Rachel Leah Childers

@donskerclass.bsky.social

2453 Followers 389 Following

Econometrics, Statistics, Computational Economics, etc http://donskerclass.github.io 🇺🇲 in 🇨🇭. 🏳️‍⚧️

The set of moment functions f(X) you can choose for the method of moments applied to a model with likelihood P_{\theta}, which will ensure that the parameter value which matches the moments is an arbitrary value \bar{\theta} chosen by the researcher is given by the set of all square integrable functions which are orthogonal to the linear span of the likelihood ratio of the true distribution P with respect to the model-implied distribution P_{\bar{\theta}} (after subtracting 1 from the likelihood ratio for centering). This set is nontrivial precisely when the model is mis-specified, meaning that the likelihood ratio of the data distribution with respect to the model implied distribution at \bar{\theta} is not equal to 1, with positive probability.
Phase diagrams of the Representative Agent New Keynesian model in continuous time in the passive monetary active fiscal regime, linearized on the left and global (under Rotemberg pricing) on the right. In both there is a saddle point normalized values of output Y=1, inflation pi=0. There is a 1d stable manifold in the Y,pi space which converges to this saddle. For a given initial debt, any point (y,pi) on this submanifold is stable. However, a government debt equation, which evolves autonomously from the (Y,pi) subsystem with Ricardian consumers, requires stable values of these variables and so selects the saddle point as unique initial condition in order to not blow up over time, a condition known as the fiscal theory of inflation (which in discrete time selects the price level, hence the "Fiscal Theory of the Price Level"). Kaplan notes that this selection is implied by transversality for the consumers holding the debt, so is a unique equilibrium at least under a boundedness restriction for (Y_t,pi_t) and not an external equilibrium refinement. In the paper he discusses why economists other than John Cochrane have been reluctant to consider this setting as plausible, and discusses the non-Ricardian case where B enters the Euler equation and picks out a similar solution under purely local criteria, though global uniqueness is still only a conjecture for that case.
Me riding a skateboard in a park. I have on a blue dress with white polka dots, leggings and off-brand skate shoes. My arms are out because I'm still learning to balance.
Cover of "The Identity Matrix" by Jack L. Chalker The cover art is a drawing of a woman below a UFO-style spacecraft.
Cover of "Causal Inference" by Paul R. Rosenbaum.
Selection from Ra'anan Abusch, "EUNUCHS AND GENDER TRANSFORMATION: Philo's exegesis of the Joseph narrative" in EUNUCHS IN ANTIQUITY AND BEYOND. Shaun Tougher, ed. 2002 p105 Eunuchs and castration in Philo Philo include castrates among a lengthy list of different types of male gender-bending and consistently censures them as transgressors of divinely ordained gender categories. In one colourful and strident passage, Philo writes: In former days the very mention of (pederasty) was a great disgrace, but now it is a matter of boasting nor only to the active partner but to the passive
A scatter plot of wages vs education from the Angrist and Krueger data with points highlighted in a variety of colors, reflecting posterior draws of cluster assignments in a Dirichlet process mixture of regressions. Sims suggested this approach in his lecture on "Sharp Econometrics", which brought his ideas about really thinking about what goes into the structure of data to microeconometric problems. See slides and video: https://www.chamberlainseminar.org/past-seminars/spring-2023#h.e0uu7eildjmq
Cover of "Candy Darling: Dreamer, Icon, Superstar" by Cynthia Carr
Coiflet of order 2, from https://en.wikipedia.org/wiki/Coiflet Coiflets are also due to Ingrid Daubechies, but she gave them to Ron Coifman and let him name them after himself I guess because she also had her own wavelet family.
