This document discusses mixing R source code and documentation in LaTeX documents using knitr. It recommends using knitr in RStudio to embed R code chunks and output (like graphs and tables) in LaTeX documents. Code chunks can include any R code to evaluate, show, or hide. Graphs and tables from R code chunks will be included in the LaTeX output.
The document contains several charts and graphs that compare the Obama administration's proposed FY2010 budget and future budgets under Democratic plans versus Republican alternatives. It shows that the Obama budget would increase government spending as a percentage of GDP above the historical average, increase the national debt level and debt held by the public as a percentage of GDP, and result in higher cumulative job losses per year under a proposed Cap and Trade program compared to no such program. The budget would also mean tax increases exceeding proposed tax cuts for 95% of Americans and increased family energy costs under Cap and Trade.
The crisis in Ireland in graphs and mapsrobkitchin
The document discusses Ireland's economic crisis in September 2012. It summarizes that Ireland had high levels of government debt and budget deficits that required a bailout from the European Union and International Monetary Fund. It also discusses Ireland's housing market issues at the time, including high vacancy rates, unfinished developments, declining property prices, and the government's National Asset Management Agency that took over bad loans from banks.
The document discusses past and projected growth in the global solar PV market from 2001-2011 and beyond. It notes that the market grew at an average annual rate of 52% from 2001-2010, with particularly rapid growth in 2009-2010. Germany has been the leading country for installed capacity but its market may be nearing saturation. Module prices declined sharply from 2008-2010. The document considers whether the solar PV market will continue growing at similar rates or begin to slow and outlines optimistic and conservative scenarios for market growth through 2020.
This presentation provides an overview of the executive aviation market from Embraer's perspective. It discusses forward-looking statements and acknowledges uncertainty in projections. Charts show projections for global GDP growth remaining steady around 3% annually through 2014. U.S. corporate profits are up significantly from 2009 levels though remain below pre-crisis averages. Global stock markets saw over a 10% drop highlighted in late 2008. Business jet traffic in the U.S. and Europe has rebounded in 2011 after declines in 2009. The used aircraft market inventory decreased in 2010 after large increases in prior years.
Executive aviation embraer day 2011 03_25(final) vimpEmbraer RI
This presentation discusses the state of the global and U.S. economy, as well as trends in the business jet industry. It notes that while the global economy is expected to grow around 3% annually through 2014, uncertainty remains. U.S. corporate profits and stock markets rebounded in recent years but volatility persists. Business jet traffic in the U.S. and Europe has increased since 2009 but remains below pre-recession levels. The supply of used business jets for sale has declined since 2008.
Summary of JUNE 2010 Existing Home Sales StatisticsNAR Research
The document summarizes existing home sales statistics for June 2010. It finds that total existing home sales increased 9.8% year-over-year in June. The median home price also increased 1.0% compared to June 2009. Regionally, the Northeast saw the largest annual sales increase at 17.1%, while the West saw a more modest 0.9% rise. Housing inventory declined 5.3% nationally from the previous year.
The document contains graphs showing traffic fatality statistics from 2006-2010 by month. It shows that the average number of total fatal crashes in July over the past 4 years was 24, but was 21 in 2010. The average number of pedestrian fatalities in July over the past 4 years was 14, but was 11 in 2010. The average total number of fatalities in July over the past 4 years was 155, but was 120 in 2010.
The document contains information about cancer funding and survival rates from the National Cancer Institute from 1999-2008. It shows that funding for pancreatic cancer was consistently lower than the other top causes of cancer death such as lung, colon, breast, and prostate cancer. It also shows that the 5-year survival rate for pancreatic cancer is much lower at 5.1% compared to 64.4-98.9% for the other cancers.
The document contains several charts and graphs that compare the Obama administration's proposed FY2010 budget and future budgets under Democratic plans versus Republican alternatives. It shows that the Obama budget would increase government spending as a percentage of GDP above the historical average, increase the national debt level and debt held by the public as a percentage of GDP, and result in higher cumulative job losses per year under a proposed Cap and Trade program compared to no such program. The budget would also mean tax increases exceeding proposed tax cuts for 95% of Americans and increased family energy costs under Cap and Trade.
