Context Of Probability Research Articles

Evidenced-Based Prior for Estimating the Treatment Effect of Phase III Randomized Trials in Oncology.

The primary results of phase III oncology trials may be challenging to interpret, given that results are generally based on P value thresholds. The probability of whether a treatment is beneficial, although more intuitive, is not usually provided. Here, we developed and released a user-friendly tool that calculates the probability of treatment benefit using trial summary statistics. We curated 415 phase III randomized trials enrolling 338,600 patients published between 2004 and 2020. A phase III prior probability distribution for the treatment effect was developed on the basis of a three-component zero-mean mixture distribution of the observed z-scores. Using this prior, we computed the probability of clinically meaningful benefit (hazard ratio [HR] <0.8). The distribution of signal-to-noise ratios and power of phase III oncology trials were compared with that of 23,551 randomized trials from the Cochrane Database. The signal-to-noise ratios of phase III oncology trials tended to be much larger than randomized trials from the Cochrane Database. Still, the median power of phase III oncology trials was only 49% (IQR, 14%-95%), and the power was <80% in 65% of trials. Using the phase III oncology-specific prior, only 53% of trials claiming superiority (114 of 216) had a ≥90% probability of clinically meaningful benefits. Conversely, the probability that the experimental arm was superior to the control arm (HR <1) exceeded 90% in 17% of trials interpreted as having no benefit (34 of 199). By enabling computation of contextual probabilities for the treatment effect from summary statistics, our robust, highly practical tool, now posted on a user-friendly webpage, can aid the wider oncology community in the interpretation of phase III trials.

Contextual measurement model and quantum theory.

We develop a contextual measurement model (CMM) that is used for the clarification of the quantum foundations. This model matches Bohr's views on the role of experimental contexts. CMM is based on a contextual probability theory that is connected with generalized probability theory. CMM covers measurements in classical, quantum and semi-classical physics. The CMM formalism is illustrated by a few examples. We consider the CMM framing of classical probability, the von Neumann measurement theory and the quantum instrument theory. CMM can also be applied outside of physics, e.g. in cognition, decision-making and psychology, the so-called quantum-like modelling.

On the Mathematical Relationship Between Contextual Probability and N400 Amplitude.

Accounts of human language comprehension propose different mathematical relationships between the contextual probability of a word and how difficult it is to process, including linear, logarithmic, and super-logarithmic ones. However, the empirical evidence favoring any of these over the others is mixed, appearing to vary depending on the index of processing difficulty used and the approach taken to calculate contextual probability. To help disentangle these results, we focus on the mathematical relationship between corpus-derived contextual probability and the N400, a neural index of processing difficulty. Specifically, we use 37 contemporary transformer language models to calculate the contextual probability of stimuli from 6 experimental studies of the N400, and test whether N400 amplitude is best predicted by a linear, logarithmic, super-logarithmic, or sub-logarithmic transformation of the probabilities calculated using these language models, as well as combinations of these transformed metrics. We replicate the finding that on some datasets, a combination of linearly and logarithmically-transformed probability can predict N400 amplitude better than either metric alone. In addition, we find that overall, the best single predictor of N400 amplitude is sub-logarithmically-transformed probability, which for almost all language models and datasets explains all the variance in N400 amplitude otherwise explained by the linear and logarithmic transformations. This is a novel finding that is not predicted by any current theoretical accounts, and thus one that we argue is likely to play an important role in increasing our understanding of how the statistical regularities of language impact language comprehension.

Contextual Ranking and Selection with Gaussian Processes and OCBA

In many real world problems, we are faced with the problem of selecting the best among a finite number of alternatives, where the best alternative is determined based on context specific information. In this work, we study the contextual Ranking and Selection problem under a finite-alternative-finite-context setting, where we aim to find the best alternative for each context. We use a separate Gaussian process to model the reward for each alternative, and derive the large deviations rate function for both the expected and worst-case contextual probability of correct selection. We propose the GP-C-OCBA sampling policy, which uses the Gaussian process posterior to iteratively allocate observations to maximize the rate function. We prove its consistency and show that it achieves the optimal convergence rate under the assumption of a non-informative prior. Numerical experiments show that our algorithm is highly competitive in terms of sampling efficiency, while having significantly smaller computational overhead.