Figure IV, Prices and Mobile Phone Service in Kerala, from R. Jensen The digital provide: information (technology), market performance, and welfare in the south Indian fisheries sector Q. J. Econ., 122 (3) (2007), pp. 879-924 https://doi.org/10.1162/qjec.122.3.879 The figure shows price time series for 3 regions in Kerala in 2001 Rs./kg average 7:30-8:30am beach price for average sardines over 250 survey weeks. Each region is marked with a vertical line showing the date at which phones are added to the market, with introduction around week 20 for Region I, week 100 for Region II, and week 200 for Region III. In all regions, the volatility decreases markedly, rapidly, and persistently after the date of introduction, with price ranges previously varying at high frequency in the 0-14 Rs/kg range subsequently varying by only a few Rupees from week to week.
Cover of "The Means of Prediction: How AI Really Works (and Who Benefits)" by Maximilian Kasy
"I'm in this photo and I don't like it" meme.
Book cover: "The Transgender Issue: Trans Justice is Justice for All" by Shon Faye
Fig 4 from Zhang, Lee, Liu "Statistical Learning Theory in Lean 4: Empirical Processes from Scratch" The dependency graph of the formalizations. Diagram shows proof of Dudley's entropy integral with preceding lemmas and Gaussian Lipschitz concentration likewise, feeding into a Gaussian Complexity inequality and an error bound for critical radius then used to prove sharp minimax error rates for linear regression.
Free Weekly Econometrics Office Hours Email: rachelleahchilders@gmail.com or Sign up form: https://forms.gle/tSk48w1msZgrCUqX8 Time: Tuesdays 4:00-6:00PM Central European Time (GMT +1) (US Eastern Standard Time 10:00AM-12:00PM) (or by appointment) Location: Zoom Link https://uzh.zoom.us/j/62894466032?pwd=M28RFSrc44buAIJtPdvBEeYAIcClip.1 Who: Anyone. Grad students, researchers, government workers. Private sector is okay but in that case if your question requires work that exceeds the allotted time I may request to negotiate a consulting fee. What I can probably help with: Theory questions. Research design. Modeling. Particular expertise: Time series. Causal inference. Bayes. Structural approaches. Machine learning. Theory: Asymptotics. Statistical learning. Bayes/MCMC. Identification. Decision theory. Semiparametrics. Fields: I know most about macro (DSGE, heterogeneous agents, VARs, etc), can help with finance and applied micro (labor, development, health, etc), and can follow along with statistics problems in other areas. Code: I think in R, can write Julia, and can get by in Python. I am likely to suggest you build a model in Stan. I know Stata but if it’s relevant to your question I suspect you can get better help elsewhere.
Profile header of Katie Tightpussy, Bluesky user @katie.bzky.team, highlighting a count of 236.6K posts.
From Larson (1964), "The Hog Cycle as Harmonic Motion", some key equations, derived from a continuous time hog cycle model with linear demand and in which quantities respond to prices linearly with a 12 month delay: (4) d/dt p_{t+12} = -bkp_t (5) d/dt q_{t+12} = -bkq_t If bk=1, this system yields a solution (7) p_t = cos(2πt/48 + e_p) (8) q_t = cos(2πt/48 + e_q) where e_p and e_q depend on initial conditions. If they differ by π radians, the solutions are consistent and the system is in resonance .
Photo of Ethel Cain and band on stage, dramatically backlit, surrounded by branches and hanging vines.
Free Weekly Econometrics Office Hours Email: rachelleahchilders@gmail.com or Sign up form: hhttps://forms.gle/tSk48w1msZgrCUqX8 Time: Wednesdays 3:30-5:30PM Central European Time (GMT +1) (US EDT 10:30AM-12:30PM/9:30-11:30AM EST) (or by appointment) Location: Zoom Link https://uzh.zoom.us/j/64132987908?pwd=OzmlySLA3A3cjZz6RX7ibIuLoeJayU.1 Who: Anyone. Grad students, researchers, government workers. Private sector is okay but in that case if your question requires work that exceeds the allotted time I may request to negotiate a consulting fee. What I can probably help with: Theory questions. Research design. Modeling. Particular expertise: Time series. Causal inference. Bayes. Structural approaches. Machine learning. Theory: Asymptotics. Statistical learning. Bayes/MCMC. Identification. Decision theory. Semiparametrics. Fields: I know most about macro (DSGE, heterogeneous agents, VARs, etc), but can follow along in finance and applied micro (labor, development, health, etc). Code: I think in R, can write Julia, and can get by in Python. I am likely to suggest you build a model in Stan. I know Stata but if it’s relevant to your question I suspect you can get better help elsewhere.
