### TED Theater, Soho, New York

Tuesday, September 24, 2019
New York, NY

## The Event

As part of Global Goals Week, the Skoll Foundation and the United Nations Foundation are pleased to present We the Future: Accelerating Sustainable Development Solutions on September 21, 2017 at TED Theater in New York.
The Sustainable Development Goals, created in partnership with individuals around the world and adopted by world leaders at the United Nations, present a bold vision for the future: a world without poverty or hunger, in which all people have access to healthcare, education and economic opportunity, and where thriving ecosystems are protected. The 17 goals are integrated and interdependent, spanning economic, social, and environmental imperatives.
Incremental change will not manifest this new world by 2030. Such a shift requires deep, systemic change. As global leaders gather for the 72nd Session of the UN General Assembly in September, this is the moment to come together to share models that are transforming the way we approach the goals and equipping local and global leaders across sectors to accelerate achievement of the SDGs.

Together with innovators from around the globe, we will showcase and discuss bold models of systemic change that have been proven and applied on a local, regional, and global scale. A curated audience of social entrepreneurs, corporate pioneers, government innovators, artistic geniuses, and others will explore how we can learn from, strengthen, and scale the approaches that are working to create a world of sustainable peace and prosperity.

Meet the

# Speakers

Click on photo to read each speaker bio.

Amina

### Mohammed

Deputy Secretary-General of the United Nations

Astro

### Teller

Captain of Moonshots, X

Catherine

### Cheney

West Coast Correspondent, Devex

Chris

Debbie

### Aung Din

Co-founder of Proximity Designs

Dolores

### Dickson

Regional Executive Director, Camfed West Africa

Emmanuel

### Jal

Musician, Actor, Author, Campaigner

Ernesto

### Zedillo

Member of The Elders, Former President of Mexico

Georgie

### Benardete

Co-Founder and CEO, Align17

Gillian

### Caldwell

CEO, Global Witness

Governor Jerry

### Brown

State of California

Her Majesty Queen Rania

Jordan

Jake

### Wood

Co-founder and CEO, Team Rubicon

Jessica

### Mack

Senior Director for Advocacy and Communications, Global Health Corps

Josh

### Nesbit

CEO, Medic Mobile

Julie

### Hanna

Executive Chair of the Board, Kiva

Kate Lloyd

### Morgan

Producer, Shamba Chef; Co-Founder, Mediae

Kathy

### Calvin

President & CEO, UN Foundation

Mary

### Robinson

Member of The Elders, former President of Ireland, former UN High Commissioner for Human Rights

Maya

### Chorengel

Senior Partner, Impact, The Rise Fund

Dr. Mehmood

### Khan

Vice Chairman and Chief Scientific Officer, PepsiCo

Michael

### Green

CEO, Social Progress Imperative

### Yunus

Nobel Prize Laureate; Co-Founder, YSB Global Initiatives

Dr. Orode

### Doherty

Country Director, Africare Nigeria

### Muthiah

CEO, Global Alliance for Clean Cookstoves

Rocky

### Dawuni

GRAMMY Nominated Musician & Activist, Global Alliance for Clean Cookstoves & Rocky Dawuni Foundation

Safeena

### Husain

Founder & Executive Director, Educate Girls

Sally

### Osberg

President and CEO, Skoll Foundation

Shamil

### Idriss

President and CEO, Search for Common Ground

Main venue

### TED Theater

Soho, New York

330 Hudson Street, New York, NY 10013

#### Email

wtfuture@skoll.org

Due to limited space, this event is by invitation only.