Contextuality, Complementarity, Signaling, and Bell Tests

This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.

Contextual Priors Guide Perception and Motor Responses to Observed Actions.

In everyday-life scenarios, prior expectations provided by the context in which actions are embedded support action prediction. However, it is still unclear how newly learned action-context associations can drive our perception and motor responses. To fill this gap, we measured behavioral (Experiment 1) and motor responses (Experiment 2) during two tasks requiring the prediction of occluded actions or geometrical shapes. Each task consisted of an implicit probabilistic learning and a test phase. During learning, we exposed participants to videos showing specific associations between a contextual cue and a particular action or shape. During the test phase, videos were earlier occluded to reduce the amount of sensorial information and induce participants to use the implicitly learned action/shape-context associations for disambiguation. Results showed that reliable contextual cues made participants more accurate in identifying the unfolding action or shape. Importantly, motor responses were modulated by contextual probability during action, but not shape prediction. Particularly, in conditions of perceptual uncertainty the motor system coded for the most probable action based on contextual informativeness, regardless of action kinematics. These findings suggest that contextual priors can shape motor responses to action observation beyond mere kinematics mapping.

Tracking who knows what: epistemic gaps and the prosodic realization of corrective focus

AbstractCorrective information is produced with higher prosodic prominence than non-corrective information. However, it remains unclear how corrective prosody is realized in different communicative settings. We conducted two production experiments to investigate whether interlocutors’ prosodic realization of corrective focus depends on each other’s knowledge state. Participants carried out a statement-response task in pairs (e.g., Speaker B:Tina had shrimp at a restaurant. Speaker A:No, she had beef at a restaurant.). Our focus is on the prosody of Speaker A’s utterance. We manipulated whether Speaker B’s statement was implausible in the context (e.g., a context where it is known that Tina actually hates seafood). Furthermore, the two experiments differed in whether Speaker B knew that their statement (e.g., about Tina eating shrimp at a restaurant) was (im)plausible. In Experiment 1, both speakers had access to the crucial context concerning the probability of Speaker A’s statement (Tina’s preferences about food). In Experiment 2, only Speaker A had access to this background information. We found that Speaker A’s prosody when responding to Speaker B was influenced by both (i) the contextual probability of Speaker B’s statements and (ii) Speaker B’s knowledge (or lack thereof) about the contextual probability. We present an analysis where the prosodic prominence associated with corrective information reflects the gap between expectation and reality – in this case, what Speaker A had expected Speaker B to say and what Speaker B actually says.

Implied speaker attributes in standard sentence materials: Implications for sociophonetic research

Studies have shown that sentence intelligibility is affected by listeners' knowledge of attributes of talkers being perceived, such as their race [e.g., Babel and Russell, J. Acoust. Soc. Am. 137 (2015)]. Some of these studies have used the standard IEEE/Harvard sentences [IEEE Trans. Audio Electroacoust. 17 (1969)] which were developed to be phonetically balanced with low contextual probability. Hence, their content alone ought to not convey anything about speaker attributes. The current study tests this by examining ratings of 124 individuals of 80 written IEEE sentences, and a comparison set of 80 sentences from the internet discussion forum Reddit. The latter served as comparisons that were more likely to convey social attributes. Individuals rated the naturalness of the sentences, and whether they conveyed the gender and race of a person who might produce them. The IEEE sentences were rated less natural than the Reddit sentences, and less likely to convey race or gender. However, on average, 25% of the raters deemed each IEEE sentence to convey speaker gender, and 18% deemed them to convey speaker race. These findings caution against using the IEEE sentences as socially neutral stimuli in studies of talker attributes and speech intelligibility. [Funded by NIH.]

