Stable arrangements persist even when they are poor ones. This corpus treats that persistence as a measurement problem, applying the apparatus of physics â potentials, first-order filters, fixed points, and effective counts â to psychological and social systems across seventy working papers (1,836,200 words) divided into four series:Series A â Foundations (6 papers): Fixes core definitions, redefining comfort as the felt total of present costs rather than pleasure, modeling life trajectories as paths through a comfort landscape governed by stationary action (δS=0), defining the reflexive loop T(x)=W(x,M(x)), and stating the contraction mapping condition.Series B â Engineering the Surplus (33 papers): Builds the core storage law as a leaky integrator, establishes the headroom gauge, and derives the interaction surplus functional f(u)=ln(1+(Nâ1)u).Series C â Frequency, Essence, and Mind (11 papers): Derives a minimum sustainable frequency threshold fminâ=kâ e2c/Ρ over an essence law.Series D â Structure and Resilience (20 papers): Applies concentration instruments (1/HHI) and effective counts into jurisdictional structure, institutional holding arrangements, and distributed ledger validator metrics.
Abstract This study provides essential insights into how diffusion processes unfold in complex networks, with a focus on cryptocurrency blockchains and infrastructure networks. The structural properties of these networks, such as hub-dominated, heavy-tailed topology, network motifs, and node centrality, significantly influence diffusion speed and reach. Using epidemic diffusion models, specifically the Kertesz threshold model and the Susceptible-Infected (SI) model, we analyze key factors affecting diffusion dynamics. To assess the uncertainty in the fraction of infected nodes over time, we employ bootstrap confidence intervals, while Bayesian credible intervals are constructed to quantify parameter uncertainties in the SI models. Our findings reveal substantial variations across different network types, including ErdoĚs-RĂŠnyi networks, Geometric Random Graphs, and Delaunay Triangulation networks, emphasizing the role of network architecture in failure propagation. We identify that network motifs are crucial in diffusion. We highlight that hub-dominated networks, which dominate blockchain ecosystems, provide resilience against random failures but remain vulnerable to targeted attacks, posing significant risks to network stability. Furthermore, centrality measures such as degree, betweenness, and clustering coefficient strongly influence the transmissibility of diffusion in both blockchain and critical infrastructure networks.
"With growing concerns about mental well-being, users want efficacious means to monitor emotions and get personalized assistance, with current solutions often sacrificing privacy or offering shallow revelations. ZenLoop overcomes the shortcomings by combining AI-based analysis of emotion with safe Web3 storage to provide both well-being support alongside privacy. This paper builds a conversational AI chatbot that offers coping mechanisms, a mood tracker to record emotion states, and an analysis dashboard to enable users to identify behavior patterns. Developed with React for frontend, Node.js for backend, and MongoDB for organized data, ZenLoop provides empathy-based responses leveraging NLP models trained on mental well-being dialogues. Journals are encrypted and stored in Web3-based storage, with immutable, decentralized protection. Trends in moods are depicted in interactive graphs, and AI-driven insights enable users to monitor emotion shifts. Tests show enhanced user engagement, improved self-perception, along with superior protection of data. The chatbot is effective in detecting levels of distress along with recommended interventions, promoting emotional resilience. By combining AI-driven tools for mental well-being with the security of blockchain, ZenLoop enables users to express emotion securely, monitor their mental well-being patterns, and get personalized advice at no cost of privacy. This work demonstrates the potential of privacy-based AI-based solutions to promote well-being at the emotional level, leading to the development of secure, user-centric applications for mental well-being.
Federated learning (FL) is increasingly recognised for addressing security and privacy concerns in traditional cloud-centric machine learning (ML), particularly within personalised health monitoring such as wearable devices. By enabling global model training through localised policies, FL allows resource-constrained wearables to operate independently. However, conventional first-order FL approaches face several challenges in personalised model training due to the heterogeneous non-independent and identically distributed (non-iid) data by each individual's unique physiology and usage patterns. Recently, second-order FL approaches maintain the stability and consistency of non-iid datasets while improving personalised model training. This study proposes and develops a verifiable and auditable optimised second-order FL framework BFEL (blockchain enhanced federated edge learning) based on optimised FedCurv for personalised healthcare systems. FedCurv incorporates information about the importance of each parameter to each client's task (through fisher information matrix) which helps to preserve client-specific knowledge and reduce model drift during aggregation. Moreover, it minimizes communication rounds required to achieve a target precision convergence for each client device while effectively managing personalised training on non-iid and heterogeneous data. The incorporation of ethereum-based model aggregation ensures trust, verifiability, and auditability while public key encryption enhances privacy and security. Experimental results of federated CNNs and MLPs utilizing mnist, cifar-10, and PathMnist demonstrate framework's high efficiency, scalability, suitability for edge deployment on wearables, and significant reduction in communication cost.