The crisis in Ireland in graphs and mapsrobkitchin
The document discusses Ireland's economic crisis in September 2012. It summarizes that Ireland had high levels of government debt and budget deficits that required a bailout from the European Union and International Monetary Fund. It also discusses Ireland's housing market issues at the time, including high vacancy rates, unfinished developments, declining property prices, and the government's National Asset Management Agency that took over bad loans from banks.
The document discusses past and projected growth in the global solar PV market from 2001-2011 and beyond. It notes that the market grew at an average annual rate of 52% from 2001-2010, with particularly rapid growth in 2009-2010. Germany has been the leading country for installed capacity but its market may be nearing saturation. Module prices declined sharply from 2008-2010. The document considers whether the solar PV market will continue growing at similar rates or begin to slow and outlines optimistic and conservative scenarios for market growth through 2020.
This presentation provides an overview of the executive aviation market from Embraer's perspective. It discusses forward-looking statements and acknowledges uncertainty in projections. Charts show projections for global GDP growth remaining steady around 3% annually through 2014. U.S. corporate profits are up significantly from 2009 levels though remain below pre-crisis averages. Global stock markets saw over a 10% drop highlighted in late 2008. Business jet traffic in the U.S. and Europe has rebounded in 2011 after declines in 2009. The used aircraft market inventory decreased in 2010 after large increases in prior years.
Executive aviation embraer day 2011 03_25(final) vimpEmbraer RI
This presentation discusses the state of the global and U.S. economy, as well as trends in the business jet industry. It notes that while the global economy is expected to grow around 3% annually through 2014, uncertainty remains. U.S. corporate profits and stock markets rebounded in recent years but volatility persists. Business jet traffic in the U.S. and Europe has increased since 2009 but remains below pre-recession levels. The supply of used business jets for sale has declined since 2008.
Summary of JUNE 2010 Existing Home Sales StatisticsNAR Research
The document summarizes existing home sales statistics for June 2010. It finds that total existing home sales increased 9.8% year-over-year in June. The median home price also increased 1.0% compared to June 2009. Regionally, the Northeast saw the largest annual sales increase at 17.1%, while the West saw a more modest 0.9% rise. Housing inventory declined 5.3% nationally from the previous year.
The document contains graphs showing traffic fatality statistics from 2006-2010 by month. It shows that the average number of total fatal crashes in July over the past 4 years was 24, but was 21 in 2010. The average number of pedestrian fatalities in July over the past 4 years was 14, but was 11 in 2010. The average total number of fatalities in July over the past 4 years was 155, but was 120 in 2010.
The document contains information about cancer funding and survival rates from the National Cancer Institute from 1999-2008. It shows that funding for pancreatic cancer was consistently lower than the other top causes of cancer death such as lung, colon, breast, and prostate cancer. It also shows that the 5-year survival rate for pancreatic cancer is much lower at 5.1% compared to 64.4-98.9% for the other cancers.
Russian insurance market growth perspectives and main directions of investmen...РОСГОССТРАХ
1) The Russian insurance market has been growing rapidly in recent years and is expected to double in size over the next 5 years.
2) Concentration in the market is increasing, with the top 10 companies now accounting for over 40% of premiums collected.
3) Key areas for future growth include life insurance, property insurance like motor casualty, and developing new products like liability insurance that can help support investment and innovation in the Russian economy.
The Rising Global Offset Challenge - addressing the half trillion dollar ques...jbarney23
The document discusses the rising global offset challenge and addressing the half trillion dollar question. It notes that offset obligations are growing worldwide, with the Middle East and Asia/Pacific representing the largest volumes and Latin America seeing the fastest growth. It advocates for three strategies for success: implementing business fundamentals, deepening involvement of all stakeholders, and communicating strategically.
Recent developments in the canadian economy dec2011Sam Batarseh
The document summarizes recent economic developments in Canada and provides projections. It finds that while global growth has weakened, emerging economies continue to lead growth. Domestic demand is projected to be the main driver of growth in Canada, with exports and business investment remaining strong. Real GDP growth is expected to pick up in Canada through 2012 as excess capacity is absorbed.