The Hemorrhaging Woman and Jairus’ Daughter as Representatives of Israel

The scope of the present study is the symbolic analysis of the two interwoven Markan narratives about the healing of the woman with the flow of blood (5:25-34) and the raising of Jairus’ daughter (5:21-24.35-43). The principal thesis of this work consists in interpreting both women as symbols of Israel. The study begins with the presentation of the methodological premises of symbolic analysis. The main methodological premise of this work is the conviction that the literary sense of this pericope is in fact imbued with symbolism. Then there is a presentation of three criteria which help in detecting symbols in the biblical text: textual probability, conventions probability and contextual probability. Subsequently, in order to lend credence to the principal thesis of the article, seventeen literary elements found in Mark 5:21-43 are discussed; each of them meets the first two criteria and lends itself to symbolic interpretation of the two women as representations of Israel. The cumulative weight of these seventeen elements creates a rather strong cumulative argument in favor of the main thesis. Finally, the conformity between the symbolic interpretation of these women and both the immediate and global contexts of this pericope is discussed. The presence of this conformity meets the third criterion of contextual probability. The article thus offers a convincing case for the symbolic interpretation of the hemorrhaging woman and Jairus’ daughter in Mark 5:21-43 as representations of Israel.

Dissociable neural effects of temporal expectations due to passage of time and contextual probability

The human brain is equipped with complex mechanisms to track the changing probability of events in time. While the passage of time itself usually leads to a mounting expectation, context can provide additional information about when events are likely to happen. In this study we dissociate these two sources of temporal expectation in terms of their neural correlates and underlying brain connectivity patterns. We analysed magnetoencephalographic (MEG) data acquired from N = 24 healthy participants listening to auditory stimuli. These stimuli could be presented at different temporal intervals but occurred most often at intermediate intervals, forming a contextual probability distribution. Evoked MEG response amplitude was sensitive to both passage of time (time elapsed since the cue) and contextual probability, albeit at different latencies: the effects of passage of time were observed earlier than the effects of context. The underlying sources of MEG activity were also different across the two types of temporal prediction: the effects of passage of time were localised to early auditory regions and superior temporal gyri, while context was additionally linked to activity in inferior parietal cortices. Finally, these differences were modelled using biophysical (dynamic causal) modelling: passage of time was explained in terms of widespread gain modulation and decreased prediction error signalling at lower levels of the hierarchy, while contextual expectation led to more localised gain modulation and decreased prediction error signalling at higher levels of the hierarchy. These results present a comprehensive account of how independent sources of temporal prediction may be differentially expressed in cortical circuits.

Mergers in Bardi: contextual probability and predictors of sound change

Abstract A crucial question for historical linguistics has been why some sound changes happen but not others. Recent work on the foundations of sound change has argued that subtle distributional facts about segments in a language, such as functional load, play a role in facilitating or impeding change. Thus not only are sound changes not all equally plausible, but their likelihood depends in part on phonotactics and aspects of functional load, such as the density of minimal pairs. Tests of predictability on the chance of phoneme merger suggest that phonemes with low functional load (as defined by minimal pair density) are more likely to merge, but this has been investigated only for a small number of languages with very large corpora and well attested mergers. Here we present work suggesting that the same methods can be applied to much smaller corpora, by presenting the results of a preliminary exploration of nine Australian languages, with a particular focus on Bardi, a Nyulnyulan language from Australia’s northwest. Our results support the hypothesis that the probability of merger is higher when phonemes distinguish few minimal pairs.

Assessing predictability effects in connected read speech

Abstract A wide range of reduction phenomena have been described in the literature as predictability effects, in which more predictable units (i.e. words, syllables, vowels) are reduced in duration or other acoustic dimensions relative to less predictable units. The goal of the current study was to critically evaluate these predictability effects on vowel duration in read speech to explore the extent to which they reflect a single underlying phenomenon. The results revealed shorter vowel duration for words with high phonotactic probability, for high-frequency words (in clear speech only), and for words in plain lab speech relative to clear speech. However, the results also revealed qualitatively different effects of three measures of contextual probability (cloze probability, written trigram probability, and spoken trigram probability). Greater spoken trigram probability predicted longer vowel duration, contrary to expectations, and this effect was limited to high-frequency words in first mentions and in plain speech. Cloze probability and written trigram probability exhibited even more complex interactions with other predictability measures. These results provide evidence for fundamental differences in these measures of predictability, suggesting that a more nuanced perspective on predictability effects and the mechanisms underlying them is necessary to account for the complexity of the empirical data.