This study introduces the Multilayer Token Network (MLTN), a mathematical framework for analyzing Ethereum token transfers while capturing inter-token transformations crucial to Decentralized Finance (DeFi). Focusing on prominent fund accounts, we propose the PageRank-CheiRank Trade Balance (PCTB), an econometric measure inspired by balance sheet principles to quantify trade behavior over time. Applying MLTN to 2018â2024 transaction data, we reveal Alameda Researchâs evolving trade strategies, fund interdependencies, and token-specific accumulation and distribution patterns, offering new insights into on-chain financial activities.
In this article, network analysis has been employed to study the dynamic evolution of the cryptocurrency market from 1 January 2020 to 1 January 2024. This approach facilitates an in-depth exploration of the marketâs response to several major events during this period, including the coronavirus disease of 2019 (COVID-19) pandemic and the bankruptcy of FTX, one of the largest cryptocurrency exchanges. The study focuses on analysing key network characteristics of the cryptocurrency market, namely: (a) degree centrality, (b) betweenness centrality, (c) clustering coefficient and (d) average path length. Additionally, we explore the co-movements within the market, categorising cryptocurrencies into functional groups for a comparative analysis. This approach enables us to examine shifts in the cryptocurrency network topology, providing insights into how different groups of cryptocurrencies interact with and influence each other. Through this network analysis, we aim to shed light on the intricate interrelationships among cryptocurrencies. The findings of this study are intended to provide investors with valuable insights, potentially guiding the development of more informed and strategic diversification strategies in the dynamic and evolving landscape of the cryptocurrency market. JEL Codes: G11, G12, D85
Nitin Kumar, S. Mirdula, Pushpa Singh, T. Gayathri ¡ 6 authors
The primary objective of this research is to comprehensively explore and analyze the dynamics of the Ethereum network using innovative methodologies and system architectures. The study aims to extract meaningful statistics from the Ethereum blockchain, focusing on account activity, popularity trends, and the distribution of transactions. Through rigorous data collection, robust query construction, and advanced analytical techniques, the research seeks to provide valuable insights into how the Ethereum network has evolved, particularly in the aftermath of the âcrypto bubble explosion.â The overarching goal is to contribute to the understanding of Ethereum's structural patterns, user behaviors, and the impact of external factors on the network. The research has yielded significant results, unveiling key insights into Ethereum network dynamics. The data collection phase, facilitated by Google BigQuery, successfully captured and filtered relevant information from a specific block range post the âcrypto bubble explosion.â The SQL queries, strategically designed for active account identification and popularity assessment, demonstrated efficiency and accuracy in handling the vast Ethereum dataset. The proposed system, introducing the novel methodology of âportation,â showcased its efficiency in extracting and interpreting Ethereum blockchain data using Google BigQuery. The system architecture, as illustrated in the diagram, proved to be a well-coordinated and dynamic framework, emphasizing the seamless flow of data and processes.
Ahmed M. Alwakeel, Mohammed M. Alwakeel, Mohammed M. Alwakeel, Syed Rameem Zahra ¡ 10 authors
Cities have undergone numerous permanent transformations at times of severe disruption. The Lisbon earthquake of 1755, for example, sparked the development of seismic construction rules. In 1848, when cholera spread through London, the first health law in the United Kingdom was passed. The Chicago fire of 1871 led to stricter building rules, which led to taller skyscrapers that were less likely to catch fire. Along similar lines, the COVID-19 epidemic may have a lasting effect, having pushed the global shift towards greener, more digital, and more inclusive cities. The pandemic highlighted the significance of smart/remote healthcare. Specifically, the elderly delayed seeking medical help for fear of contracting the infection. As a result, remote medical services were seen as a key way to keep healthcare services running smoothly. When it comes to both human and environmental health, cities play a critical role. By concentrating people and resources in a single location, the urban environment generates both health risks and opportunities to improve health. In this manuscript, we have identified the most common mental disorders and their prevalence rates in cities. We have also identified the factors that contribute to the development of mental health issues in urban spaces. Through careful analysis, we have found that multimodal feature fusion is the best method for measuring and analysing multiple signal types in real time. However, when utilizing multimodal signals, the most important issue is how we might combine them; this is an area of burgeoning research interest. To this end, we have highlighted ways to combine multimodal features for detecting and predicting mental issues such as anxiety, mood state recognition, suicidal tendencies, and substance abuse.
