Data Science at Berkeley

48
Data Science at Berkeley Joshua Bloom UC Berkeley, Astronomy @pro%sb PyData, May 4. 2014

description

Keynote talk at PyData Silicon Valley 2014 (Facebook Headquarters) on May 4, 2014, by Prof. Joshua Bloom.

Transcript of Data Science at Berkeley

Page 1: Data Science at Berkeley

Data$Science$at$Berkeley

Joshua'Bloom'UC'Berkeley,'Astronomy

@pro%sb

PyData,'May'4.'2014

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The$First$Rule$of$Data$Science...

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diagram'from'Drew'Conway

Data$Science$as$a$Discipline

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diagram'from'Drew'Conway

Data$Science$as$a$Discipline• What'are'the'Core$Principles?

• Is'it'an'academic$pursuit'to'be'taught'or'a'skillset'to'be'trained?

• When'should'they'be'taught?'At'what'level'of'depth/breath?

• Who'should'teach'them'and'who'should'know'data'science?

• Where'should'investments'be'made?'Does'Data'Science'need'an'intellectual'home'within'insHtuHons?'

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“I'love'working'with'astronomers,'since'their'data'is'worthless.”

K'Jim'Gray,'Microso'

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Bayesian FrequenHst

Theory/HypothesisDriven

DataDriven

non-parametric

parametric

Data$Inference$Space

Hardware---laptops-→-clusters/supercomputersSo6ware---Python/Scipy,-R,-...

Carbonware---(astro)-grad-students,-postdocs

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mij = µi +M0j

+ ↵j log10 (Pi/P0)

+ E(B � V )i ⇥ [RV ⇥ a (1/�i) + b (1/�i)]

+ ✏ij

Bayesian$Distance$LadderSome-Variable-Stars-show-a-PeriodDBrightness-CorrelaFon

i'indexes'over'individual'starsj'indexes'over'wavebandsa'and'b'are'fixed'constants'at'each'color

Data--134'RR'Lyrae'(ultraviolet'to'infrared)

Fit--307-dimensional-model-parameter-inferenceK'determinisHc'MCMC'model'with'PyMCK'~6'days'for'a'single'run'(one'core)K'parallelism'for'convergence'tests

Klein+12;'Klein,JSB+14,

“Leavitt Law”

HenrieKa-Swan-LeaviK

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4 C. R. Klein et al.

Figure 6. Multi-band period–luminosity relations. RRab stars are in blue, RRc stars in red. Blazhko-a↵ected stars are denoted with

diamonds, stars not known to exhibit the Blazhko e↵ect are denoted with squares. Solid black lines are the best-fitting period–luminosity

relations in each waveband and dashed lines indicate the 1� prediction uncertainty for application of the best-fitting period–luminosity

relation to a new star with known period.

c� 2013 RAS, MNRAS 000, 1–11

• Sub-1% distance uncertainty

• Precision 3D dust in the Milky Way

Bayesian$Distance$LadderMilky Wayprojection

distancedust

Brightne

ss

Period Klein+12;'Klein,JSB+14,

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Morphology of LMC RR Lyrae stars 3

exposure, 61 of the 62 individual science CCDs2 were pro-cessed using standard reduction algorithms (bias subtrac-tion, flat-fielding, etc.) using the computational resources atthe National Energy Research Scientific Computing Center(NERSC3).

Astrometry on individual frames was calibrated withrespect to reference sources from the Two Micron All SkySurvey (2MASS; Skrutskie et al. 2006) using the astrom-etry.net software package (Lang et al. 2010). Photometriccalibration was performed using same-night observations ofsources in the Sloan Digital Sky Survey Stripe 82 StandardStar Catalog (Ivezic et al. 2007). Applying standard cali-bration methodology (e.g., Ofek et al. 2012), we find thatwe can achieve a robust scatter in our absolute photometriccalibration of . 0.02mag on clear nights (& 50% of the ob-serving time from the Science Verification run). While thiscalibration can be improved with more advanced modelingof instrumental signatures (e.g., Tucker et al. 2014), we findthat 2% precision is su�cient for our scientific objectives.