The document summarizes the current economic situation in the Euro area based on data presented in charts and graphs. It shows that real GDP growth has been negative or very low in recent years. Unemployment has risen significantly since 2007 and now stands at 12% overall. Current account balances among member states have diverged, with surpluses in some countries and deficits in others. Bank lending to firms has declined sharply since 2010. Government deficits remain high in some countries and government debt levels are above 90% of GDP in several Euro area nations.
Road safety is a major public health issue in India. The number of road traffic injuries and deaths has increased substantially over the past few decades as the number of vehicles on the road has grown rapidly. While roads are critical infrastructure, safety has not kept pace. Available data shows high rates of road deaths in many Indian states and cities. Effective interventions include enforcement of traffic laws on helmets and drink driving, improving road engineering for pedestrian safety, increasing road visibility, public education campaigns, strengthening emergency response systems, and improving vehicle safety standards. However, there remains a disconnect between responsibility, leadership and coordination among different agencies and departments regarding road safety in India.
2007* Airline Marketing Embraer Day 2007Embraer RI
This document summarizes an Embraer Day 2007 presentation on the airline market and Embraer programs for aircraft in the 30-120 seat segment. It includes the following key points:
1) The air transport industry has seen strong demand growth in recent years and is projected to continue growing. However, airlines have had to work hard to reduce costs to offset rising fuel prices.
2) The regional jet market served by Embraer's ERJ145 family and the 70-120 seat market served by Embraer's E-Jets have both evolved in recent years.
3) Projections show the airline industry as a whole and most regions are expected to have positive net results in 2007 and 2008
- The document discusses Bayesian deep learning, including introducing Bayesian approaches, modeling uncertainty, and challenges such as scaling algorithms and building interpretable priors.
- It describes early work showing infinite width neural networks behave as Gaussian processes.
- For wide Bayesian neural networks with certain properties, the marginal prior distribution of units converges to a Gaussian process in the wide limit. This "wide regime" property extends to deep networks.
Bayesian neural networks increasingly sparsify their units with depthJulyan Arbel
This document analyzes deep Bayesian neural networks with Gaussian priors on weights and ReLU-like activations. It proves that the marginal prior distributions of hidden units become heavier-tailed (sub-Weibull) with increasing layer depth, with an optimal tail parameter of layer depth divided by 2. This indicates that units in deeper layers will be more sparsely represented under maximum a posteriori estimation, explaining the natural shrinkage properties of these networks.
Species sampling models in Bayesian NonparametricsJulyan Arbel
This document discusses species sampling models and discovery probabilities. It introduces the problem of estimating the probability of observing a new species given a sample. Good and Turing proposed an estimator for this during World War II. Bayesian nonparametric models provide an alternative approach by placing a prior on unknown species proportions. The document outlines BNP estimators for discovery probabilities and how credible intervals can be derived. It applies these methods to genomic datasets of expressed sequence tags to estimate discovery probabilities for observing new genes.
Dependent processes in Bayesian NonparametricsJulyan Arbel
This document summarizes dependent processes in Bayesian nonparametrics. It motivates the need for dependent random probability measures to accommodate temporal dependence structures beyond the exchangeability assumption. It describes modeling collections of random probability measures indexed by time as either discrete-time or continuous-time processes. The diffusive Dirichlet process is introduced as a dependent Dirichlet process with Dirichlet marginal distributions at each time point and continuous sample paths. Simulation and estimation methods are discussed for this model.
Asymptotics for discrete random measuresJulyan Arbel
This document provides an introduction to asymptotics for discrete random measures, specifically the Dirichlet process and two-parameter Poisson-Dirichlet process. It discusses several key aspects in 3 sentences or less:
1) It outlines the stick-breaking construction of the two-parameter Poisson-Dirichlet process and defines related notation. 2) It introduces the truncation error Rn and discusses how its asymptotic behavior differs between the Dirichlet and two-parameter Poisson-Dirichlet cases. 3) It briefly describes some applications of these processes in mixture modeling and summarizes different sampling approaches like blocked Gibbs and slice sampling that rely on truncation of the infinite-dimensional distributions.
