Safe Testing

We present a new theory of hypothesis testing. The main concept is the S-value, a notion of evidence which, unlike p-values, allows for effortlessly combining evidence from several tests, even in the common scenario where the decision to perform a new test depends on the previous test outcome: safe tests based on S-values generally preserve Typ

Better predictions when models are wrong or underspecified

Many statistical methods rely on models of reality in order to learn from data and to make predictions about future data. By necessity, these models usually do not match reality exactly, but are either wrong (none of the hypotheses in the model provides an accurate description of reality) or underspecified (the hypotheses in the model describe only part of the data). In this thesis, we discuss three scenarios involving models that are wrong or underspecified. In each case, we find that standard statistical methods may fail, sometimes dramatically, and present different methods that continue to perform well even if the models are wrong or underspecified. The first two of these scenarios involve regression problems and investigate AIC (Akaike's Information Criterion) and Bayesian statistics. The third scenario has the famous Monty Hall problem as a special case, and considers the question how we can update our belief about an unknown outcome given new evidence when the precise relation between outcome and evidence is unknown.UBL - phd migration 201

Székfoglalók a Magyar Tudományos Akadémián : 2001 : Matematikai és természettudományok

Székfoglalók 2001. Matematikai és természettudományok, 1. (Budapest, 2013) III. Matematikai Tudományok Osztálya - Csörgő Sándor: A szentpétervári paradoxon feloldása - Fritz József: Sztochasztikus hiperbolikus rendszerek kompenzált kompaktságáról - Kiss Elemér: Bolyai János, a 20. század matematikusa - Rónyai Lajos: Véges testek feletti polinomok felbontása - Totik Vilmos: Egy versenyfeladattól az analízis egy módszeréig - Tusnády Gábor: Fák evolúciója VI. Műszaki Tudományok Osztálya - Arató Péter: Rendszerszintű szintézismódszerek - Bokor József: Rendszer- és irányításelmélet - Ginsztler János: Erőművi acélok károsodásanalízise és élettartam-növelési lehetőségei - Győrfi László: Egy nemparaméteres elv predikció konstruálására: szakértők kombinálása - Karádi Gábor: Szennyezett területek feltárása és helyreállítása - Kollár László Péter: Kompozitszerkezetek: lehetőségek és realitás - Kozák Imre: Szilárd test egyensúlyi állapotainak 3d-s statikai stabilitásanalízise alakváltozástól függő felületi terhelések esetén - Pap László: A kódosztásos többszörös hozzáférés szerepe a korszerű mobil hírközlésben - Stépán Gábor: Nemlineáris dinamika, a technológiai fejlesztés eszköze - Szablya János: Energia - a társadalom és az egyén Székfoglalók 2001. Matematikai és természettudományok, 2. (Budapest, 2013) VII. Kémiai Tudományok Osztálya - Alexandru T. Balaban: A Chemical Journey: Experiment and Theory - Blaskó Gábor: Biológiailag aktív természetes szerves anyagok és analogonjaik szerkezetfelderítése és sztereoszelektív szintézise - Dékány Imre: Nanoszerkezetű kolloidok és határfelületi rétegek - Farkas József: Új, nem termikus módszerek élelmiszerek mikrobiológiai biztonságának és minőségmegőrzésének javítására - Inczédy János: Dinamikus kémiai rendszerek működésének ellenőrzése - Joó Ferenc: Fémorganikus katalízis vizes közegben - Kálmán Alajos: Kristályarchitektúra: a szupermolekuláris szerveződések szépségei - Sohár Pál: Szerkezetvadászat spektroszkópiával a molekularengetegben X. Földtudományok Osztálya - Hetényi Magdolna: Az olajpala mint alapkutatási nyersanyag - Zoran Mamsimović: Genesis of some Mediterranean karstic bauxites and karstic nickel deposits - Marosi Sándor: Geomorfológia-geoökológia-tájelemzés - Márton Péter: Földmágnesség a régmúlt időkben - Mészáros Rezső: A térpályákról a kibertérig - Reiner Rummel: Gravity Gradiometry: from Loránd Eötvös to modern Space Age - Verő József: Geomágneses pulzációk az 1999. augusztus 11-i teljes napfogyatkozás alatt XI. Fizikai Tudományok Osztálya - Faigel Gyula: A szerkezetkutatás jövője, a jövő szerkezetkutatása - Patkós András: A vákuum változatossága (Descartes és Pascal között