Tweet from Rachel Leah Childers, @donskerclass Favorite Banach spaces, ranked (partial order): W^k_2, Cameron-Martin space (any), L^2, L^∞, L^p (2<p<∞), W^k_p,..., L^1, L^p (1<p<2) 9:18 PM, August 27, 2015 Ranking does not necessarily reflect current views of the author. Apologies due to L^1 and their friends and loved ones....
Office meme from Nan Jiang blog post Frame 1: Two cards reading "policy gradient with 100 tweaks" and "policy gradient with another different 100 tweaks", respectively. "Corporate needs you to find the differences between this picture and this picture." Frame 2: Pam Office: "They're the same picture"
Set list for jasmine.4.t's show in Zurich last night, given to me by the band afterwards Skin on Skin Tall Girl Breaking In Reverse Find Ur Pppl I Can't Believe I Don't Think Kitchen You Are The Morning Tesco Elephant Woman Did U No
Figure 7: Information aggregation in naïve model. From "Treasure Hunt: Social Learning in the Field" by Möbius, Phan, Szeidl https://www.markusmobius.org/sites/default/files/markusmobius/files/treasure_03_01_2015_0.pdf Lefthand figure: "No multiple paths" Diagram of directed graph with arrows C->B, B->A, D->A, with root nodes C, D highlighted. Arrows depict transmission of independent signals from B, C, and D to A, which in total are counted once each. Righthand figure: "Multiple paths" Diagram of directed graph with arrows C->B, B->A, D->A, and now also C->D with nodes C, D highlighted. Arrows depict transmission of independent signals from B, C, and D to A. Because both B and D are downstream of C and upstream of A, the signal from A contributes along both paths. Under naive (DeGroot) learning, signals from correlated sources are not discounted, so A "double counts" the signal from C. Identities of A, B, C, and D may be filled in by the reader.
The Sisters of Dorley Welcome to Dorley Hall By Alyson Greaves Book cover. To spoil the joke, this is a book about a torture basement which I probably shouldn’t be mentioning to cis people.
NBER WP 32602, the earlier version of the paper. Formerly titled "The Macroeconomics of Narratives", now "Contagious Business Cycles" Joel P. Flynn and Karthik Sastry Abstract: We study the macroeconomic implications of narratives, defined as beliefs about the economy that spread contagiously. In an otherwise standard business-cycle model, narratives generate persistent and belief-driven fluctuations. Sufficiently contagious narratives can "go viral," generating hysteresis in the model's unique equilibrium. Empirically, we use natural-language-processing methods to measure firms' narratives. Consistent with the theory, narratives spread contagiously and firms expand after adopting optimistic narratives, even though these narratives have no predictive power for future firm fundamentals. Quantitatively, narratives explain 32% and 18% of the output reductions over the early 2000s recession and Great Recession, respectively, and 19% of output variance.
Hand-size ringed ruled notebook with Rilakkuma (a Hello Kitt teddy bear) on it, with friends, dressed in a variety of nautical costumes including a seal, an octopus, a ray, and a shark. The contents of the notebook are primarily proofs related to the Generalized Method of Moments, and some derivations about Sobolev spaces.
The latest version of "Debiased Semiparametric U-statistics", with a new title: Machine Learning Inference on Inequality of Opportunity Juan Carlos Escanciano, Joël Robert Terschuur [Submitted on 10 Jun 2022 (v1), last revised 4 Oct 2023 (this version, v3)] https://arxiv.org/abs/2206.05235
The paper I found on semiparametric U-statistics: Debiased Semiparametric U-Statistics: Machine Learning Inference on Inequality of Opportunity Juan Carlos Escanciano, Joël Robert Terschuur Submitted on 10 Jun 2022 (this version, v1), latest version 4 Oct 2023 (v3)] https://arxiv.org/abs/2206.05235v1
Fig 4 from Cattaneo Crump Farrll Fung (2024) "On Binscatter" https://maxhfarrell.com/research/Cattaneo-Crump-Farrell-Feng2024_AER.pdf Panel A, B, C "Oversmoothed", "Optimal", and "Undersmoothed" show binned scatter plots with J=5, 11, and 50 categories, respectively, and accompanying best fit line.