The DECam observing program produced on averageone 1-second exposure for each of the 30 frames each night.This sub-optimal exposure depth and cadence was neces-sitated by the oversubscription of DECam and the desireto test the instrument performance in unusual or extrememodes of operation during the science verification period.Most of the RR Lyrae targets are marginally detected insingle exposures, but this was not su�cient to produce thetraditional phase-folded light curves that provide mean-fluxmeasurements through harmonic modeling. To recover z-band mean-flux magnitudes the individual epochs of eachCCD were flux-scaled using relative photometric zero pointsmeasured with PSFex (Bertin 2011) and SExtractor (Bertin& Arnouts 1996), and then average combined with Swarp(Bertin et al. 2002). This procedure resulted in a mean er-ror on the z-band mean-flux magnitude measurements forthe final RR Lyrae sample of 0.0387 mag, which includesthe errors introduced by absolute photometric calibrationand the relative epoch-to-epoch flux-scaling.

3 RR LYRAE DISTANCE MEASUREMENTS

Distances for the individual RR Lyrae stars are measuredby using the observed, extinction-corrected V , I, and zmagnitudes in combination with the period–magnitude rela-tions. The method employed is similar to the simultaneousBayesian linear regression methodology described in Klein &Bloom (2014). A significant di↵erence is that in the presentanalysis the colour excess is considered part of the observeddata, not as a prior to which a posterior distribution is fit.The following two subsections detail the derivation of indi-vidual RR Lyrae colour excess and provide more descriptionof the specific period–magnitude relations fitting procedure.

3.1 Colour excess

The E(V � I) colour excess for each RR Lyrae star is de-rived from the observed OGLE III mean-flux magnitudes

2 One chip, C61, was not fully operable during the Science Veri-fication run.3 See http://www.nersc.gov.

Figure 2. Map of the LMC RR Lyrae stars coloured by colourexcess value, E(V � I). Median RR Lyrae colour excess value is0.228 mag, and the median error per star is 0.093 mag.

and the previously-calibrated V and I period–magnitude re-lations published in Klein & Bloom (2014). This approachis conceptually similar to that of Haschke et al. (2011), withthe main di↵erence being that the earlier study used the the-oretical V -band metallicity–luminosity and I-band period–metallicity–luminosity relations of Catelan et al. (2004). Inthe present work, colour excess is given by the subtraction ofthe absolute colour (from the period–magnitude relations)from the observed colour,

E(V � I) = (mV

�mI

)� [MV

(P )�MI

(P )]. (1)

The dominant source of error in the colour excess cal-culation is the intrinsic scatter of the period–magnitude re-lations. The median colour excess for the LMC RR Lyraepopulation is found to be 0.228 mag, with a median errorof 0.093 mag. This is significantly greater than the medianvalue of 0.11 mag (with standard deviation of 0.06 mag)found by Haschke et al. (2011). Fig. 2 is a map of the RRLyrae distribution coloured by color excess. Two promi-nent regions of large extinction are apparent, one shapedlike a downward-pointing wedge located at a right ascension⇡ 87�, and the other a band running north-south centred atright ascension ⇡ 73�. Both of these features are also notedby Haschke et al. (2011) and depicted in their Fig. 10.

The band-specific extinction for each star was derivedfrom the measured colour excess value using the extinctioncurve data given in Table 6 of Schlegel et al. (1998), in com-bination with the colour excess conversion factor to trans-form from E(V � I) to the conventional E(B � V ), 1.62,reported in Johnson (1968) and referenced by Schultz &Wiemer (1975) and Rieke & Lebofsky (1985). The correctedmean-flux magnitudes are thus given by

mV

= mV,obs

� 3.240⇥ [E (V � I) /1.62] (2)

mI

= mI,obs

� 1.962⇥ [E (V � I) /1.62] (3)

mz

= mz,obs

� 1.479⇥ [E (V � I) /1.62] . (4)

c� 2014 RAS, MNRAS 000, 1–7

4 Klein et al.

3.2 Period–magnitude relations

The V , I, and z extinction-corrected mean-flux magnitudeswere used to calibrate period–magnitude relations througha method similar to the Bayesian simultaneous linear regres-sion formalism employed for 13 simultaneous fits in Klein &Bloom (2014). The primary di↵erence in this application isthat the colour excess is not fitted as a model parameter, andis instead incorporated into the likelihood (observed data).The framework easily accommodates the extra model pa-rameters, but the augmented processing time, which goesroughly as O(n2), is unreasonable for fitting a model with15,040 stars (compared to the calibration sample size of 134for Klein & Bloom 2014).