Self-Translation of Mathematical Texts in Seventeenth-Century France: The Cases of Pascal, Mersenne and Hérigone

This study investigates self-translation – the process of producing a second version of a text in another language – as it relates to three pairs of mathematical works created in Latin and French in mid-seventeenth-century France: Pierre Hérigone’s Cursus mathematicus and Cours mathématique, Marin Mersenne’s Harmonicorum libri and Harmonie universelle, and Blaise Pascal’s treatises on the Arithmetic Triangle. The investigation uses case-study methodology and self-translation research as a framework to examine why and how the three scholars produced bilingual versions of their texts, and does so against the background of the most significant contemporary social and historical factors. As research into pre-twentieth-century non-literary self-translation, it examines material and practices that have largely fallen outside the most frequently investigated areas of self-translation research. The study shows that the most common reasons for writing bilingual works in France during the period in question were related to the emergence of new and changing audiences. This was particularly attributable to the changing relationship between Latin and French: the early seventeenth century was a time of flux, where French was gradually taking over from Latin in French scholarly writing and was the language of the scientific cabinets, attended by an increasingly educated populace, while, at the same time, Latin was consolidating its position as the language of the pan-European Republic of Letters. Many French scholars who wished to maximise their audiences, both within France and across Europe, chose to write their works in Latin, slightly more opted for French, while others, including the case-study scholars, chose to compose their books in both languages. Other, more individual factors were involved in the case-study authors’ decision to self-translate, including the desire to develop ideas, teach mathematics and compose a significant musical work for as large an audience as possible. The different types of text composed by the three mathematicians and their differing motivations led to a range of approaches to self-translation and a variety of outcomes. Some features of the bilingual works are common to all three case studies, including the use of French mathematical terminology derived from its Latin equivalents, a desire to accommodate different audiences for the texts in the two languages, and the use of rhetoric, including ‘mathematical rhetoric’, in both Latin and French

Talking About Uncertainty

In the first article we review existing theories of uncertainty. We devote particular attention to the relation between metacognition, uncertainty and probabilistic expectations. We also analyse the role of natural language and communication for the emergence and resolution of states of uncertainty. We hypothesize that agents feel uncertainty in relation to their levels of expected surprise, which depends on probabilistic expectations-gaps elicited during communication processes. Under this framework above tolerance levels of expected surprise can be considered informative signals. These signals can be used to coordinate, at the group and social level, processes of revision of probabilistic expectations. When above tolerance levels of uncertainty are explicated by agents through natural language, in communication networks and public information arenas, uncertainty acquires a systemic role of coordinating device for the revision of probabilistic expectations. The second article of this research seeks to empirically demonstrate that we can crowd source and aggregate decentralized signals of uncertainty, i.e. expected surprise, coming from market agents and civil society by using the web and more specifically Twitter as an information source that contains the wisdom of the crowds concerning the degree of uncertainty of targeted communities/groups of agents at a given moment in time. We extract and aggregate these signals to construct a set of civil society uncertainty proxies by country. We model the dependence among our civil society uncertainty indexes and existing policy and market uncertainty proxies, highlighting contagion channels and differences in their reactiveness to real-world events that occurred in the year 2016, like the EU-referendum vote and the US presidential elections. In the third article, we propose a new instrument, called Worldwide Uncertainty Network, to analyse the uncertainty contagion dynamics across time and areas of the world. Such an instrument can be used to identify the systemic importance of countries in terms of their civil society uncertainty social percolation role. Our results show that civil society uncertainty signals coming from the web may be fruitfully used to improve our understanding of uncertainty contagion and amplification mechanisms among countries and between markets, civil society and political systems