Tomas Scagliarini, Giuseppe Pappalardo, Alessio Emanuele Biondo, Alessandro Pluchino ¡ 6 authors
In this paper we analyse the effects of information flows in cryptocurrency markets. We first define a cryptocurrency trading network, i.e. the network made using cryptocurrencies as nodes and the Granger causality among their weekly log returns as links, later we analyse its evolution over time. In particular, with reference to years 2020 and 2021, we study the logarithmic US dollar price returns of the cryptocurrency trading network using both pairwise and high-order statistical dependencies, quantified by Granger causality and O-information, respectively. With reference to the former, we find that it shows peaks in correspondence of important events, like e.g., Covid-19 pandemic turbulence or occasional sudden prices rise. The corresponding network structure is rather stable, across weekly time windows in the period considered and the coins are the most influential nodes in the network. In the pairwise description of the network, stable coins seem to play a marginal role whereas, turning high-order dependencies, they appear in the highest number of synergistic information circuits, thus proving that they play a major role for high order effects. With reference to redundancy and synergy with the time evolution of the total transactions in US dollars, we find that their large volume in the first semester of 2021 seems to have triggered a transition in the cryptocurrency network toward a more complex dynamical landscape. Our results show that pairwise and high-order descriptions of complex financial systems provide complementary information for cryptocurrency analysis.
The purpose of our study is to figure out the transitions of the cryptocurrency market due to the outbreak of COVID-19 through network analysis, and we studied the complexity of the market from different perspectives. To construct a cryptocurrency network, we first apply a mutual information method to the daily log return values of 102 digital currencies from January 1, 2019, to December 31, 2020, and also apply a correlation coefficient method for comparison. Based on these two methods, we construct networks by applying the minimum spanning tree and the planar maximally filtered graph. Furthermore, we study the statistical and topological properties of these networks. Numerical results demonstrate that the degree distribution follows the power-law and the graphs after the COVID-19 outbreak have noticeable differences in network measurements compared to before. Moreover, the results of graphs constructed by each method are different in topological and statistical properties and the network's behavior. In particular, during the post-COVID-19 period, it can be seen that Ethereum and Qtum are the most influential cryptocurrencies in both methods. Our results provide insight and expectations for investors in terms of sharing information about cryptocurrencies amid the uncertainty posed by the COVID-19 pandemic.
With the development of blockchain technology, many new social networks based on blockchain technology have emerged. The unique consensus mechanism and incentive mechanism of blockchain technology makes the law of information propagation in the new social network different from that in the traditional social network. Based on the information propagation characteristics of blockchain social network, this paper considers the influence of opposing groups of opinions, incentive mechanism and userâs conformity psychology in blockchain social network, and uses the evolutionary game to define the transfer process and probability between states and puts forward a new information propagation model. This paper analyses the influence of group density, state transition probability, and incentive policy on information transmission trends in the network through simulation experiments. The comparative experiment with the traditional model shows that the model in this paper can describe the propagation behaviour choices of different propagators under different incentive policies, which the traditional model cannot describe. Using the model in this paper to analyse the information propagation of blockchain social networks can effectively inhibit the propagation of inferior information and further build a good network public opinion environment.
Timothy Tzen Vun Yap, Ting Fong Ho, Hu Ng, Vik Tor Goh
<ns3:p> <ns3:bold>Background:</ns3:bold> This research uses exploratory graph analysis to analyze the transaction data of the Ethereum network. This is achieved through network visualization and mathematical and statistical modelling of the network data. </ns3:p> <ns3:p> <ns3:bold>Methods:</ns3:bold> The dataset used in this study was extracted from the Ethereum in the BigQuery public dataset, specifically selected transactions in July 2019. The transactions were firstly modelled as network graphs and then visualized using the Kamada-Kawai and force-directed graphs layouts. Further modelling was explored with classical random graph and network block, with emphasis on network cohesion, hierarchical clustering and community membership. </ns3:p> <ns3:p> <ns3:bold>Results:</ns3:bold> Looking at the network visualization and hierarchical clustering of the data, the network shows 170 clusters, the largest having 135 members. Through random graph modelling the optimum number of clusters is shown to be 95. Referring to the generated dendrograms, notable large transactions center around the DRINK token, the Maximine Exchange, the Upbit2 Exchange and the IDEX Exchange, identified through public disclosure of their Ethereum addresses. The network graphs tend to go towards the DRINK smart contract and the Maximine Exchange, indicating deposit actions, while it is the opposite for the IDEX Exchange. Further analysis also shows a different number of communities than the expected number. Falling short of the expected 170 clusters, the model is not able to capture additional mechanism that may be present at the density and social interaction distribution level of the network. On the other hand, network block modelling shows only four major clusters out of the 170 expected clusters, an indication that the model is not able to capture the network sufficiently. </ns3:p> <ns3:p> <ns3:bold>Conclusions:</ns3:bold> The study was able to capture and model the interconnectedness of the system with its notion of elements, in this case, the transactions on the network. </ns3:p>
Blockchain is an innovative data management technology using distributed ledgers that has potential to achieve efficiency in data processing and greater control over healthcare record access. Interest is growing beyond uses for cryptocurrency, but blockchain technologies remain poorly understood in the general public and healthcare community. While there are many promising uses for healthcare and supply chain, most potential uses of blockchain for mental health are still in the pilot or development stage. This chapter presents blockchain to the mental health community with a detailed introduction to the unique facets blockchain with a few examples of current uses of blockchain in healthcare with promising proposed uses for mental health.