Before the Bayesian MCMC fitting procedure was per-formed, the dataset of 17,629 stars was cleaned to reject out-liers. These are most likely foreground stars or stars withpoorly measured photometry resulting from crowding ef-fects. All stars with a median absolute deviation in mag-nitude greater than 5� for any of the three wavebands wereremoved, and then a simple least-squares linear regressionwas performed to fit preliminary period–magnitude relationsand all stars more than 4� from the best fitted line for anywaveband’s relation were also removed. 15,040 RR Lyraestars survived the cuts and made it into the calibration sam-ple.

The calibration sample is composed of 11,846 RRabstars (fundamental mode pulsators) and 3,194 RRc stars(first overtone pulsators). The RRc stars’ periods must be“fundamentalised” before deriving the period–magnitude re-lations. As in Dall’Ora et al. (2004), an RRc star’s funda-mentalised period is given by

log10

(Pf

) = log10

(Pfo

) + 0.127. (5)

The general form of the period–magnitude relation is then

mij

= µi

+M0,j

+ ↵j

log10

(Pi

/P0

) + ✏ij

, (6)

where mij

is the observed apparent, extinction-correctedmean-flux magnitude of the ith RR Lyrae star in the jthwaveband, µ

i

is the distance modulus for the ith RR Lyraestar, M

0,j

is the absolute magnitude zero point for the jthwaveband, ↵

j

is the slope in the jth waveband, Pi

is the fun-damentalised period of the ith RR Lyrae star in days, P

0

isa period normalisation factor (for consistency with Klein &Bloom 2014 we use P

0

= 0.52854 d), and the ✏ij

error termsare independent zero-mean Gaussian random deviates withvariance (�2

intrinsic,j

+ �2

mij).

The error on the extinction-corrected mean-flux magni-tudes, �

mij , was derived by propagating the error from thecontributing observed apparent magnitudes and colour ex-cess terms (see equations 2, 3, and 4). The intrinsic scatter ofthe period–magnitude relations, �

intrinsic,j

, which is addedin quadrature with �2

mijto calculate the standard deviation

of the likelihood, is adopted from the findings of Klein &Bloom (2014): �

intrinsic,V

= 0.0320, �intrinsic,I

= 0.0713, and�intrinsic,z

= 0.1153.The prior distributions for M

0,j

and ↵j

were normaldistributions centred at the fitted values for the V , I, and zperiod–magnitude relations found by Klein & Bloom (2014),with standard deviations expanded to 0.2 for M

0

and 1.5 for↵ (to allow the MCMC traces freedom to explore a widerparameter-space). The same prior, N (18.5, 0.21632), was

Figure 3. V -, I-, and z-band period–magnitude relations (solidlines) derived for the LMC RR Lyrae population, superimposedon scatter plots of the RR Lyrae posteriors (M computed usingµPost

). The dashed lines denote the 1� prediction intervals for anew RR Lyrae star with known period.

used for all of the µi

. This standard deviation was selected tobe a fractional distance error of 10 per cent (⇡ 5 kpc), whichis much larger than the depth of the LMC and significantlylarger than (> 2 times) the median posterior �

µi .To fit the model given by equation 6 ten identical

MCMC traces were run, each generating 3.5 million iter-ations. The first 0.5 million were discarded as burn-in andthe remaining 3 million were thinned by 300 to result in tentraces of 10,000 iterations each. The Gelman-Rubin conver-gence diagnostic, R, (Gelman & Rubin 1992) was computedfor each posterior model parameter (3 zero points, 3 slopes,and 15,040 distance moduli) and all are found to be well-converged (R < 1.1).