Bayesian Nonparametrics, Applications to biology, ecology, and marketingJulyan Arbel
This document discusses applications of Bayesian nonparametric methods to various domains including toxicology, ecology, marketing, human fertility, and more. It provides examples of using rounded Gaussian mixtures and Dirichlet process mixtures to model count data from developmental toxicity studies and animal abundance data. Applications to modeling multivariate mobile phone usage data and basal body temperature curves are also described. The document emphasizes that Bayesian nonparametric approaches allow inclusion of prior information and flexible modeling of complex data structures.
A Gentle Introduction to Bayesian NonparametricsJulyan Arbel
The document provides an introduction to Bayesian nonparametrics and the Dirichlet process. It explains that Bayesian nonparametrics aims to fit models that can adapt their complexity based on the data, without strictly imposing a fixed structure. The Dirichlet process is described as a prior distribution on the space of all probability distributions, allowing the model to utilize an infinite number of parameters. Nonparametric mixture models using the Dirichlet process provide a flexible approach to density estimation and clustering.
The document outlines a paper on Bayesian linear models. It introduces a simple example of a linear model with exchangeable priors. It then presents the general Bayesian linear model and theorems for the posterior distribution given multiple stages of priors. It applies this to an experimental design setting, deriving Bayes estimates that shrink treatment and block effects towards zero based on their variances.
This document discusses different approaches to Bayesian analysis including objective, subjective, robust, frequentist, and quasi Bayesian analysis. It provides examples and discusses the advantages and disadvantages of each approach. Objective Bayesian analysis uses objective prior distributions designed to be minimally informative, while subjective Bayesian analysis aims to fully specify subjective priors but has challenges in practice. Robust Bayesian analysis considers classes of models and priors to provide interval estimates. Frequentist Bayesian analysis combines Bayesian and frequentist ideas, and quasi Bayesian analysis uses ad hoc priors. Computational techniques for Bayesian analysis include calculating integrals and posterior modes using Laplace approximation, Monte Carlo sampling, and MCMC methods.
Lewis Carroll wrote "Pillow Problems", a collection of 72 logic and probability puzzles, while lying in bed at night. Many had clever but flawed solutions due to Carroll's limited understanding of modern probability concepts. For example, in one problem about breaking rods, Carroll incorrectly assumed the probability of breaking at the middle was nonzero. Overall, "Pillow Problems" reflects the nascent state of English probability in Carroll's time and his personal difficulties with more rigorous concepts like continuous probabilities.
The document discusses several key ideas in statistics and modeling:
1. Fisher and Neyman had different views on model specification - Fisher saw it as practical while Neyman emphasized theoretical building blocks.
2. Statistics can contribute a "reservoir of models", model selection techniques, and classification of theoretical vs empirical models.
3. Theoretical models aim to explain underlying mechanisms while empirical models guide actions based on forecasts.
4. Examples like Mendel's inheritance models, Pearson distributions, and Galileo's trial illustrate the development and application of statistical modeling.
This document discusses different approaches to specifying prior distributions in Bayesian statistics. It begins by introducing the binomial model for coin tossing and how priors and posteriors are calculated. It then describes three categories of Bayesian priors: classical Bayesians use a flat prior, modern parametric Bayesians use a Beta distribution prior, and subjective Bayesians quantify existing knowledge about a process. The document shows that different priors lead to different posteriors. It further explains that any prior density can be approximated by mixtures of Beta densities, and extends this concept to the exponential family. The exponential family conjugate prior is also discussed. Finally, connections are made between the exponential family, Beta density priors, and a generalization about conditional expected posteriors.
The Metropolis Hastings algorithm is an MCMC method for obtaining a sequence of samples from a probability distribution when direct sampling is difficult. It constructs a Markov chain that has the desired target distribution as its stationary distribution. At each step, a candidate sample is generated and either accepted, replacing the current state, or rejected, keeping the current state. The acceptance ratio is determined by the ratio of probabilities of the candidate and current states. The algorithm is a generalization of the Metropolis algorithm that allows for non-symmetric proposal distributions. When the chain satisfies ergodicity conditions, the sample distribution will converge to the target distribution as the number of samples increases.