Bayesian Bullshit Sajan Srivastava Tymofiy Mylovanov Rakesh Vohra August 2024 Abstract A bullshitter neither knows nor cares about the truth, and therefore, it has been asserted, is more pernicious than a liar. We examine this assertion within the standard model of cheap talk communication where a bullshitter is modeled as an uninformed Sender. We show that in some circumstances, uncertainty about whether the Sender is informed or not can increase the welfare of the Receiver. Keywords: Bayesian Persuasion, Information Design, Cheap Talk JEL Classification: C6, D82, D83
Casey helping my dad as he's watering the garden at the old place. He takes some sips from the hose as my dad goes from plant to plant.
Casey Corgi Childers, cuddling his pillow, earlier today.
Screenshot of tweets: Quoting Tweet: I see that you have taken on a weighty vow. I respect it. tell the world. Quoted tweet (by me): PSA that due to long-ago choice of username, I am morally obligated to engage with any tweet regarding Donsker's theorem. Please use this power wisely.
Estimated productivities, amenities, and coercion Maps of the US South c1860 with county-level values from an estimated structural model based on population and production data. Of the 3, the most visually notable is the estimated coercion, a measure of the gap between enslaved and free worker populations, which concentrates in the cotton belt and around the Mississippi. Results in the presentation show amenities correlate negatively with malaria, while productivity shows weak correlation with cotton production, which should explain the lack of geographic concentration,
Table of Bowdoin 2024-2025 Cost of Attendance Direct Costs Tuition $67,198 Fees $634 Housing $9,148 Food $9,340 Direct Costs Total $86,320 Indirect Costs Books, Course Materials, Supplies and Equipment $840 Miscellaneous Personal Expenses $1,660 Transportation varies Indirect Costs Total $2,500+ Total Cost of Attendance $88,820+ This page is meant to be an overview and an introduction to costs and aid at Bowdoin. When you're ready to talk about detailed numbers and processes, the Office of Student Aid employs five of the best listeners we've ever met—they work with each applicant's family, one-on-one.
Illustration of posterior marginal densities from Bradley-Terry model for values of 4 possible options, under a sequence of online ranking updates chosen via Thompson Sampling. Densities for options 1 and 4 shift right and narrow as more samples are drawn, while densities for options 2 and 3 shift left. Densities fluctuate a bit more than they should due to MCMC variability.
Screenshot of tweet by user kassanove @deuxnan *** Call Me By Your Name was the first socially acceptable movie for fujoshi's to hit the mainstream. i think Sufjan Stevens bridged the divided between girls on tumblr who stink bad and the judges at Cannes. Timothee Chalamet has live action anime adaptation yaoi boy physiognomy
Header for Archive of Our Own followed by search results: "You searched for: back pain sort by: best match descending 22,199 Found"
Text from van der Vaart, "Asymptotic Statistics" Ch 27, http://www.stat.yale.edu/~pollard/Books/LeCamFest/VanderVaart.pdf The theorem may have looked to somewhat too complicated to gain popularity. Nevertheless Hájek's result, for general locally asymptotically normal models and general loss functions, is now considered the final result in this direction, Hájek wrote: "The proof that local asymptotic minimax implies local asymptotic admissibility was first given by LeCam (1953, Theorem 14). ... Apparently not many people have studied Le Cam's paper so far as to read this very last theorem, and the present author is indebted to Professor LeCam for giving him the reference" Not reading to the end of Le Cam's papers became not uncommon in later years. His ideas have been regularly rediscovered
Iterated analysis filter bank, with 2X downsampling Diagram from https://rafat.github.io/sites/wavebook/intro/fb.html
Figure 2 of https://arxiv.org/abs/2203.00837 Graph showing convergence rate for CATE estimation as function of smoothness of conditional means and the CATE function itself (Hölder exponents "s" and "γ"), showing that smoothness of the CATE determines the rate at the typical nonparametric rate if the means are sufficiently smooth (after the "elbow") while both matter if the means are sufficiently rough. Caption: "The minimax rate for CATE estimation, as a function of average nuisance smoothness s and CATE smoothness γ, each scaled by covariate dimension d. The black dotted line denotes a threshold on the nuisance smoothness s/d, below which the oracle nonparametric regression rate n�1/(2+d/γ) is unachievable (the “elbow” phenomenon)."