Two Enactive Approaches to Psychiatry: Two Contrasting Views on What it Means to Be Human Sanneke de Haan (bio) Shared Sources and Different Aims The relevance and potential value of insights from enactivism for the field of psychiatry have been recognized for some time now. Recently, two overarching frameworks have been proposed, one by Nielsen (Nielsen, 2020; Nielsen & Ward, 2018, 2020), and one by me (De Haan 2017; 2020a; 2020b; 2020c).1 As mentioned by Nielsen (2021), we developed our approaches largely in parallel: I was not aware of Nielsenâs work, and he only became aware of my work in the last phase of his PhD. Nielsen (2021) compares our approaches and concludes that our frameworks are âlargely compatible, do different work to one another, and are best understood as complimentaryâ (p. 175). I think, however, that the differences between our positions run much deeper, so that they are, in fact, incompatible. These differences result from fundamentally opposed views on what it means to be human. But before I get into our differences, let me acknowledge what we share. Nielsen and I are attracted to enactivism2 for similar reasons. We are both critical of neuroreductionist views that depict psychiatric disorders as internal problems in individual brains, and instead stress the relevance of taking the individualâs whole body and larger (sociocultural) context into account. In enactivism, we find a framework that spells out how the mind is fundamentally tied to the body and to interactions with the environment (Thompson, 2007; Varela, Thompson, & Rosch, 1991). More specifically, âmindâ refers to the sense-making activities of an organism interacting with its environment, which it depends on for its survival. Enactivism, furthermore, argues that the organism in its environment is best described as a complex, dynamical system. Applied to psychiatry, enactivism offers a) an integrative perspective on the relation between body, mind, and world;, and b) a complex systems approach which acknowledges causal complexity without ascribing a priory primacy to any of the processes involved. Our aimsâwhat we use enactivism forâare different though. My aim is to solve psychiatryâs integration problem, that is, the problem of how to relate the heterogeneous factors that are at stake in the development and persistence of psychiatric [End Page 191] disorders. Even though many people would be willing to embrace the (potential) influence of biological, psychological and social factors, the proof of the pudding will be in providing a proper explanation of how these factors work together and how (causal) interaction between them works. Enactivism provides an excellent basis for explaining such interactions, without resorting to either reductionism or dualism (de Haan, 2020a). As such it can offer an extended and improved version of Engelâs (1977, 1980) biopsychosocial model (de Haan, 2020c). My enactive approach to psychiatry is thus clearly not a âfirst person or phenomenological approach,â as Nielsen (2021) calls it. Personal experiences are indeed vital when trying to understand and explain psychiatric disordersâbut so are (neuro) physiological processes, sociocultural influences, and existential considerations. The purpose of my account is precisely to relate personal experiences to these other processes and explain how these four heterogeneous dimensions affect one another. Enactivismâs thesis about the continuity of life and mind and its concept of sense-making are useful to explicate how âmatters of the mindâ are necessarily also matters of the body and matters of the world too (de Haan, 2020a, 2020b). Nielsen, in contrast, is primarily interested in solving the demarcation problem between mental health and mental illness, or: âwhy some behaviors should be considered disorderedâ (Nielsen & Ward, 2018, p. 801). This should in turn help to carve out psychiatryâs âdiagnostic entitiesâ (Idem, p. 813) and classify mental disorders accordingly. Nielsen mainly draws on enactive ideas to ânaturalize normativityâ (Nielsen & Ward, 2020, p. 121) as he calls it. Because mere statistical rarity is not enough to establish a phenomenon as âdisorderedâ, we need to adopt some norms to distinguish between âdysfunction and functionalityâ (Nielsen & Ward, 2018, p. 811). Nielsen appeals to the enactive idea of organismic self-maintenance to establish such norms. Being alive is a precarious condition that requires constant, adaptive interaction...
