Skill Rating by Bayesian Inference

Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players’ skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of games by players across a broad FIDE Elo range, and is in principle applicable to any scenario where high-value decisions are being made under pressure

Intrinsic chess rating

This paper develops and tests formulas for representing playing strength at chess by the quality of moves played, rather than by the results of games. Intrinsic quality is estimated via evaluations given by computer chess programs run to high depth, ideally so that their playing strength is sufficiently far ahead of the best human players as to be a `relatively omniscient' guide. Several formulas, each having intrinsic skill parameters s for `sensitivity' and c for `consistency', are argued theoretically and tested by regression on large sets of tournament games played by humans of varying strength as measured by the internationally standard Elo rating system. This establishes a correspondence between Elo rating and the parameters. A smooth correspondence is shown between statistical results and the century points on the Elo scale, and ratings are shown to have stayed quite constant over time. That is, there has been little or no `rating inflation'. The theory and empirical results are transferable to other rational-choice settings in which the alternatives have well-defined utilities, but in which complexity and bounded information constrain the perception of the utility values

A Simpler Proof of PH C BP[ӨP]

We simplify the proof by S. Toda [Tod89] that the polynomial hierarchy PH is contained in BP[ӨP]. Our methods bypass the technical quantifier interchange lemmas in the original proof, and clarify the counting principles on which the result depends. We also show that relative to a random oracle R, PHR is strictly contained in ӨPR

The "ART" of Linkage: Pre-Treatment Loss to Care after HIV Diagnosis at Two PEPFAR Sites in Durban, South Africa

BACKGROUND. Although loss to follow-up after antiretroviral therapy (ART) initiation is increasingly recognized, little is known about pre-treatment losses to care (PTLC) after an initial positive HIV test. Our objective was to determine PTLC in newly identified HIV-infected individuals in South Africa. METHODOLOGY/PRINCIPAL FINDINGS. We assembled the South African Test, Identify and Link (STIAL) Cohort of persons presenting for HIV testing at two sites offering HIV and CD4 count testing and HIV care in Durban, South Africa. We defined PTLC as failure to have a CD4 count within 8 weeks of HIV diagnosis. We performed multivariate analysis to identify factors associated with PTLC. From November 2006 to May 2007, of 712 persons who underwent HIV testing and received their test result, 454 (64%) were HIV-positive. Of those, 206 (45%) had PTLC. Infected patients were significantly more likely to have PTLC if they lived =10 kilometers from the testing center (RR=1.37; 95% CI: 1.11-1.71), had a history of tuberculosis treatment (RR=1.26; 95% CI: 1.00-1.58), or were referred for testing by a health care provider rather than self-referred (RR=1.61; 95% CI: 1.22-2.13). Patients with one, two or three of these risks for PTLC were 1.88, 2.50 and 3.84 times more likely to have PTLC compared to those with no risk factors. CONCLUSIONS/SIGNIFICANCE. Nearly half of HIV-infected persons at two high prevalence sites in Durban, South Africa, failed to have CD4 counts following HIV diagnosis. These high rates of pre-treatment loss to care highlight the urgent need to improve rates of linkage to HIV care after an initial positive HIV test.US National Institute of Allergy and Infectious Diseases (R01 AI058736, K24 AI062476, K23 AI068458); the Harvard University Center for AIDS Research (P30 AI42851); National Institutes of Health (K24 AR 02123); the Doris Duke Charitable Foundation (Clinical Scientist Development Award); the Harvard University Program on AID

Minimum-complexity pairing functions

AbstractPairing functions are bijections from N x N to N, and they are important in logic, computing, and mathematics on the whole. We exhibit the first known pairing function 〈 ·, ·〉 which is computable in linear time and constant space. In fact, both 〈·, ·〉 and its inverse are computable by finite-state transducers which run in real time. By contrast, the familiar examples of pairing functions in the literature are computable in linear time if and only if integer multiplication can be accomplished in linear time, which is considered doubtful by many. We also present two kinds of monotone pairing functions which are computable on-line in linear time and log space; the first is also computable off-line in zero space. We conjecture that every monotone pairing function requires log space to compute on-line

Diagonalization, uniformity, and fixed-point theorems

AbstractWe derive new fixed-point theorems for subrecursive classes, together with a theorem on the uniformity of certain reductions, from a general formulation of the technique of delayed diagonalization. This formulation extends the main theorem of U. Schöning (Theoret. Comput. Sci. 18 (1982), 95–103) to cases which involve infinitely many diagonal classes Ck, and which allow each Ck to contain uncountably many members. The main technical work ties the familiar concept of a witness function directly to the often-studied Cantor-set topology on languages, and provides a “delay construction” which refines those due to Schöning, S. Breidtbart, and D. Schmidt. Our “a.e.” fixed-point theorems do not require that the “programming system” for the subrecursive class in question be well-behaved; we compare them to results which do. The other theorem is similar to the “uniform boundedness theorem” of classical analysis, and extends work of J. Grollmann and A. Selman

Index sets and presentations of complexity classes

AbstractThis paper draws close connections between the ease of presenting a given complexity class b and the position of the index sets Ib = [lcub]i : L(Mi) ϵ b[rcub] and Jb = [lcub]i : Miis total ΛL(Mi) ∉ b[rcub] in the arithmetical hierarchy. For virtually all classes b studied in the literature, the lowest levels attainable are Ib ϵ ∑03 and Jb ϵ Π02; the first holds iff b is Δ02-presentable, and the second iff b is recursively presentable. A general kind of priority argument is formulated, and it is shown that every property enforcible by it is not recursively presentable. It follows that the classes of P-immune and P-biimmune languages in exponential time are not recursively presentable. It is shown that for all b with Ib ∉ ∑03, “many” members of b do not provably (in true Π2-arithmetic) belong to b. A class H is exhibited such that IH ϵ ∑03 is open, and IH ∉ ∑03 implies that the polynomial hierarchy is infinite