State of Maine Cumberland County Probate Court In Re: ***** ******** CHILDERS CERTIFICATE OF NAME CHANGE I, Susan G. Schwartz, Register of Probate of Cumberland County Probate Court in and for said County, on the 7th day of MARCH 2025 the name of ***** ******** CHILDERS of BRUNSWICK, ME in said County was changed to RACHEL LEAH CHILDERS which shall hereafter be this person's legal name. IN WITNESS WHEREOF, I have hereunto set my hand and affixed the official seal of said Court, this 7th day of MARCH 2025. S. G. Shwartz Register of Probate
Lars Ljungqvist Thomas J. Sargent recursive macroeconomic theory, second edition (红色的)
Free Weekly Econometrics Office Hours Email: rachelleahchilders@gmail.com or Sign up form: https://forms.gle/XS55FASiGGHqAZKa6 Time: Wednesdays 10:00-12:00AM Eastern US (or by appointment) Location: Zoom Link https://bowdoin.zoom.us/j/96039587180 Who: Anyone. Grad students, researchers, government workers. Private sector is okay but in that case if your question requires work that exceeds the allotted time I may request to negotiate a consulting fee. What I can probably help with: Theory questions. Research design. Modeling. Particular expertise: Time series. Causal inference. Bayes. Structural approaches. Machine learning. Theory: Asymptotics. Statistical learning. Bayes/MCMC. Identification. Decision theory. Semiparametrics. Fields: I know most about macro (DSGE, heterogeneous agents, VARs, etc), but can follow along in applied micro (labor, development, health, etc) & some finance. Code: I think in R, can write Julia, and can get by in Python. I am likely to suggest you build a model in Stan. I know Stata but if it’s relevant to your question I suspect you can get better help elsewhere.
Figure V from Healy and Leo, "Minimal Experiments", depicting two polyhedrons with vertices labeled by 4-tuples representing permutations over 4 items. Shortest paths between selected edges are highlighted. Figure Caption: "The shortest path from abcd to cabd and one of the two shortest paths from cabd to adcb. The edges have been labeled along each path."
Partially Linear Fixed Effects Model derivations I sent to Ben Hanowell on 7-22-2023: Consider the following partially linear panel data model with $a_i$ what an economist would call a fixed effect and a statistician a correlated random effect, ie $Cov(a_i,X_{it})\neq 0$. $$Y_{it}=a_i+\theta D_{it}+f(X_{it})+u_{it}$$ Apply within demeaning $\bar{V}_i:=\frac{1}{T}\sum_{t=1}^{T}V_{it}$ $$Y_{it}-\frac{1}{T}\sum_{t=1}^{T}Y_{it}=\theta(D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it})+f(X_{it})-\frac{1}{T}\sum_{t=1}^{T}f(X_{it})+u_{it}-\frac{1}{T}\sum_{t=1}^{T}u_{it}$$ Take conditional expectations given $\vec{X}_i=(X_{i1},\ldots,X_{it})$ Assume strict exogeneity $E[u_{it}|\vec{X}_i]=0\ \forall t$. $$E[Y_{it}-\frac{1}{T}\sum_{t=1}^{T}Y_{it}|\vec{X}_i]=\theta E[D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it}|\vec{X}_i]+f(X_{it})-\frac{1}{T}\sum_{t=1}^{T}f(X_{it})$$ Subtract (this is the "Robinson transformation") $$Y_{it}-\frac{1}{T}\sum_{t=1}^{T}Y_{it}-E[Y_{it}-\frac{1}{T}\sum_{t=1}^{T}Y_{it}|\vec{X}_i]=\theta(D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it}-E[D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it}|\vec{X}_i])+u_{it}-\frac{1}{T}\sum_{t=1}^{T}u_{it}$$ Estimate the conditional expectations by your favorite nonparametric regression method in a split sample (w/ or w/o crossfitting), plug in, and regress LHS on $(D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it}-\widehat{E}[D_{it}-\frac{1}{T}\sum_{t=1}^{T}D_{it}|\vec{X}_i])$ by OLS. Under regularity conditions (eg $o(n^{-1/4})$ rates), $\widehat{\theta}$ will be consistent and asymptotically normal.
