaluated throughout this volume.

Environmental flow assessment and effective management require capacity to predict the future ecological condition of a river ecosystem after its flow regime has been altered. This chapter is devoted to recent developments in modeling ecological responses to flow in natural, regulated, and restored river systems. The main themes are flow and thermal regime; water chemistry; aquatic and riparian vegetation; and invertebrate and fish habitats, populations, and assemblage models. Bayesian methods receive particular attention. The chapter ends with an outline of several tenets from the Riverine Ecosystem Synthesis, recently proposed as a framework for predicting how patterns of individual species distributions, community regulation, ecosystem processes, and floodplain interactions can be expected to vary over the hydrogeomorphic zones and patches of river systems.

This chapter considers some very simple learning problems to make accurate predictions. It reviews the least mean squared (LMS) algorithm. It shows that internal model is simply a link between motor commands and their sensory consequences. The driving force in learning an internal model is the sensory prediction error. This chapter also reveals that when motor commands are generated, perturbations like force fields or visuomotor rotations produce discrepancies between the predicted and observed sensory consequences. It illustrates that in some forms of biological learning, as in backward blocking, animals seem to learn in a way that resembles the Bayesian method and not LMS.