This document discusses the connection between Ockham's Razor and Bayesian analysis. It explains that Ockham's Razor favors the simplest hypothesis consistent with the data, and Bayesian analysis can help determine how much a simpler model should be preferred. It provides Galileo's problem of developing the law of falling bodies as an example. Jeffrey and Wrinch suggested using prior probabilities to represent simplicity, with the hypothesis having fewer parameters being assigned a higher prior probability. However, defining simplicity based solely on prior probabilities is problematic. Alternatively, a simpler hypothesis that makes precise predictions should be given greater credence if those predictions are confirmed. The key idea linking Bayesian analysis and Ockham's Razor is how simplicity in a hypothesis is represented and
This document provides a list of 33 papers related to Bayesian statistics for students to choose from for a presentation. It includes brief descriptions of several theoretical and general audience journals. The papers cover a range of topics in Bayesian statistics published between 1763 and 2013. Students will be evaluated on their understanding and presentation of the chosen paper.
Russian insurance market growth perspectives and main directions of investmen...РОСГОССТРАХ
1) The Russian insurance market has been growing rapidly in recent years and is expected to double in size over the next 5 years.
2) Concentration in the market is increasing, with the top 10 companies now accounting for over 40% of premiums collected.
3) Key areas for future growth include life insurance, property insurance like motor casualty, and developing new products like liability insurance that can help support investment and innovation in the Russian economy.
The Rising Global Offset Challenge - addressing the half trillion dollar ques...jbarney23
The document discusses the rising global offset challenge and addressing the half trillion dollar question. It notes that offset obligations are growing worldwide, with the Middle East and Asia/Pacific representing the largest volumes and Latin America seeing the fastest growth. It advocates for three strategies for success: implementing business fundamentals, deepening involvement of all stakeholders, and communicating strategically.
Recent developments in the canadian economy dec2011Sam Batarseh
The document summarizes recent economic developments in Canada and provides projections. It finds that while global growth has weakened, emerging economies continue to lead growth. Domestic demand is projected to be the main driver of growth in Canada, with exports and business investment remaining strong. Real GDP growth is expected to pick up in Canada through 2012 as excess capacity is absorbed.
The document summarizes the current economic situation in the Euro area based on data presented in charts and graphs. It shows that real GDP growth has been negative or very low in recent years. Unemployment has risen significantly since 2007 and now stands at 12% overall. Current account balances among member states have diverged, with surpluses in some countries and deficits in others. Bank lending to firms has declined sharply since 2010. Government deficits remain high in some countries and government debt levels are above 90% of GDP in several Euro area nations.
Road safety is a major public health issue in India. The number of road traffic injuries and deaths has increased substantially over the past few decades as the number of vehicles on the road has grown rapidly. While roads are critical infrastructure, safety has not kept pace. Available data shows high rates of road deaths in many Indian states and cities. Effective interventions include enforcement of traffic laws on helmets and drink driving, improving road engineering for pedestrian safety, increasing road visibility, public education campaigns, strengthening emergency response systems, and improving vehicle safety standards. However, there remains a disconnect between responsibility, leadership and coordination among different agencies and departments regarding road safety in India.
2007* Airline Marketing Embraer Day 2007Embraer RI
This document summarizes an Embraer Day 2007 presentation on the airline market and Embraer programs for aircraft in the 30-120 seat segment. It includes the following key points:
1) The air transport industry has seen strong demand growth in recent years and is projected to continue growing. However, airlines have had to work hard to reduce costs to offset rising fuel prices.
2) The regional jet market served by Embraer's ERJ145 family and the 70-120 seat market served by Embraer's E-Jets have both evolved in recent years.
3) Projections show the airline industry as a whole and most regions are expected to have positive net results in 2007 and 2008
- The document discusses Bayesian deep learning, including introducing Bayesian approaches, modeling uncertainty, and challenges such as scaling algorithms and building interpretable priors.
- It describes early work showing infinite width neural networks behave as Gaussian processes.
- For wide Bayesian neural networks with certain properties, the marginal prior distribution of units converges to a Gaussian process in the wide limit. This "wide regime" property extends to deep networks.
Bayesian neural networks increasingly sparsify their units with depthJulyan Arbel
This document analyzes deep Bayesian neural networks with Gaussian priors on weights and ReLU-like activations. It proves that the marginal prior distributions of hidden units become heavier-tailed (sub-Weibull) with increasing layer depth, with an optimal tail parameter of layer depth divided by 2. This indicates that units in deeper layers will be more sparsely represented under maximum a posteriori estimation, explaining the natural shrinkage properties of these networks.