Blueberry and pear pie, with homemade crumble topping, made with Comice pears received as a holiday gift. Recipe loosely adapted from a combination of a few recipes in Kate Lebo, "Pie School; Lessons in Fruit, Flour, and Butter"
Excerpt from my blog post, "Papers I Liked 2023" https://donskerclass.github.io/post/papers-2023/ "Egami, Hinck, Stewart, Wei “Using Large Language Model Annotations for Valid Downstream Statistical Inference in Social Science: Design-Based Semi-Supervised Learning” You can and should use classical semiparametric techniques with sample-splitting to get confidence intervals when using large language models. The methods are old and well established, but LLM users need to hear it. See also Zrnic and Candès and Mozer and Miratrix who also suggested exactly the same estimator (literally the same formula in all 3 papers), but who cares, any good idea should be published multiple times."
Histograms of forecasts for the upcoming Employment Situation Report from my Economic Forecasting students Unemployment mean: 4.112581 Payrolls growth mean: 137.5832
Screenshot of tweet thread from https://x.com/DonskerClass/status/1753624011026694170 In response to a request on Bayesian Instrumental Variables approaches, I wrote: "There is no unique Bayesian version of IV (or any semiparametric method), but I like Rossi's BNP textbook for triangular IV, Richardson for binary/LATE style models and a number of "Bayesian GMM" methods: https://academic.oup.com/jrsssb/article/81/1/5/7048378 " Referencing quote: "I'd be interested to see real data examples comparing modeled errors vs sandwich-adjusted posteriors vs full Bayes semiparametrics like BETEL https://doi.org/10.1093/biomet/92.1.31 or https://scholar.harvard.edu/shephard/publications/moment-conditions-and-bayesian-nonparametrics or https://arxiv.org/abs/2204.09862 or AM quasi-Bayes https://scholar.harvard.edu/iandrews/publications/optimal-decision-rules-weak-gmm" and followed up with "Notably missing, AFAIK, but possible: Gaussian Process approaches to Bayesian MTE, NPIV (though it is equivalent to the huge lit on Bayesian linear inverse problems), Bayesian proximal causal inference (though related to measurement error models). Lots of space to explore." I have highlighted the sentence on Gaussian Processes for Bayesian MTE, which is the topic of the article in the quoted skeet.
Comic by Haus of Decline depicting Liv Agar raising a finger and saying "Only chumps do spiro it's true" followed by a frame with her face in the frame of the "Canadian Heritage Moments" title screen.
Free Weekly Econometrics Office Hours Email: davidbchilders@gmail.com or Sign up form: https://forms.gle/yVz8RtVALDXTmv5u7 Time: Wednesdays 10:00-12:00AM Eastern US (or by appointment) Location: Zoom Link https://bowdoin.zoom.us/j/7322488068 Who: Anyone. Grad students, researchers, government workers. Private sector is okay but in that case if your question requires work that exceeds the allotted time I may request to negotiate a consulting fee. What I can probably help with: Theory questions. Research design. Modeling. Particular expertise: Time series. Causal inference. Bayes. Structural approaches. Machine learning. Theory: Asymptotics. Statistical learning. Bayes/MCMC. Identification. Decision theory. Semiparametrics. Fields: I know most about macro (DSGE, heterogeneous agents, VARs, etc), but can follow along in applied micro (labor, development, health, etc) & some finance. Code: I think in R, can write Julia, and can get by in Python. I am likely to suggest you build a model in Stan. I know Stata but if it’s relevant to your question I suspect you can get better help elsewhere.