Muhammad Abubakr Naeem, Imen Mbarki, Muhammad Tahir Suleman, Xuan Vinh Vo ¡ 5 authors
Abstract We examine the predictive ability of Twitter Happiness Sentiment for six major cryptocurrencies using daily data from August 7, 2015 to December 31, 2019. At first instance, our results conclude a significant nonlinear relationship between Twitter Happiness Sentiment and cryptocurrencies. The nonlinear dependence structure is further enhanced when using the quantileâonâquantile (QQ) analysis, which indicates that high and low sentiment predicts returns of five cryptocurrencies. These findings are statistically and economically significant.
Md. Ibrahim Khan, Fahim Faisal, Sami Azam, Asif Karim ¡ 6 authors
Abstract Modern storage technology has shifted from traditional offline state to cloud based technology since some time now. Because of this transition, the present society is now more dependent on the online storage solutions. Synchronization of files and keeping a history of changes are critical parts of any cloud system. Therefore, an implementation of Blockchain Technology with traditional file synchronization and versioning system can be extremely fruitful. Blockchain is not a new technology, but recently its importance has sky-rocketed as the society is moving towards the decentralized World Wide Web. Blockchain is âan open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent wayâ [1]. Blockchain provides immutable data storage and access with the combination of Proof-of-Work [2, 3]. Due to such appealing features, the study undertaken here investigates and proposes a Blockchain based resilient cloud storage solution that makes a sound utilization of various properties fundamental to any Blockchain based framework.
Psychology tests are widely used in mental health diagnoses, education assessments, and recruitment assessments. There are several major problems in using the traditional way to manage psychology test data. First, there is no single source of truth for psychology test data due to centralized storage. Second, the data are mutable and have the risk of a single point of failure. Third, people have very weak or no control of their own data. This thesis explores the possibility of adopting the new distributed ledger technology, represented by blockchain, to address the problems. The relevant literature of blockchain and psychology tests was reviewed. A complete academic solution was proposed. It includes a permissioned blockchain, a no-SQL database, a web service, and a front-end. The blockchain stores user profile, metadata of psychology tests, final test scores, and access control data of the tests and test scores. The no-SQL database stores test materials and raw test results. The web service interacts with the blockchain and the no-SQL database. The front-end interacts with the web service. The solution was implemented, and the performance was evaluated. The evaluation results showed that the Post request is slower than the Get request and as the number of clients grows linearly, the latency of the requests grows linearly. The slower latency for the Post request compared to the Get request reflects the time it takes for the blockchain system to write information and change the common ledger status. The solution proposed here provides a new way to manage psychology test data with satisfactory performance. Future research can focus on extending the current solution to other questionnaire data management and to non-questionnaire-based psychology assessment data management.
The year 2017 saw the rise and fall of the crypto-currency market, followed by high variability in the price of all crypto-currencies. In this work, we study the abrupt transition in crypto-currency residuals, which is associated with the critical transition (the phenomenon of critical slowing down) or the stochastic transition phenomena. We find that, regardless of the specific crypto-currency or rolling window size, the autocorrelation always fluctuates around a high value, while the standard deviation increases monotonically. Therefore, while the autocorrelation does not display signals of critical slowing down, the standard deviation can be used to anticipate critical or stochastic transitions. In particular, we have detected two sudden jumps in the standard deviation, in the second quarter of 2017 and at the beginning of 2018, which could have served as early warning signals of two majors price collapses that have happened in the following periods. We finally propose a mean-field phenomenological model for the price of crypto-currency to show how the use of the standard deviation of the residuals is a better leading indicator of the collapse in price than the time series' autocorrelation. Our findings represent a first step towards a better diagnostic of the risk of critical transition in the price and/or volume of crypto-currencies.