The best fitted period–magnitude relations and a scat-ter plot of the RR Lyrae posteriors (M computed usingµPost

) is presented in Fig. 3. The equations for the period–magnitude relations are

MV

= (0.448± 0.003)� (0.999± 0.038)⇥ log10

(P/P0

) (7)

MI

= (0.073± 0.002)� (1.701± 0.034)⇥ log10

(P/P0

) (8)

Mz

= (0.483± 0.002)� (1.774± 0.034)⇥ log10

(P/P0

) . (9)

These results are consistent (within 2�) with the findingspublished in Klein & Bloom (2014). The new slopes areconspicuously systematically lower, although the previousconstraints are considerably wider. The extremely tight dis-tributions for the posterior M

0

and ↵ are due to the verylarge number of RR Lyrae stars in the calibration dataset,as compared to previous studies that have used calibrationsamples of a few dozen to slightly more than one hundredstars collated from the local Milky Way field RR Lyrae pop-ulation.

c� 2014 RAS, MNRAS 000, 1–7

now with15,040 stars...

scipy.sparse,'hdf5

Klein..JSB+14

Dust Map basemap

4-✕'improvement'in'distance'error

3D density projection

mayavi2

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Astronomical$Data$DelugeSerious$Challenge$to$Tradi;onal$Approaches$&$Toolkits

Large$Synop;c$Survey$Telescope$(LSST)$A$2020$' Light'curves'for'800M'sources'every'3'days'''''106'supernovae/yr,'105'eclipsing'binaries'''''3.2'gigapixel'camera,'20'TB/night

LOFAR$&$SKA''''150'Gps'(27'Tflops)'→'20'Pps'(~100'Pflops)

Gaia$space$astrometry$mission$A$2014''''1'billion'stars'observed'∼70'Hmes'over'5'years'''''''Will'observe'20K'supernovae

Many'other'astronomical'surveys'are'already'producing'data:SDSS,'iPTF,'CRTS,'PanKSTARRS,'Hipparcos,'OGLE,'ASAS,'Kepler,'LINEAR,'DES'etc.,

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strategyscheduling

observingreducFon

findingdiscovery

classificaFonfollowup

inference

Towards$a$Fully$Automated$ScienAfic$Stack$for$Transients}currentstate)of)the)art

stack

automatednot-(yet)-automated

published-work

NSF/CDINSF/BIGDATA

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Our$ML$framework$found$the$Nearest$Supernova$in$3$

Decades$..‣ Built'&'Deployed'robust,'realKHme'machine'learning'framework,'discovering'>10,000'events'in'>'10'TB'of'imaging'''''''''→'50+'journal'arHcles

‣ Built'ProbabilisHc'Event'classificaHon'catalogs'with'innovaHve'acHve'learning'

hhp://Hmedomain.org hhps://www.nsf.gov/news/news_summ.jsp?cntn_id=122537

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What is the toolbox of the modern (data-driven) scientist?

domaintraining

statistics

advancedcomputing

database

GUI

parallel

visualization

Bayesian

machine learning

Physics

laboratory techniques

MCMC

MapReduce

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And...How do we teach this with what little time the students have?

What is the toolbox of the modern (data-driven) scientist?

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Data-Centric Coursework, Bootcamps, Seminars, & Lecture Series

BDAS: Berkeley Data Analytics Stack[Spark, Shark, ...]

parallelprogrammingbootcamp

...and entire degree programs

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2010: 85 campers 2012a: 135 campers

Python Bootcamps at Berkeley

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a modern superglue computing language for (data) science

‣ high-level scripting language‣ open source, huge & growing community in academia & industry‣ Just in time compilation but also fast numerical computation‣ Extensive interfaces to 3rd party frameworks

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a modern superglue computing language for (data) science

‣ high-level scripting language‣ open source, huge & growing community in academia & industry‣ Just in time compilation but also fast numerical computation‣ Extensive interfaces to 3rd party frameworks

A reasonable lingua franca for scientists...