Species sampling models in Bayesian NonparametricsJulyan Arbel
This document discusses species sampling models and discovery probabilities. It introduces the problem of estimating the probability of observing a new species given a sample. Good and Turing proposed an estimator for this during World War II. Bayesian nonparametric models provide an alternative approach by placing a prior on unknown species proportions. The document outlines BNP estimators for discovery probabilities and how credible intervals can be derived. It applies these methods to genomic datasets of expressed sequence tags to estimate discovery probabilities for observing new genes.
Dependent processes in Bayesian NonparametricsJulyan Arbel
This document summarizes dependent processes in Bayesian nonparametrics. It motivates the need for dependent random probability measures to accommodate temporal dependence structures beyond the exchangeability assumption. It describes modeling collections of random probability measures indexed by time as either discrete-time or continuous-time processes. The diffusive Dirichlet process is introduced as a dependent Dirichlet process with Dirichlet marginal distributions at each time point and continuous sample paths. Simulation and estimation methods are discussed for this model.
Asymptotics for discrete random measuresJulyan Arbel
This document provides an introduction to asymptotics for discrete random measures, specifically the Dirichlet process and two-parameter Poisson-Dirichlet process. It discusses several key aspects in 3 sentences or less:
1) It outlines the stick-breaking construction of the two-parameter Poisson-Dirichlet process and defines related notation. 2) It introduces the truncation error Rn and discusses how its asymptotic behavior differs between the Dirichlet and two-parameter Poisson-Dirichlet cases. 3) It briefly describes some applications of these processes in mixture modeling and summarizes different sampling approaches like blocked Gibbs and slice sampling that rely on truncation of the infinite-dimensional distributions.
Bayesian Nonparametrics, Applications to biology, ecology, and marketingJulyan Arbel
This document discusses applications of Bayesian nonparametric methods to various domains including toxicology, ecology, marketing, human fertility, and more. It provides examples of using rounded Gaussian mixtures and Dirichlet process mixtures to model count data from developmental toxicity studies and animal abundance data. Applications to modeling multivariate mobile phone usage data and basal body temperature curves are also described. The document emphasizes that Bayesian nonparametric approaches allow inclusion of prior information and flexible modeling of complex data structures.
A Gentle Introduction to Bayesian NonparametricsJulyan Arbel
The document provides an introduction to Bayesian nonparametrics and the Dirichlet process. It explains that Bayesian nonparametrics aims to fit models that can adapt their complexity based on the data, without strictly imposing a fixed structure. The Dirichlet process is described as a prior distribution on the space of all probability distributions, allowing the model to utilize an infinite number of parameters. Nonparametric mixture models using the Dirichlet process provide a flexible approach to density estimation and clustering.
The document outlines a paper on Bayesian linear models. It introduces a simple example of a linear model with exchangeable priors. It then presents the general Bayesian linear model and theorems for the posterior distribution given multiple stages of priors. It applies this to an experimental design setting, deriving Bayes estimates that shrink treatment and block effects towards zero based on their variances.
This document discusses different approaches to Bayesian analysis including objective, subjective, robust, frequentist, and quasi Bayesian analysis. It provides examples and discusses the advantages and disadvantages of each approach. Objective Bayesian analysis uses objective prior distributions designed to be minimally informative, while subjective Bayesian analysis aims to fully specify subjective priors but has challenges in practice. Robust Bayesian analysis considers classes of models and priors to provide interval estimates. Frequentist Bayesian analysis combines Bayesian and frequentist ideas, and quasi Bayesian analysis uses ad hoc priors. Computational techniques for Bayesian analysis include calculating integrals and posterior modes using Laplace approximation, Monte Carlo sampling, and MCMC methods.
Lewis Carroll wrote "Pillow Problems", a collection of 72 logic and probability puzzles, while lying in bed at night. Many had clever but flawed solutions due to Carroll's limited understanding of modern probability concepts. For example, in one problem about breaking rods, Carroll incorrectly assumed the probability of breaking at the middle was nonzero. Overall, "Pillow Problems" reflects the nascent state of English probability in Carroll's time and his personal difficulties with more rigorous concepts like continuous probabilities.