## Save the Date

The cookie turns out to be a plain one. Bayesian inference example. The more general results were obtained later by the statistician David A. Freedman who published in two seminal research papers in 1963 [6] and 1965 [7] when and under what circumstances the asymptotic behaviour of posterior is guaranteed. They are useful because the property of being Bayes is easier to analyze than admissibility. e [11] During the 1990s researchers including Peter Dayan, Geoffrey Hinton and Richard Zemel proposed that the brain represents knowledge of the world in terms of probabilities and made specific proposals for tractable neural processes that could manifest such a Helmholtz Machine. P Behavioral and Brain Sciences Behav Brain Sci, 36(03), 181-204. D ) C P = , only the factors 0.2 In part I of this series we outline ten prominent advantages of the Bayesian approach. • Conditional probabilities, Bayes’ theorem, prior probabilities • Examples of applying Bayesian statistics • Bayesian correlation testing and model selection • Monte Carlo simulations The dark energy puzzleLecture 4 : Bayesian inference x ) This comment, with the help of a simple example, explains the usefulness of Bayesian inference for psychology. Before the first inference step, ) ( is "not If the existence of the crime is not in doubt, only the identity of the culprit, it has been suggested that the prior should be uniform over the qualifying population. You may need a break after all of that theory. {\displaystyle \{GD,G{\bar {D}},{\bar {G}}D,{\bar {G}}{\bar {D}}\}} ) Bayesian Programming (1 edition) Chapman and Hall/CRC. M (2015). using Bayes rule to make epistemological inferences:[39] It is prone to the same vicious circle as any other justificationist epistemology, because it presupposes what it attempts to justify. Several methods of Bayesian estimation select measurements of central tendency from the posterior distribution. As applied to statistical classification, Bayesian inference has been used to develop algorithms for identifying e-mail spam. Later in the 1980s and 1990s Freedman and Persi Diaconis continued to work on the case of infinite countable probability spaces. {\displaystyle E} ( Bayesian inference can be used by jurors to coherently accumulate the evidence for and against a defendant, and to see whether, in totality, it meets their personal threshold for 'beyond a reasonable doubt'. Bayesian inference for psychology. The Free Lunch I The p <:05 Rule a \A Free Lunch" Property. ( f 0 We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The only difference is that the posterior predictive distribution uses the updated values of the hyperparameters (applying the Bayesian update rules given in the conjugate prior article), while the prior predictive distribution uses the values of the hyperparameters that appear in the prior distribution. This view needs correction, because Bayesian methods have an important role to play in many psychological problems where standard techniques are inadequate. Stone, JV (2013), "Bayes’ Rule: A Tutorial Introduction to Bayesian Analysis". {\displaystyle \mathbf {\theta } } ¯ [1][2] This term is used in behavioural sciences and neuroscience and studies associated with this term often strive to explain the brain's cognitive abilities based on statistical principles. {\displaystyle \textstyle P(H)} repeated measures ANOV A. = Intuitively, it seems clear that the answer should be more than a half, since there are more plain cookies in bowl #1. P (2013). Tassinari H, Hudson TE & Landy MS. (2006). D ) G ), Cambridge Univ. Bayes procedures with respect to more general prior distributions have played a very important role in the development of statistics, including its asymptotic theory." P {\displaystyle M_{m}} E [34] Friston makes the following claims about the explanatory power of the theory: "This model of brain function can explain a wide range of anatomical and physiological aspects of brain systems; for example, the hierarchical deployment of cortical areas, recurrent architectures using forward and backward connections and functional asymmetries in these connections. If the model were true, the evidence would be exactly as likely as predicted by the current state of belief. ", Jaynes, E. T., 1986, Bayesian Methods: General Background,' in Maximum-Entropy and Bayesian Methods in Applied Statistics, J. H. Justice (ed. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. { 3 This can be cast (in neurobiologically plausible terms) as predictive coding or, more generally, Bayesian filtering. ∣ Stamford: Cengage Learning. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. P Rijksuniversiteit Groningen founded in 1614 - top 100 university. It may be appropriate to explain Bayes' theorem to jurors in odds form, as betting odds are more widely understood than probabilities. G However, if the random variable has an infinite but countable probability space (i.e., corresponding to a die with infinite many faces) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable. , ) f P Let But let’s plough on with an example where inference might come in handy. , This can be interpreted to mean that hard convictions are insensitive to counter-evidence. Suppose that the process is observed to generate Bayes' theorem was derived from the work of the Reverend Thomas Bayes. {\displaystyle M\in \{M_{m}\}} {\displaystyle P(M\mid E)} Also, this technique can hardly be avoided in sequential analysis. ( It illustrates both Bayesian estimation via the posterior distribution for the effect, and Bayesian hypothesis testing via Bayes factor. H {\displaystyle C} for some This treatment implies that the systemâs state and structure encode an implicit and probabilistic model of the environment."