Contextual predictability influences word and morpheme duration in a morphologically complex language (Kaqchikel Mayan).

The probability is one of the many factors which influence phonetic variation. Contextual probability, which describes how predictable a linguistic unit is in some local environment, has been consistently shown to modulate the phonetic salience of words and other linguistic units in speech production (the probabilistic reduction effect). In this paper the question of whether the probabilistic reduction effect, as previously observed for majority languages like English, is also found in a language (Kaqchikel Mayan) which has relatively rich morphology is explored. Specifically, whether the contextual predictability of words and morphemes influences their phonetic duration in Kaqchikel is examined. It is found that the contextual predictability of a word has a significant effect on its duration. The effect is manifested differently for lexical words and function words. It is also found that the contextual predictability of certain prefixes in Kaqchikel affects their duration, showing that contextual predictability may drive reduction effects at multiple levels of structure. While the findings are broadly consistent with many previous studies (primarily on English), some of the details of the results are different. These differences highlight the importance of examining the probabilistic reduction effect in languages beyond the majority, Indo-European languages most commonly investigated in experimental and corpus linguistics.

Toward A database of intracranial electrophysiology during natural language presentation

ABSTRACT Intracranial electrophysiology (iEEG) studies using cognitive tasks contribute to the understanding of the neural basis of language. However, though iEEG is recorded continuously during clinical treatment, due to patient considerations task time is limited. To increase the usefulness of iEEG recordings for language study we provided patients with a tablet pre-loaded with media filled with natural language, wirelessly synchronised to clinical iEEG. This iEEG data collected and time-locked to natural language presentation is particularly applicable for studying the neural basis of combining words into larger contexts. We validate this approach with pilot analyses involving words heard during a movie, tagging syntactic properties and verb contextual probabilities. Event-related averages of high-frequency power (70–170 Hz) identified bilateral perisylvian electrodes with differential responses to syntactic class and a linear regression identified activity associated with contextual probabilities, demonstrating the usefulness of aligning media to iEEG. We imagine future multi-site collaborations building an “intracranial neurolinguistic corpus”.

Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management.

The paper starts with a brief review of the literature about uncertainty in geological, geophysical and petrophysical data. In particular, we present the viewpoints of experts in geophysics on the application of Bayesian inference and subjective probability. Then we present arguments that the use of classical probability theory (CP) does not match completely the structure of geophysical data. We emphasize that such data are characterized by contextuality and non-Kolmogorovness (the impossibility to use the CP model), incompleteness as well as incompatibility of some geophysical measurements. These characteristics of geophysical data are similar to the characteristics of quantum physical data. Notwithstanding all this, contextuality can be seen as a major deviation of quantum theory from classical physics. In particular, the contextual probability viewpoint is the essence of the Växjö interpretation of quantum mechanics. We propose to use quantum probability (QP) for decision-making during the characterization, modelling, exploring and management of the intelligent hydrocarbon reservoir Quantum Bayesianism (QBism), one of the recently developed information interpretations of quantum theory, can be used as the interpretational basis for such QP decision-making in geology, geophysics and petroleum projects design and management.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Syntax and operational semantics of a probabilistic programming language with scopes

