Bayesian modeling is pervasive in economics and cognitive science. I formalize a general notion of a Bayes model and illustrate it using a variety of examples.

Observed choices are random in psychological experiments on perception and in economics experiments on choice. I discuss a number of possible explanations and introduce the random utility model.

Agents typically make choices in succession. This may lead to situations where past choices seem to influence future choices, but often such a correlation is spurious and goes away if the analyst has as much information as the agent.

I discuss a number of models widely used in the literature, including logit, mixed logit, Fechnerian utility, and perturbed utility. Axiomatic underpinnings of every model are discussed.

In discrete-choice econometrics, the alternatives are characterized by attributes and choice probabilities are a function of those attributes. Classical models are reviewed.

I introduce the basic notion of a statistical model, its identification and partial identification. I discuss axiomatic characterizations of the random utility model.

Most of this chapter documents the prevalence of incredible certitude. Section 2.1 calls attention to the core role that certitude has played in major streams of religion and philosophy. Section 2.2 describes conventional certitude in official economic statistics reported by federal statistical agencies in the United States. Section 2.3 discusses dueling certitudes in research on criminal justice. Section 2.4 documents wishful extrapolation from medical research to patient care. Section 2.5 remarks on the complementary practice of sacrificing relevance for certitude, again using medical research to illustrate.

The closing part of chapter poses and assesses arguments that seek to explain incredible certitude. Section 2.6 discusses psychological arguments asserting that expression of incredible certitude in policy analysis is necessary because the public is unable to cope with uncertainty. Section 2.7 considers arguments asserting that incredible certitude is useful or necessary as a device to simplify collective decision making.

I discuss my work on diversified treatment under ambiguity. I begin with a simple illustration and then provide the formal analysis. I consider the deontological issue of possible societal preference for equal treatment. I discuss adaptive diversification, which is possible when a planner treats a sequence of cohorts over time.

Section 1.1 calls attention to the prevalent research practice that studies planning with incredible certitude. Section 1.2 contrasts the conceptions of uncertainty in consequentialist and axiomatic decision theory. Section 1.3 presents the formal structure of consequentialist theory, which is used throughout the book. Section 1.4 explains the prevalent econometric characterization of uncertainty, which distinguishes identification problems and statistical imprecision. Section 1.5 discusses the distinct perspectives on social welfare expressed in various strands of research on planning.