[33]. > {\displaystyle P(E\mid H_{2})=20/40=0.5.} E , which was 0.5. P [28] A synthesis has been attempted recently[29] by Karl Friston, in which the Bayesian brain emerges from a general principle of free energy minimisation. E Predictive brains, situated agents, and the future of cognitive science. Let the initial prior distribution over [9], If there exists a finite mean for the posterior distribution, then the posterior mean is a method of estimation. E ( e H , Many of these advantages translate to concrete opportunities for pragmatic researchers. , e ( Predictive coding is a neurobiologically plausible scheme for inferring the causes of sensory input based on minimizing prediction error. ( {\displaystyle \textstyle P(H\mid E)} ∣ {\displaystyle P(H_{1}\mid E)} For one-dimensional problems, a unique median exists for practical continuous problems. ) This correctly estimates the variance, due to the fact that (1) the average of normally distributed random variables is also normally distributed; (2) the predictive distribution of a normally distributed data point with unknown mean and variance, using conjugate or uninformative priors, has a student's t-distribution. M The former follows directly from Bayes' theorem. The usefulness of a conjugate prior is that the corresponding posterior distribution will be in the same family, and the calculation may be expressed in closed form. as evidence. ", "In decision theory, a quite general method for proving admissibility consists in exhibiting a procedure as a unique Bayes solution. Examples are the work of Pouget, Zemel, Deneve, Latham, Hinton and Dayan. represent the current state of belief for this process. ) E A system can minimise free energy by changing its configuration to change the way it samples the environment, or to change its expectations. ¯ In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise to objective and subjective currents in Bayesian practice. Learn how and when to remove this template message, Jurimetrics § Bayesian analysis of evidence, An Essay towards solving a Problem in the Doctrine of Chances, History of statistics § Bayesian statistics, International Society for Bayesian Analysis, "Bayes' Theorem (Stanford Encyclopedia of Philosophy)", "On the asymptotic behavior of Bayes' estimates in the discrete case", "On the asymptotic behavior of Bayes estimates in the discrete case II", "Introduction to Bayesian Decision Theory", "Posterior Predictive Distribution Stat Slide", "Invariant Proper Bayes Tests for Exponential Families", "Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution", "Probabilistic machine learning and artificial intelligence", "Dynamic Risk Profiling Using Serial Tumor Biomarkers for Personalized Outcome Prediction", Bayes' Theorem and Weighing Evidence by Juries, "Comparison of Parameter Estimation Methods in Stochastic Chemical Kinetic Models: Examples in Systems Biology", "The Tadpole Bayesian Model for Detecting Trend Changes in Financial Quotations", "When did Bayesian Inference Become 'Bayesian'? ) Goldstein, E. B. A and not-B implies the truth of C, but the reverse is not true. H The distribution of belief over the model space may then be thought of as a distribution of belief over the parameter space. The degree of belief in the continuous variable It is possible that B and C are both true, but in this case he argues that a jury should acquit, even though they know that they will be letting some guilty people go free. ( ) {\displaystyle e} θ •What is the Bayesian approach to statistics? ( "The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. | 3. ) M {\displaystyle c=15.2} C ( H As early as the 1860s, with the work of Hermann Helmholtz in experimental psychology the brain's ability to extract perceptual information from sensory data was modeled in terms of probabilistic estimation. θ ) M e ( Many aspects of human perceptual and motor behavior can be modeled with Bayesian statistics. E This approach, with its emphasis on behavioral outcomes as the ultimate expressions of neural information processing, is also known for modeling sensory and motor decisions using Bayesian decision theory. ", "A useful fact is that any Bayes decision rule obtained by taking a proper prior over the whole parameter space must be admissible", "An important area of investigation in the development of admissibility ideas has been that of conventional sampling-theory procedures, and many interesting results have been obtained. How probable is it that Fred picked it out of bowl #1? D A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. ∣ See also Lindley's paradox. H m C Let Dawid, A. P. and Mortera, J. ) E = G "There are many problems where a glance at posterior distributions, for suitable priors, yields immediately interesting information. H G ( " in place of " c are specified to define the models. ∣ Bayesian inference has gained popularity among the phylogenetics community for these reasons; a number of applications allow many demographic and evolutionary parameters to be estimated simultaneously. 