Dzhafarov and Kujala (2015) have introduced a contextual probability theory called Contextuality-by-Default (C-b-D) which is based on three principles. The first of these principles states that each random variable should be automatically labelled by all conditions under which it is recorded. The aim of this article is to relate this principle to block structured computer programming languages where variables are declared local to a construct called a “scope”. Scopes are syntactic constructs which correspond to the notion of condition used by C-b-D. In this way a variable declared in two scopes can be safely overloaded meaning that they can have the same label but preserve two distinct identities without the need to label each variable in each condition as advocated by C-b-D. By means of examples, the notion of a probabilistic program, or P-program, is introduced which is based on scopes. The semantics of P-programs will be illustrated using the well known relational database language SQL which provides an efficient and understandable operational semantics. A core issue addressed is how to construct a single probabilistic model from the various interim probability distributions returned by each syntactic scope. For this purpose, a probabilistic variant of the natural join operator of relational algebra is used to “glue” together interim distributions into a single distribution. More generally, this article attempts to connect contextuality with probabilistic programming by means of relational database theory.

Data-mining to build a knowledge representation store for clinical decision support. Studies on curation and validation based on machine performance in multiple choice medical licensing examinations

Extracting medical knowledge by structured data mining of many medical records and from unstructured data mining of natural language source text on the Internet will become increasingly important for clinical decision support. Output from these sources can be transformed into large numbers of elements of knowledge in a Knowledge Representation Store (KRS), here using the notation and to some extent the algebraic principles of the Q-UEL Web-based universal exchange and inference language described previously, rooted in Dirac notation from quantum mechanics and linguistic theory. In a KRS, semantic structures or statements about the world of interest to medicine are analogous to natural language sentences seen as formed from noun phrases separated by verbs, prepositions and other descriptions of relationships. A convenient method of testing and better curating these elements of knowledge is by having the computer use them to take the test of a multiple choice medical licensing examination. It is a venture which perhaps tells us almost as much about the reasoning of students and examiners as it does about the requirements for Artificial Intelligence as employed in clinical decision making. It emphasizes the role of context and of contextual probabilities as opposed to the more familiar intrinsic probabilities, and of a preliminary form of logic that we call presyllogistic reasoning.

Context and paradigms

A small but growing body of research on English and Dutch has found that pronunciation of affixes in a word form is sensitive to paradigmatic probability – i.e., the probability of using that form over other words in the same morphological paradigm. Yet it remains unclear (a) how paradigmatic probability is best measured; (b) whether an increase in paradigmatic probability leads to phonetic enhancement or reduction; and (c) by what mechanism paradigmatic probability can affect pronunciation. The current work examines pronunciation variation of Russian verbal agreement suffixes. I show that there are two distinct patterns of variation, corresponding to two different measures of paradigmatic probability. One measure, pairwise paradigmatic probability, is associated with a pronunciation pattern that resembles phonetic enhancement. The second measure, lexeme paradigmatic probability, can show enhancement effects, but can also yield reduction effects more similar to those of contextual probability. I propose that these two patterns can be explained in an exemplar model of lexical storage. Reduction effects are the consequence of faster retrieval and encoding of an articulatory target, while effects that resemble enhancement result when the pronunciation target of both members of a pair of competing word forms is shifted towards the more frequent of two.

Quantum-like modeling of cognition

This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

Probabilistic reduction and probabilistic enhancement

Research on probabilistic pronunciation variation has generally focused on contextual probability, or the probability of using a linguistic unit (segment, syllable, word, etc.) in the context of a particular utterance. Overwhelmingly, this research has found that higher contextual probability leads to phonetic reduction. Less attention, however, has been given to paradigmatic probability, or the probability of using a particular linguistic form from a paradigm of related forms. The research that has addressed this type of probability has found inconsistent results: Sometimes higher paradigmatic probability leads to phonetic enhancement, and sometimes to phonetic reduction. In this paper I present the results of an experiment exploring the effects of both types of probability simultaneously on the pronunciation of agreement suffixes on English verbs. I find that (i) singular verb suffixes and stems are phonetically reduced when singular agreement is contextually probable; (ii) the nature of the reduction is modulated by verb frequency, consistent with dual-route models of lexical retrieval; and (iii) suffixes are phonetically enhanced when they are paradigmatically probable. I conclude by discussing how the patterns observed in this study shed light on the previous contradictory findings regarding the effects of paradigmatic probability on pronunciation.