The document discusses several key ideas in statistics and modeling:
1. Fisher and Neyman had different views on model specification - Fisher saw it as practical while Neyman emphasized theoretical building blocks.
2. Statistics can contribute a "reservoir of models", model selection techniques, and classification of theoretical vs empirical models.
3. Theoretical models aim to explain underlying mechanisms while empirical models guide actions based on forecasts.
4. Examples like Mendel's inheritance models, Pearson distributions, and Galileo's trial illustrate the development and application of statistical modeling.
This document discusses different approaches to specifying prior distributions in Bayesian statistics. It begins by introducing the binomial model for coin tossing and how priors and posteriors are calculated. It then describes three categories of Bayesian priors: classical Bayesians use a flat prior, modern parametric Bayesians use a Beta distribution prior, and subjective Bayesians quantify existing knowledge about a process. The document shows that different priors lead to different posteriors. It further explains that any prior density can be approximated by mixtures of Beta densities, and extends this concept to the exponential family. The exponential family conjugate prior is also discussed. Finally, connections are made between the exponential family, Beta density priors, and a generalization about conditional expected posteriors.
The Metropolis Hastings algorithm is an MCMC method for obtaining a sequence of samples from a probability distribution when direct sampling is difficult. It constructs a Markov chain that has the desired target distribution as its stationary distribution. At each step, a candidate sample is generated and either accepted, replacing the current state, or rejected, keeping the current state. The acceptance ratio is determined by the ratio of probabilities of the candidate and current states. The algorithm is a generalization of the Metropolis algorithm that allows for non-symmetric proposal distributions. When the chain satisfies ergodicity conditions, the sample distribution will converge to the target distribution as the number of samples increases.
This document discusses the connection between Ockham's Razor and Bayesian analysis. It explains that Ockham's Razor favors the simplest hypothesis consistent with the data, and Bayesian analysis can help determine how much a simpler model should be preferred. It provides Galileo's problem of developing the law of falling bodies as an example. Jeffrey and Wrinch suggested using prior probabilities to represent simplicity, with the hypothesis having fewer parameters being assigned a higher prior probability. However, defining simplicity based solely on prior probabilities is problematic. Alternatively, a simpler hypothesis that makes precise predictions should be given greater credence if those predictions are confirmed. The key idea linking Bayesian analysis and Ockham's Razor is how simplicity in a hypothesis is represented and
This document provides a list of 33 papers related to Bayesian statistics for students to choose from for a presentation. It includes brief descriptions of several theoretical and general audience journals. The papers cover a range of topics in Bayesian statistics published between 1763 and 2013. Students will be evaluated on their understanding and presentation of the chosen paper.
This document provides a list of 35 references related to Bayesian statistics. It includes journal articles published between 1963 and 2013 in publications like The Annals of Probability, Journal of the American Statistical Association, and Bayesian Analysis. These references cover topics such as Markov chain Monte Carlo sampling methods, Bayesian model specification, consistency of Bayes estimates, and nonparametric Bayesian inference.
The document discusses using a dependent Dirichlet process (DDP) to model ecological data measuring microbe abundance across different pollution sites. It first introduces the biology question and data, which contains measurements of various microbes found at sites with different pollution levels. It then summarizes the Dirichlet process and introduces the DDP as a way to model dependence between sites. The DDP defines a process on the beta distribution parameters that determine the weights in the Dirichlet process mixture, allowing weights to vary based on pollution level.
This document introduces a dependent Dirichlet process (DDP) model that allows the cluster weights and locations to vary based on a covariate x. It defines a measure of dependence between data points based on x, and derives a Polya urn-style predictive rule. It then presents a novel DDP construction based on simulating gamma random variables, which allows for easy posterior computation. This model generalizes previous dependent DP work and can handle multidimensional covariates.
This document summarizes a discussion on the differences between assessing the "causes of effects" versus the "effects of causes". It outlines that the two questions, while related, require different statistical analyses and frameworks. The causes of effects question aims to determine what caused an observed outcome, while effects of causes looks at the impact of a treatment or exposure. Examples from legal cases, epidemiology, and discrimination studies are provided to illustrate how the perspective taken influences statistical analyses and interpretations.
