Empirical bayes estimates of domain scores under binomial and hypergeometric distributions for test scores

We introduce two simple empirical approximate Bayes estimators (EABEs)— and —for estimating domain scores under binomial and hypergeometric distributions, respectively. Both EABEs (derived from corresponding marginal distributions of observed test scorex without relying on knowledge of prior domain score distributions) have been proven to hold -asymptotic optimality in Robbins' sense of convergence in mean. We found that, where and are the monotonized versions of and under Van Houwelingen's monotonization method, respectively, the convergence rate of the overall expected loss of Bayes risk in either or depends on test length, sample size, and ratio of test length to size of domain items. In terms of conditional Bayes risk, and outperform their maximum likelihood counterparts over the middle range of domain scales. In terms of mean-squared error, we also found that: (a) given a unimodal prior distribution of domain scores, performs better than both and a linear EBE of the beta-binomial model when domain item size is small or when test items reflect a high degree of heterogeneity; (b) performs as well as when prior distribution is bimodal and test items are homogeneous; and (c) the linear EBE is extremely robust when a large pool of homogeneous items plus a unimodal prior distribution exists.The authors are indebted to both anonymous reviewers, especially Reviewer 2, and the Editor for their invaluable comments and suggestions. Thanks are also due to Yuan-Chin Chang and Chin-Fu Hsiao for their help with our simulation and programming work.     

What Conditional Probability Could Not Be

Kolmogorov's axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0"> Call this the ratio analysis of conditional probability. It has become so entrenched that it is often referred to as the definition of conditional probability.I argue that it is not even an adequate analysis of that concept. I prove what I call the Four Horn theorem, concluding that every probability assignment has uncountably many trouble spots. Trouble spots come in four varieties: assignments of zero togenuine possibilities; assignments of infinitesimals to such possibilities; vague assignments to such possibilities; and no assignment whatsoever to such possibilities. Each sort of trouble spot can create serious problems for the ratio analysis. I marshal manyexamples from scientific and philosophical practice against the ratio analysis. I conclude more positively: we should reverse the traditional direction of analysis. Conditional probability should be taken as the primitive notion, and unconditional probability should be analyzed in terms of it. I'd probably be famous now If I wasn't such a good waitress. Jane Siberry, Waitress     

The new experimental aesthetics—The beginning or the end?

In reference to recent work in aesthetics from a scientific perspective, Berlyne coined the phrase the new experimental aesthetics. Berlyne's contributions to this research area are discussed in terms of the philosophical, theoretical, and methodological issues central to the current literature. The paper concludes with a consideration of the future prospects for experimental aesthetics.This paper was presented at a symposium in honor of Daniel E. Berlyne at the annual meeting of the American Psychological Association, San Francisco, August 27, 1977. The presentation of this paper was supported by a grant from York University.     

The resting membrane potential of cells are measures of electrical work,not of ionic currents

Living cells create electric potential force,E, between their various phases by at least three distinct mechanisms. Charge separation,

Comparison of ranks of cross-product and covariance solutions in component analysis

SupposeD is a data matrix forN persons andn variables, and is the matrix obtained fromD by expressing the variables in deviation-score form. It is shown that ifD has rankr, will always have rank (r−1) ifr=N<n, otherwise it will generally have rankr. If has ranks,D will always have ranks ifs=n, but ifs<n it will generally have rank (s+1). Thus two cases can arise, Case A in whichD has rank one greater than , and Case B in whichD has rank equal to . Implications of this distinction for analysis of cross products versus analysis of covariances are briefly indicated.     

On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

Completeness theorems for some intermediate predicate calculi

We give completeness results — with respect to Kripke's semantic — for the negation-free intermediate predicate calculi: (1) $$\begin{gathered} BD = positive predicate calculus PQ + B:(\alpha \to \beta )v(\beta \to \alpha ) \hfill \\ + D:\forall x\left( {a\left( x \right)v\beta } \right) \to \forall xav\beta \hfill \\ \end{gathered}$$ (2) $$T_n D = PQ + T_n :\left( {a_0 \to a_1 } \right)v \ldots v\left( {a_n \to a_{n + 1} } \right) + D\left( {n \geqslant 0} \right)$$ and the superintuitionistic predicate calculus: (3) $$B^1 DH_2^ \urcorner = BD + intuitionistic negation + H_2^ \urcorner : \urcorner \forall xa \to \exists x \urcorner a.$$ The central point is the completeness proof for (1), which is obtained modifying Klemke's construction [3]. For a general account on negation-free intermediate predicate calculi — see Casari-Minari [1]; for an algebraic treatment of some superintuitionistic predicate calculi involving schemasB andD — see Horn [4] and Görnemann [2].     

Realisms

It is argued that the general thesis of realism is ill-defined, as are various versions of its denial. Only specific theses of the form There areK's make clear sense. It is also argued that various efforts to deny realism always turn out to deny specific existential theses. Thus, it is argued, van Fraassen and Schwartz deny the existence of electrons.     

Rhetoric and Double Hermeneutics in the Human Sciences

Based on an analysis of double hermeneutics in the human sciences, a distinction between a weak and a strong rhetorical analysis of human-scientific research is introduced, taking account of the self-reflective character of hermeneutic interpretation. The paper argues that there are three hermeneutic topics in the research process for human-scientific experience, which are associated with applying specific rhetorical tools. The three topics are described under the following rubrics: (a) bridging the gap between experience-near and experience-distant concepts; (b) achieving integrity of the cultural objects dispersed in different interpretive strategies; and (c) taking into consideration that an important task of hermeneutic interpretation in human-scientific research is to give an account of the object's immanent narrative coherence. The paper is written in the conviction that a kind of re-methodologization of philosophical hermeneutics which does not rehabilitate epistemological foundationalism can provide a new philosophical identity to the human sciences.     