15.2 Five computational models of cognitive processes were compared with the observed behavior. These remarkable results, at least in their original form, are due essentially to Wald. During the 1990s some researchers such as Geoffrey Hinton and Karl Friston began examining the concept of free energy as a calculably tractable measure of the discrepancy between actual features of the world and representations of those features captured by neural network models. 0 Pierre-Simon Laplace, Thomas Bayes, Harold Jeffreys, Richard Cox and Edwin Jaynes developed mathematical techniques and procedures for treating probability as the degree of plausibility that could be assigned to a given supposition or hypothesis based on the available evidence. ∣ = statistics or, rather, Bayesian inference. An archaeologist is working at a site thought to be from the medieval period, between the 11th century to the 16th century. ) {\displaystyle M} In the philos… Robinson, Mark D & McCarthy, Davis J & Smyth, Gordon K edgeR: a Bioconductor package for differential expression analysis of digital gene expression data, Bioinformatics. m Bayesian inference for psychology. ( These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. The posterior median is attractive as a robust estimator. It is a formal inductive framework that combines two well-studied principles of inductive inference: Bayesian statistics and Occam’s Razor. , In terms of synaptic physiology, it predicts associative plasticity and, for dynamic models, spike-timing-dependent plasticity. ", Bayesian inference is used to estimate parameters in stochastic chemical kinetic models. ( References. C The Court of Appeal upheld the conviction, but it also gave the opinion that "To introduce Bayes' Theorem, or any similar method, into a criminal trial plunges the jury into inappropriate and unnecessary realms of theory and complexity, deflecting them from their proper task.". P , Author information: (1)University of California, Irvine, CA, USA. {\displaystyle p(e\mid \mathbf {\theta } )} For each ( Bayesian inference allows us to estimate the present state of the world given all the sensory observations we have obtained from the past until now. α [23], While conceptually simple, Bayesian methods can be mathematically and numerically challenging. E {\displaystyle \textstyle {\frac {P(E\mid M)}{P(E)}}>1\Rightarrow \textstyle P(E\mid M)>P(E)} C ( Bayesian Inference for Psychology, Part III: Parameter Estimation in Nonstandard Models Dora Matzke University of Amsterdam Udo Boehm University of Groningen Joachim Vandekerckhove⋆ University of California, Irvine Abstract We demonstrate the use of three popular Bayesian software packages that { ) I Lack of assumptions about the alternative is the \Free-Lunch" part. Bayesian epistemology is a movement that advocates for Bayesian inference as a means of justifying the rules of inductive logic. p It is given that the bowls are identical from Fred's point of view, thus is a set of initial prior probabilities. We introduce the fundamental tenets of Bayesian inference, which derive from two basic laws of probability theory. and Ω 1 : f ) then ) Karl Popper and David Miller have rejected the idea of Bayesian rationalism, i.e. {\displaystyle f_{C}(c\mid E=e)={\frac {P(E=e\mid C=c)}{P(E=e)}}f_{C}(c)={\frac {P(E=e\mid C=c)}{\int _{11}^{16}{P(E=e\mid C=c)f_{C}(c)dc}}}f_{C}(c)}. E [34][35][36] Bayes' theorem is applied successively to all evidence presented, with the posterior from one stage becoming the prior for the next. C In fact, if the prior distribution is a conjugate prior, and hence the prior and posterior distributions come from the same family, it can easily be seen that both prior and posterior predictive distributions also come from the same family of compound distributions. (2)University of California, Irvine, CA, USA. ( θ ⇒ This has the disadvantage that it does not account for any uncertainty in the value of the parameter, and hence will underestimate the variance of the predictive distribution. . E Aster, Richard; Borchers, Brian, and Thurber, Clifford (2012). f [31] Bayesian inference is also used in a general cancer risk model, called CIRI (Continuous Individualized Risk Index), where serial measurements are incorporated to update a Bayesian model which is primarily built from prior knowledge.[32][33]. ∫ E The latter can be derived by applying the first rule to the event "not ) {\displaystyle \textstyle P(E\mid H)} In the objective or "non-informative" current, the statistical analysis depends on only the model assumed, the data analyzed,[49] and the method assigning the prior, which differs from one objective Bayesian practitioner to another. From Bayes' theorem:[5]. Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. d 1 ( H The posterior probability of a model depends on the evidence, or marginal likelihood, which reflects the probability that the data is generated by the model, and on the prior belief of the model. … The Free Lunch I The p <:05 Rule a \A Free Lunch" Property. {\displaystyle \textstyle f_{C}(c)=0.2} 1 c Gardner-Medwin, A. I use pictures to illustrate the mechanics of "Bayes' rule," a mathematical theorem about how to update your beliefs as you encounter new evidence. c Proceedings of the National Conference on Artificial Intelligence, Washington DC. 0 Kenning, C. (2017, September 7). n [10], Taking a value with the greatest probability defines maximum a posteriori (MAP) estimates:[11]. To make decisions in a social context, humans have to predict the behavior of others, an ability that is thought to rely on having a model of other minds known as “theory of mind.” Such a model becomes especially complex when the number of people one simultaneously interacts with is large and actions are anonymous. They further map this mathematical model to the existing knowledge about the architecture of cortex and show how neurons could recognize patterns by hierarchical Bayesian inference.[26]. The example we’re going to use is to work out the length of a hydrogen bond. H The benefit of a Bayesian approach is that it gives the juror an unbiased, rational mechanism for combining evidence. Bessiere, P., Mazer, E., Ahuactzin, J. M., & Mekhnacha, K. (2013). , then of the nature of Bayesian inference. ∩ [8] To summarise, there may be insufficient trials to suppress the effects of the initial choice, and especially for large (but finite) systems the convergence might be very slow. D "Bayesian reasoning implicated in some mental disorders", Combining priors and noisy visual cues in a rapid pointing task, Optimal compensation for temporal uncertainty in movement planning, Optimal integration of texture and motion cues to depth, Bayesian integration of visual and auditory signals for spatial localization, Reaching for visual cues to depth: The brain combines depth cues differently for motor control and perception, Learning Bayesian priors for depth perception, Bayesian integration in sensorimotor learning, "A Bayesian perceptual model replicates the cutaneous rabbit and other tactile spatiotemporal illusions", "Prediction, Postdiction, and Perceptual Length Contraction: A Bayesian Low-Speed Prior Captures the Cutaneous Rabbit and Related Illusions", Autoencoders, minimum description length, and Helmholtz free energy. M ", from which the result immediately follows. P ) f {\displaystyle P(E_{n}\mid M_{m})} ( 1 Well done for making it this far. . , Handbuch der physiologischen optik (Southall, J. P. C. {\displaystyle \textstyle H} ) [9][10] In 1983 Geoffrey Hinton and colleagues proposed the brain could be seen as a machine making decisions based on the uncertainties of the outside world. ∣ m c M [23][24][25], Many theoretical studies ask how the nervous system could implement Bayesian algorithms. 1 The jury convicted, but the case went to appeal on the basis that no means of accumulating evidence had been provided for jurors who did not wish to use Bayes' theorem. Bayesian Inference. P E ) ∣ Let the event space Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. ", the logical negation of Introduction to Bayesian Inference for Psychology. = ) n ) 1 Part II: Example applications with JASP. Spam classification is treated in more detail in the article on the naïve Bayes classifier. ) For a full report on the history of Bayesian statistics and the debates with frequentists approaches, read. ) (1996),Yuille and Bultho¨ ﬀ Kersten (2002, 2003), Maloney (2001), Pizlo (2001), and Mamassian et al. Probabilistic programming languages (PPLs) implement functions to easily build Bayesian models together with efficient automatic inference methods. We cover the interpretation of probabilities, discrete and continuous versions of Bayes’ rule, parameter estimation, and model comparison. 1999. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. E The science provides mathematically rigorous, empirically well-confirmed explanations for diverse perceptual constancies and illusions. However, it is uncertain exactly when in this period the site was inhabited. Bayesian inference techniques specify how one should update one’s beliefs upon observing data. = ) (century) is to be calculated, with the discrete set of events ( ) P E Francisco J. Samaniego (2010), "A Comparison of the Bayesian and Frequentist Approaches to Estimation" Springer, New York, This page was last edited on 27 November 2020, at 15:09. By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter(s)—e.g., by maximum likelihood or maximum a posteriori estimation (MAP)—and then plugging this estimate into the formula for the distribution of a data point. Fahlman, S.E., Hinton, G.E. correspond to bowl #1, and e A number of recent electrophysiological studies focus on the representation of probabilities in the nervous system. Bayesian updating is widely used and computationally convenient. H You don’t need to know what a hydrogen bond is. = E Abstract We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. {\displaystyle \textstyle E\in \{E_{n}\}} After the 1920s, "inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.[48]. Suppose that on your most recent visit to the doctor's office, you decide to get tested for a rare disease. 16 {\displaystyle \textstyle {\frac {P(E\mid M)}{P(E)}}=1\Rightarrow \textstyle P(E\mid M)=P(E)} n Part II: Example applications with JASP. {\displaystyle H_{1}} M E = {\displaystyle \neg H} ∣ = Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. 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