Sander Greenland and Charles Poole1 accept that P values are here to stay but recognize that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, for example, by Greenland in 2011).2 The formal view of the P value as a probability conditional on the null is mathematically correct but typically irrelevant to research goals (hence, the popularity of alternativeâif wrongâinterpretations). A Bayesian interpretation based on a spike-and-slab model makes little sense in applied contexts in epidemiology, political science, and other fields in which true effects are typically nonzero and bounded (thus violating both the âspikeâ and the âslabâ parts of the model). I find Greenland and Pooleâs1 perspective to be valuable: it is important to go beyond criticism and to understand what information is actually contained in a P value. These authors discuss some connections between P values and Bayesian posterior probabilities. I am not so optimistic about the practical value of these connections. Conditional on the continuing omnipresence of P values in applications, however, these are important results that should be generally understood. Greenland and Poole1 make two points. First, they describe how P values approximate posterior probabilities under prior distributions that contain little information relative to the data: This misuse [of P values] may be lessened by recognizing correct Bayesian interpretations. For example, under weak priors, 95% confidence intervals approximate 95% posterior probability intervals, one-sided P values approximate directional posterior probabilities, and point estimates approximate posterior medians. I used to think this way, too (see many examples in our books), but in recent years have moved to the position that I do not trust such direct posterior probabilities. Unfortunately, I think we cannot avoid informative priors if we wish to make reasonable unconditional probability statements. To put it another way, I agree with the mathematical truth of the quotation above, but I think it can mislead in practice because of serious problems with apparently noninformative or weak priors. Second, the main proposal made by Greenland and Poole is to interpret P values as bounds on posterior probabilities: [U]nder certain conditions, a one-sided P value for a prior median provides an approximate lower bound on the posterior probability that the point estimate is on the wrong side of that median. This is fine, but when sample sizes are moderate or small (as is common in epidemiology and social science), posterior probabilities will depend strongly on the prior distribution. Although I do not see much direct value in a lower bound, I am intrigued by Greenland and Pooleâs1 point that âif one uses an informative prior to derive the posterior probability of the point estimate being in the wrong direction, P0/2 provides a reference point indicating how much the prior information influenced that posterior probability.â This connection could be useful to researchers working in an environment in which P values are central to communication of statistical results. In presenting my view of the limitations of Greenland and Pooleâs1 points, I am leaning heavily on their own work, in particular on their emphasis that, in real problems, prior information is always available and is often strong enough to have an appreciable impact on inferences. Before explaining my position, I will briefly summarize how I view classical P values and my experiences. For more background, I recommend the discussion by Krantz3 of null hypothesis testing in psychology research. WHAT IS A P VALUE IN PRACTICE? The P value is a measure of discrepancy of the fit of a model or ânull hypothesisâ H to data y. Mathematically, it is defined as Pr(T(yrep)>T(y)|H), where yrep represents a hypothetical replication under the null hypothesis and T is a test statistic (ie, a summary of the data, perhaps tailored to be sensitive to departures of interest from the model). In a model with free parameters (a âcomposite null hypothesisâ), the P value can depend on these parameters, and there are various ways to get around this, by plugging in point estimates, averaging over a posterior distribution, or adjusting for the estimation process. I do not go into these complexities further, bringing them up here only to make the point that the construction of P values is not always a simple or direct process. (Even something as simple as the classical chi-square test has complexities to be discovered; see the article by Perkins et al4). In theory, the P value is a continuous measure of evidence, but in practice it is typically trichotomized approximately into strong evidence, weak evidence, and no evidence (these can also be labeled highly significant, marginally significant, and not statistically significant at conventional levels), with cutoffs roughly at P = 0.01 and 0.10. One big practical problem with P values is that they cannot easily be compared. The difference between a highly significant P value and a clearly nonsignificant P value is itself not necessarily statistically significant. (Here, I am using âsignificantâ to refer to the 5% level that is standard in statistical practice in much of biostatistics, epidemiology, social science, and many other areas of application.) Consider a simple example of two independent experiments with estimates (standard error) of 25 (10) and 10 (10). The first experiment is highly statistically significant (two and a half standard errors away from zero, corresponding to a normal-theory P value of about 0.01) while the second is not significant at all. Most disturbingly here, the difference is 15 (14), which is not close to significant. The naive (and common) approach of summarizing an experiment by a P value and then contrasting results based on significance levels, fails here, in implicitly giving the imprimatur of statistical significance on a comparison that could easily be explained by chance alone. As discussed by Gelman and Stern,5 this is not simply the well-known problem of arbitrary thresholds, the idea that a sharp cutoff at a 5% level, for example, misleadingly separates