Positive modal logic

We give a set of postulates for the minimal normal modal logicK ₊ without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are

Kotarbiński As A Scientific Realist

Tadeusz Kotarbiski is widely recognized as a major philosopher of theLvov–Warsaw school. His reism, which is a contribution to semantics andontology, is still discussed and debated, and his most original creation, praxiology,has grown into an entire research field. However, Kotarbiski's philosophy ofscience has not received much attention by later commentators. This paper attemptsto correct this situation by considering the hypothesis that Kotarbiski succeededalready in 1929 in formulating a position that can be regarded as an early version ofscientific realism. Unlike most other ``scientific philosophers' before the mid-thirties,he was able to combine ontological realism (by defending a form of physicalism andnominalism) and semantical realism (by defending the classical correspondence theoryof truth). He was also a critical epistemological realist. Further, in spite of theinstrumentalist flavour of his reductionist programme in eliminating terms apparentlyreferring to abstract entities, Kotarbiski accepted theories as statements with truth values and theoretical entities as long as they can be understood as physical bodies.     

Unique Events: The Underdetermination of Explanation

The paper explicates unique events and investigates their epistemology. Explications of unique events as individuated, different, and emergent are philosophically uninteresting. Unique events are topics of why-questions that radically underdetermine all their potential explanations. Uniqueness that is relative to a level of scientific development is differentiated from absolute uniqueness. Science eliminates relative uniqueness by discovery of recurrence of events and properties, falsification of assumptions of why-questions, and methodological simplification e.g. by explanatory methodological reduction. Finally, an overview of contemporary philosophical disputes that hinge on issues of uniqueness emphasizes its philosophical significance.     

Axiomatizing collective judgment sets in a minimal logical language

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of individuals accepts, consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.     

A Theory of Belief for Scientific Refutations

A probability function on an algebra of events is assumed. Some of the events are scientific refutations in the sense that the assumption of their occurrence leads to a contradiction. It is shown that the scientific refutations form a a boolean sublattice in terms of the subset ordering. In general, the restriction of to the sublattice is not a probability function on the sublattice. It does, however, have many interesting properties. In particular, (i) it captures probabilistic ideas inherent in some legal procedures; and (ii) it is used to argue against the commonly held view that behavioral violations of certain basic conditions for qualitative probability are indicative of irrationality. Also discussed are (iii) the relationship between the formal development of scientific refutations presented here and intuitionistic logic, and (iv) an interpretation of a belief function used in the behavioral sciences to explain empirical results about subjective, probabilistic estimation, including the Ellsberg paradox.     

Beyond Psychotherapy: Dialectical Therapy

Dialectical therapy is a common factors approach to psychotherapy integration, in which four general therapeutic strategies are taken as the cardinal points of a map of the field. It is said to be beyond psychotherapy because what is commonly referred to as psychotherapy is more than psychological treatment. It is a dialectic between two basic levels or axes: the psychological remaking, which deals with defect-driven disorders, and the philosophical uncovering, which deals with conflict-driven problems. The first level can be graphically represented as the horizontal axis of the field, connecting a maternal and a paternal pole, in which the therapist responds to the basic psychological needs of secure attachment and responsible cooperation. The second level can be represented as the vertical axis of the field, connecting a K (knowledge) vertex and an O (unknown) vertex, in which the therapist responds to the basic philosophical needs of knowledge (know thyself) and of unknown as unknowable (the noumenon of all phaenomena, the source of generative and healing powers). A map is necessary to organize the basic therapeutic needs and the range of responses to them in a coherent pattern. As a good map can help in orienting empirical research, this in turn can help in constructing better maps.     

Crossan on the Couch, Along with the Rest of Us: Part Two: Six Proposals Toward a New Paradigm for a Psychologically Realistic Approach to the Search for the Historical Jesus as Suggested by the Work of Hal Childs

Building on the theoretical basis spelled out in my first article on Hal Childs' The Myth of the Historical Jesus and the Evolution of Consciousness, the present article engages in dialogue with Crossan's 2000 autobiography, A Long Way From Tipperary. The dialogue focuses on six proposals emerging from Childs' work that advocate the inclusion of psychological realism in rethinking the task, practice, and outcome of historical Jesus research. The six proposals are as follows: first, that psychological realism is an essential part of historical realism; second, that unconscious factors are to be considered at work in the viewer as well as in the viewed in historical Jesus research; third, that every reconstruction of the historical Jesus is mythic; fourth, that the preunderstanding that the Jesus scholar brings to historical Jesus research is generated within a hermeneutical circle constituted by a vast web of relationships, purposes, and meanings that include every aspect of the scholar's life; fifth, that the final goal of historical Jesus research is not the facts about the historic Jesus, but the meaning of these facts as archetypal images for self-understanding, world-understanding, and the evolution of consciousness; and sixth, that the purpose of the Gospel is to evoke new archetypal projections in the reader that can lead to new incarnations of the archetypal Self awakened and informed by the story of Jesus, often as recovered by the Jesus historian.     

Comment: Duhem's middle way

Duhem attempted to find a middle way between two positions he regarded as extremes, the conventionalism of Poincaré and the scientific realism of the majority of his scientific colleagues. He argued that conventionalism exaggerated the arbitrariness of scientific formulations, but that belief in atoms and electrons erred in the opposite direction by attributing too much logical force to explanatory theories. The instrumentalist sympathies so apparent in Duhem's writings on the history of astronomy are only partially counterbalanced by his view that science is progressing toward a natural classification of the world.