Slide 9 of presentation: Extending to Heterogeneous Agents Image of Geoffrey Hinton with modified quote: "To deal with a ∞-dimensional space, visualize a 3-D space and say 'Hilbert' to yourself very loudly. Everyone does it." ∞ and 'Hilbert' are replacing the original, which said '14'. However, the same principle applies.
2023 Sveriges Riksbank Prize in Economics in Honor of Alfred Nobel predictions/wishlist - BLP: Berry, Levinsohn, and Pakes for "new empirical industrial organization". Alternates: Bresnahan, Porter - New Keynesian macro: Mike Woodford? Alternates: Galí, Blanchard, Calvo, Kiyotaki, Mankiw, Taylor. - Heterogeneous agents: Truman Bewley. Alternates: Axtell. - Chuck Manski - Papadimitriou and Daskalakis for computational complexity of Nash equilibria - Trade: Eaton, Kortum, and Melitz
How Many Licks Does It Take To Get To The Tootsie Roll Center Of A Tootsie Pop? Helen Zhang Heather Chalfin David Childers May 16, 2005
NY Magazine Approval Matrix for week of July 15, 2024. Cartesian plot with Y axis labeled "Highbrow" at top and "Lowbrow" at bottom, and X axis labeled "Despicable" at right and "Brilliant" at left. Placed on the chart at various locations are various current events, with images. E.g. Papaya King hot dogs are "Lowbrow" and "Brilliant", the "skeletons in Alice Munro's closet" are highbrow and despicable.
First: the paper covers many settings, from toy tractable models, to qualitative results, to empirics: not all settings use the same assumptions. Re: 3.1: these assumptions are "phenomenological" for the parametric Multivariate normal case (estimate $\mu_i$, $\Sigma_i$, resample from $\mathcal{N}(\mu_i,\Sigma_i)$ each time). They do not demonstrate that standard estimators obey them. The 1d, for which they have a sort of closed form, approximately satisfies them. Think of this as saying: a procedure "like" a real one can be modeled this way. 3a and 3b are separate models, 3a ignores higher order terms, 3b imposes a bound. It might be possible to prove them rigorously as limits, but they don't. The data processing inequality holds here but strictly shows KL divergence increases over iterates: it is possible for $W^2$ to remain bounded while KL $\uparrow\infty$. But yes, just the idea is basically the same. (Text continues beyond character limit)
Fig 1 from https://www.aeaweb.org/articles?id=10.1257/jep.28.2.29 The “Double Selection” Approach to Estimation and Inference versus a Naive Approach: A Simulation from Belloni, Chernozhukov, and Hansen (forthcoming) (distributions of estimators from each approach) The left distribution is multimodal and biased, the right is centered and approximately Gaussian. Notes: The left panel shows the sampling distribution of the estimator of α based on the first naive procedure described in this section: applying LASSO to the equation yi = di + x′i θy + ryi + ζi while forcing the treatment variable to remain in the model by excluding α from the LASSO penalty. The right panel shows the sampling distribution of the “double selection” estimator (see text for details) as in Belloni, Chernozhukov, and Hansen (forthcoming). The distributions are given for centered and studentized quantities.
Pairs plot for Normal-Half Laplace distribution, produced by variational parallel tempering in Pigeons.jl based on Stan code of Meager (2019). Parameter posteriors demonstrate high curvature and narrow tails, but vary smoothly.
Trace plots for univariate parameters from normal-half Laplace model, showing clear periods of alternation between modes, which often indicates poor ability to distinguish relative mode densities.