Estimating the population size of transgender women in San Francisco using multiple methods, 2013

Purpose: To estimate the number of adult transgender women (TGW) in San Francisco and to provide an example of how estimation can be conducted.

Methods: Using nine different services accessed by the TGW population, the service multiplier, integrated into a respondent-driven sampling (RDS) survey of TGW, was used to calculate nine estimates of the TGW population in San Francisco. Both the successive sampling method, also integrated into the RDS survey of TGW, and a population proportion from the literature each calculated an additional estimate of the TGW population. The median of all 11 estimates was calculated to present a single estimate of the TGW population in San Francisco.

Results: The median of estimates was 978 TGW in San Francisco (plausibility bounds 635 – 1,400). This estimate is consistent with known cases of HIV among TGW and surveys on the prevalence of infection in the TGW population.

Conclusion: Using multiple methods, we estimate the TGW population size to be 0.13% of the San Francisco population. Despite small numbers, TGW bear a disproportionate burden of HIV infection in San Francisco. TGW are a priority for HIV care and prevention services.     

Probabilistic argumentation systems: A new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster–Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.     

Notes on selective influence, probabilistic causality, and probabilistic dimensionality

The paper provides conceptual clarifications for the issues related to the dependence of jointly distributed systems of random entities on external factors. This includes the theory of selective influence as proposed in Dzhafarov [(2003a). Selective influence through conditional independence. Psychometrika, 68, 7-26] and generalized versions of the notions of probabilistic causality [Suppes, P., & Zanotti, M. (1981). When are probabilistic explanations possible? Synthese, 48, 191-199] and dimensionality in the latent variable models [Levine, M. V. (2003). Dimension in latent variable models. Journal of Mathematical Psychology, 47, 450-466]. One of the basic observations is that any system of random entities whose joint distribution depends on a factor set can be represented by functions of two arguments: a single factor-independent source of randomness and the factor set itself. In the case of random variables (i.e., real-valued random entities endowed with Borel sigma-algebras) the single source of randomness can be chosen to be any random variable with a continuous distribution (e.g., uniformly distributed between 0 and 1).     

Judging the accuracy of a likelihood judgment: the case of smoking risk

A standard method for assessing whether people have appropriate internal representations of an event's likelihood is to check whether their subjective probability or frequency estimates for the event correspond with the assumed objective value for that event. When a person's estimate for the event exceeds its assumed objective probability or frequency, the person's expectancy for the event is concluded to be greater than warranted. This paper describes three lines of reasoning as to why conclusions of this sort can be problematic. Recently published findings as well as data from two new experiments are described to support this main thesis. The case of smoking risk is used to illustrate the more general problem, and issues that must be considered to avoid or contend with the problem are discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Supersize My Chances: Promotional Lotteries Impact Product Size Choices

Promotional lotteries offer consumers a chance to win one of many prizes along with their purchase. Critically, as is often the case, these campaigns not only include an assortment of prizes but also an assortment of offerings that one can buy to enter the lottery—such as a small or an extra‐large coffee. While companies regularly advertise that the objective odds of winning do not vary by the size of their product offerings, recent anecdotal evidence suggest that consumers behave as if it does. The net result is that consumers seem to be supersizing during promotional lotteries, and thus purchasing larger sized items. Eight studies (four core and four supplementary in Supporting information ) and a single‐paper meta‐analysis confirm that the supersizing phenomenon is indeed real and provides evidence that this behavior is the manifestation of consumers elevating their sense of control. Specifically, supersizing serves to gain psychological control over the pursuit of a desirable, but seemingly unobtainable, outcome.     

The Consistency Argument for Ranking Functions

The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Reducing cognitive biases in probabilistic reasoning by the use of logarithm formats

Research on probability judgment has traditionally emphasized that people are susceptible to biases because they rely on “variable substitution”: the assessment of normative variables is replaced by assessment of heuristic, subjective variables. A recent proposal is that many of these biases may rather derive from constraints on cognitive integration, where the capacity-limited and sequential nature of controlled judgment promotes linear additive integration, in contrast to many integration rules of probability theory (Juslin, Nilsson, & Winman, 2009). A key implication by this theory is that it should be possible to improve peoples’ probabilistic reasoning by changing probability problems into logarithm formats that require additive rather than multiplicative integration. Three experiments demonstrate that recasting tasks in a way that allows people to arrive at the answers by additive integration decreases cognitive biases, and while people can rapidly learn to produce the correct answers in an additive formats, they have great difficulty doing so with a multiplicative format.     

Formalization of Reliability Block Diagrams in Higher-order Logic

Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability and maintainability analyses. Traditionally, these RBD-based analyses are done using paper-and-pencil proofs or computer simulations, which cannot ascertain absolute correctness due to their inaccuracy limitations. As a complementary approach, we propose to use the higher-order logic theorem prover HOL to conduct RBD-based analysis. For this purpose, we present a higher-order logic formalization of commonly used RBD configurations, such as series, parallel, parallel-series and series-parallel, and the formal verification of their equivalent mathematical expressions. A distinguishing feature of the proposed RBD formalization is the ability to model nested RBD configurations, which are RBDs having blocks that also represent RBD configurations. This generality allows us to formally analyze the reliability of many real-world systems. For illustration purposes, we formally analyze the reliability of a generic Virtual Data Center (VDC) in a cloud computing infrastructure exhibiting the nested series-parallel RBD configuration.     

Updating a progic

This paper presents a progic, or probabilistic logic, in the sense of Haenni et al. [8]. The progic presented here is based on Bayesianism, as the progic discussed by Williamson [15]. However, the underlying generalised Bayesianism differs from the objective Bayesianism used by Williamson, in the calibration norm, and the liberalisation and interpretation of the reference probability in the norm of equivocation. As a consequence, the updating dynamics of both Bayesianisms differ essentially. Whereas objective Bayesianism is based on a probabilistic re-evaluation, orthodox Bayesianism is based on a probabilistic revision. I formulate a generalised and iterable orthodox Bayesian revision dynamics. This allows to define an updating procedure for the generalised Bayesian progic. The paper compares the generalised Bayesian progic and Williamson's objective Bayesian progic in strength, update dynamics and with respect to language (in)sensitivity.