the P = 0.051 cases from P = 0.049. This is a more serious problem: even an apparently huge difference between clearly significant and clearly nonsignificant is not itself statistically significant. In short, the P value is itself a statistic and can be a noisy measure of evidence. This is a problem not just with P values but with any mathematically equivalent procedure, such as summarizing results by whether the 95% confidence interval includes zero. GOOD, MEDIOCRE, AND BAD P VALUES For all their problems, P values sometimes âworkâ to convey an important aspect of the relation of data to model. Other times, a P value sends a reasonable message but does not add anything beyond a simple confidence interval. In yet other situations, a P value can actively mislead. Before going on, I will give examples of each of these three scenarios. A P Value that Worked Several years ago, I was contacted by a person who suspected fraud in a local election.6 Partial counts had been released throughout the voting process and he thought the proportions for the various candidates looked suspiciously stable, as if they had been rigged to aim for a particular result. Excited to possibly be at the center of an explosive news story, I took a look at the data right away. After some preliminary graphsâwhich indeed showed stability of the vote proportions as they evolved during election dayâI set up a hypothesis test comparing the variation in the data to what would be expected from independent binomial sampling. When applied to the entire data set (27 candidates running for six offices), the result was not statistically significant: there was no less (and, in fact, no more) variance than would be expected by chance alone. In addition, an analysis of the 27 separate chi-square statistics revealed no particular patterns. I was left to conclude that the election results were consistent with random voting (even though, in reality, voting was certainly not randomâfor example, married couples are likely to vote at the same time, and the sorts of people who vote in the middle of the day will differ from those who cast their ballots in the early morning or evening). I regretfully told my correspondent that he had no case. In this example, we cannot interpret a nonsignificant result as a claim that the null hypothesis was true or even as a claimed probability of its truth. Rather, nonsignificance revealed the data to be compatible with the null hypothesis; thus, my correspondent could not argue that the data indicated fraud. A P Value that Was Reasonable but Unnecessary It is common for a research project to culminate in the estimation of one or two parameters, with publication turning on a P value being less than a conventional level of significance. For example, in our study of the effects of redistricting in state legislatures (Gelman and King),7 the key parameters were interactions in regression models for partisan bias and electoral responsiveness. Although we did not actually report P values, we could have: what made our article complete was that our findings of interest were more than two standard errors from zero, thus reaching the P < 0.05 level. Had our significance level been much greater (eg, estimates that were four or more standard errors from zero), we would doubtless have broken up our analysis (eg, studying Democrats and Republicans separately) to broaden the set of claims that we could confidently assert. Conversely, had our regressions not reached statistical significance at the conventional level, we would have performed some sort of pooling or constraining of our model to arrive at some weaker assertion that reached the 5% level. (Just to be clear: we are not saying that we would have performed data dredging, fishing for significance; rather, we accept that sample size dictates how much we can learn with confidence; when data are weaker, it can be possible to find reliable patterns by averaging.) In any case, my point is that in this example it would have been just fine to summarize our results in this example via P values even though we did not happen to use that formulation. A Misleading P Value Finally, in many scenarios P values can distract or even mislead, either a nonsignificant result wrongly interpreted as a confidence statement in support of the null hypothesis or a significant P value that is taken as proof of an effect. A notorious example of the latter is the recent article by Bem,8 which reported statistically significant results from several experiments on extrasensory perception (ESP). At brief glance, it seems impressive to see multiple independent findings that are statistically significant (and combining the P values using classical rules would yield an even stronger result), but with enough effort it is possible to find statistical significance anywhere (see the report by Simmons et al9). The focus on P values seems to have both weakened that study (by encouraging the researcher to present only some of his data so as to draw attention away from nonsignificant results) and to have led reviewers to inappropriately view a low P value (indicating a misfit of the null hypothesis to data) as strong evidence in favor of a specific alternative hypothesis (ESP) rather than other, perhaps more scientifically plausible, alternatives such as measurement error and selection bias. PRIORS, POSTERIORS, AND P VALUES Now that I have established my credentials as a pragmatist who finds P values useful in some settings but not others, I want to discuss Greenland and Pooleâs proposal to either interpret one-sided P values as probability statements under uniform priors (an idea they trace back to Gossett)10 or else to use one-sided P values as bounds on posterior probabilities (a result they trace back to Casella and Berger).11 The general problem I have with noninformatively derived Bayesian probabilities is that they tend to be too strong. At first, this may sound paradoxical, that a noninformative or weakly informative prior yields posteriors that are too forcefulâand let me deepen the paradox by stating that a stronger, more informative prior will tend to yield weaker, more