1. Mix source code and documentation together
A
Write R code in LTEX using knitr, xtable and RStudio
Julyan Arbel
CREST-INSEE, Universit´ Paris-Dauphine
e
February 28, 2013
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 1 / 10
2. Goal
To have a single document which includes source code for easy update.
A
Use a single software: R interfaces LTEX, as it does with C++, JAGS,
(Word, Excel?), etc.
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 2 / 10
3. First things
We will use the knitr package which allows you to embed R code and figures
A
in LTEX documents (it is an evolution of Sweave). See the package
homepage http://yihui.name/knitr/
A
You need a valid LTEX distribution
We will use knitr in RStudio, because it’s well integrated in it
install.packages("knitr")
library("knitr")
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 3 / 10
4. Write a first document
Open a new ”R Sweave” document in RStudio
You can check that the toolbar now includes Format and Compile PDF
buttons
documentclass{article}
begin{document}
end{document}
Write your text, and insert
code chunks [Ctrl+Alt+I] for graphs or tables. A code chunk consists in R
code inside the following lines (mind to write both on single lines, with no
comment)
<<>>=
@
code values in the text with
Compile [Ctrl+Shift+I]
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 4 / 10
5. What to put in code chunks
Any code that you want to evaluate / not to evaluate, or show / hide: you can
either show the code, or its result, or both.
Functions
Graphs
Tables
Global options
Set working directory, etc.
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 5 / 10
6. Number of CRAN Packages
100
200
300
400
500
600
800
1200
1500
2000
2001−06−21 1.3
Julyan Arbel (CREST-INSEE)
2001−12−17 1.4
2002−06−12 1.5
2003−05−27 1.7
2003−11−16 1.8
2004−06−05 1.9
2004−10−12 2
Number of R packages (lien)
2005−06−18 2.1
AT
R code in L EX
2005−12−16 2.2
R Version
2006−05−31 2.3
2006−12−12 2.4
2007−04−12 2.5
2007−11−16 2.6
2008−03−18 2.7
2008−10−18 2.8
2009−09−17 2.9
110
129
162
219
273
357
406
548
647
739
911
1000
1300
1427
1614
1952
February 28, 2013
6 / 10
7. Number of R packages: now the code
rv <- seq(1.3, 2.9, .1)
pckg.num <- c(110,129,162,219,273,357,406,548,647,739,911,1000,1300,
rv.dates <- c("2001-6-21", "2001-12-17","2002-06-12","2003-05-27",
"2003-11-16","2004-06-05","2004-10-12","2005-06-18","2
"2006-12-12","2007-04-12","2007-11-16","2008-03-18","2
pckg.fit <- lm(pckg.num~rv)
par(mar=c(7, 5, 5, 3), las=2)
plot(as.POSIXct(rv.dates), pckg.num, xlab="",ylab="",col="red", log=
axis.POSIXct(1, 1:16, rv.dates, format="%Y-%m-%d")
axis(2, at=c(100,200,300,400,500,600,800,100,1200,1500,2000))
mtext("Number of CRAN Packages", side=2, line=3, las=3)
axis.POSIXct(3, rv.dates, rv.dates, labels=as.character(rv))
mtext("R Version", side=3, line=3, las=1)
axis(4, pckg.num)
abline(v=as.POSIXct(rv.dates), col="lightgray", lty="dashed")
abline(h=pckg.num, col="lightgray", lty="dashed")
abline(lm(log10(pckg.num)~as.POSIXct(rv.dates)), col="red")
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 7 / 10
8. To show graphs
Use that kind of code chunk
<<echo=FALSE,out.width=’.7textwidth’,fig=TRUE,include=TRUE>>=
library(ggplot2)
qplot(speed, dist, data=cars)+geom_smooth()
@
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 8 / 10
9. To show graphs: result
100
dist
50
0
5 10 15 20 25
speed
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 9 / 10
10. To show data tables
Use that kind of code chunk
<<echo=FALSE,results=asis>>=
load(file="data.Rdata")
row.names(data) = c(...)
library(xtable)
tab=xtable(data)
digits(tab)=1
print(tab,floating=FALSE,include.rownames=TRUE,type="latex")
@
Julyan Arbel (CREST-INSEE) R code in L EX
AT February 28, 2013 10 / 10