plausible posterior statements. How can it be that adding prior information weakens the posterior? It has to do with the sort of probability statements we are often interested in making. Here is an example from Gelman and Weakliem.12 A sociologist examining a publicly available survey discovered a pattern relating attractiveness of parents to the sexes of their children. He found that 56% of the children of the most attractive parents were girls, when compared with 48% of the children of the other parents, and the difference was statistically significant at P < 0.02. The assessments of attractiveness had been performed many years before these people had children, so the researcher felt he had support for a claim of an underlying biological connection between attractiveness and sex ratio. The original analysis by Kanazawa13 had multiple-comparisons issues, and after performing a regression analysis rather than selecting the most significant comparison, we get a P value closer to 0.2 rather than the stated 0.02. For the purposes of our present discussion, though, in which we are evaluating the connection between P values and posterior probabilities, it will not matter much which number we use. We shall go with P = 0.2 because it seems like a more reasonable analysis given the data. Let θ be the true (population) difference in sex ratios of attractive and less attractive parents. Then the data under discussion (with a two-sided P value of 0.2), combined with a uniform prior on θ, yield a 90% posterior probability that θ is positive. Do I believe this? No. Do I even consider this a reasonable data summary? No again. We can derive these âNoâ responses in three different ways: first, by looking directly at the evidence; second, by considering the prior; and third, by considering the implications for statistical practice if this sort of probability statement were computed routinely. First, a claimed 90% probability that θ > 0 seems too strong. Given that the P value (adjusted for multiple comparisons) was only 0.2âthat is, a result that strong would occur a full 20% of the time just by chance alone, even with no true differenceâit seems absurd to assign a 90% belief to the conclusion. I am not prepared to offer 9-to-1 odds on the basis of a pattern someone happened to see that could plausibly have occurred by chance alone, nor for that matter would I offer 99-to-1 odds based on the original claim of the 2% significance level. Second, the prior uniform distribution on θ seems much too weak. There is a large literature on sex ratios, with factors such as ethnicity, maternal age, and season of birth corresponding to difference in probability of girl birth of <0.5 percentage points. It is a priori implausible that sex-ratio differences corresponding to attractiveness are larger than for these other factors. Assigning an informative prior centered on zero shrinks the posterior toward zero, and the resulting posterior probability that θ > 0 moves to a more plausible value in the range of 60%, corresponding to the idea that the result is suggestive but not close to convincing. Third, consider what would happen if we routinely interpreted one-sided P values as posterior probabilities. In that case, an experimental result that is 1 standard error from zeroâthat is, exactly what one might expect from chance aloneâwould imply an 83% posterior probability that the true effect in the population has the same direction as the observed pattern in the data at hand. It does not make sense to me to claim 83% certaintyâ5-to-1 oddsâbased on data that not only could occur by chance alone but in fact represent an expected level of discrepancy. This system-level analysis accords with my criticism of the flat prior: as Greenland and Poole1 note in their article, the effects being studied in epidemiology are typically range from â1 to 1 on the logit scale; hence, analyses assuming broader priors will systematically overstate the probabilities of very large effects and will overstate the probability that an estimate from a small sample will agree in sign with the corresponding population quantity. Rather than relying on noninformative priors, I prefer the suggestion of Greenland and Poole1 to bound posterior probabilities using real prior information. I would prefer to perform my Bayesian inferences directly without using P values as in intermediate step, but given the ubiquity of P values in much applied work, I can see that it can be helpful for researchers to understand their connection to posterior probabilities under informative priors. SUMMARY Like many Bayesians, I have often represented classical confidence intervals as posterior probability intervals and interpreted one-sided P values as the posterior probability of a positive effect. These are valid conditional on the assumed noninformative prior but typically do not make sense as unconditional probability statements. As Sander Greenland has discussed in much of his work over the years, epidemiologists and applied scientists in general have knowledge of the sizes of plausible effects and biases. I believe that a direct interpretation of P values as posterior probabilities can be a useful startâif we recognize that such summaries systematically overestimate the strength of claims from any particular dataset. In this way, I am in agreement with Greenland and Pooleâs interpretation of the one-sided P value as a lower bound of a posterior probability, although I am less convinced of the practical utility of this bound, given that the closeness of the bound depends on a combination of sample size and prior distribution. The default conclusion from a noninformative prior analysis will almost invariably put too much probability on extreme values. A vague prior distribution assigns much of its probability on values that are never going to be plausible, and this disturbs the posterior probabilities more than we tend to expectâsomething that we probably do not think about enough in our routine applications of standard statistical methods. Greenland and Poole1 perform a valuable service by opening up these calculations and placing them in an applied context.