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2012b: 210 campers

Python Bootcamps at Berkeley

2013a: 253 campers

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‣ 3 days of live/archive streamed lectures‣ all open material in GitHub‣ widely disseminated (e.g., @ NASA)

http://pythonbootcamp.info

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Part of the DesignatedEmphasis in Computational Science & Engineering at Berkeley

visualization

machine learning

database interaction

user interface & web frameworks

timeseries & numerical computing

interfacing to other languagesBayesian inference & MCMC

hardware control

parallelism

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“Are we alone in the universe? What makes up the missing mass of the universe? ... And maybe the biggest question of all: How in the wide world can you add $3 billion in market capitalization simply by adding .com to the end of a name?”

President William Jefferson Clinton Science and Technology Policy Address

21 January 2000

“Add Data Science or Big Data to your course name to increase enrollment by tenfold.”

Joshua BloomJust Now

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Python for Data Science @ Berkeley [Sept 2013]

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64%

36%female male

8%4%

8%

12%

4%12% 8%

16%

16%

12%PsychologyAstronomyNeuroscienceBiostatisticsPhysicsChemical EngineeringISchoolEarth and Planetary SciencesIndustrial EngineeringMechanical Engineering

“Parallel Image Reconstruction from Radio Interferometry Data”

“Graph Theory Analysis of Growing Graphs”

http://mb3152.github.io/Graph-Growth/

“Realtime Prediction of Activity Behavior from Smartphone”

“Bus Arrival Time Prediction in Spain”

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Time domain preprocessing

- Start with raw photometry!

- Gaussian process detrending!

- Calibration!

- Petigura & Marcy 2012!

!Transit search

- Matched filter!

- Similar to BLS algorithm (Kovcas+ 2002)!

- Leverages Fast-Folding Algorithm O(N^2) → O(N log N) (Staelin+ 1968)!

!Data validation

- Significant peaks in periodogram, but inconsistent with exoplanet transit

TERRA – optimized for small planets

Detrended/calibrated photometry

TERRA

Raw

Flu

x (p

pt)

Cal

ibra

ted

Flux

Erik PetiguraBerkeley Astro Grad Student

Petigura, Howard, & Marcy (2013)

Prevalence of Earth-size planets orbiting Sun-like starsErik A. Petiguraa,b,1, Andrew W. Howardb, and Geoffrey W. Marcya

aAstronomy Department, University of California, Berkeley, CA 94720; and bInstitute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822

Contributed by Geoffrey W. Marcy, October 22, 2013 (sent for review October 18, 2013)

Determining whether Earth-like planets are common or rare loomsas a touchstone in the question of life in the universe. We searchedfor Earth-size planets that cross in front of their host stars byexamining the brightness measurements of 42,000 stars fromNational Aeronautics and Space Administration’s Kepler mission.We found 603 planets, including 10 that are Earth size (1−2 R⊕)and receive comparable levels of stellar energy to that of Earth(0:25− 4 F⊕). We account for Kepler’s imperfect detectability ofsuch planets by injecting synthetic planet–caused dimmings intothe Kepler brightness measurements and recording the fractiondetected. We find that 11 ± 4% of Sun-like stars harbor an Earth-size planet receiving between one and four times the stellar inten-sity as Earth. We also find that the occurrence of Earth-size planets isconstant with increasing orbital period (P), within equal intervals oflogP up to∼200 d. Extrapolating, one finds 5:7+1:7

−2:2% of Sun-like starsharbor an Earth-size planet with orbital periods of 200–400 d.

extrasolar planets | astrobiology

The National Aeronautics and Space Administration’s (NASA’s)Kepler mission was launched in 2009 to search for planets

that transit (cross in front of) their host stars (1–4). The resultingdimming of the host stars is detectable by measuring their bright-ness, and Kepler monitored the brightness of 150,000 stars every30 min for 4 y. To date, this exoplanet survey has detected morethan 3,000 planet candidates (4).The most easily detectable planets in the Kepler survey are

those that are relatively large and orbit close to their host stars,especially those stars having lower intrinsic brightness fluctua-tions (noise). These large, close-in worlds dominate the list ofknown exoplanets. However, the Kepler brightness measurementscan be analyzed and debiased to reveal the diversity of planets,including smaller ones, in our Milky Way Galaxy (5–7). Theseprevious studies showed that small planets approaching Earthsize are the most common, but only for planets orbiting close totheir host stars. Here, we extend the planet survey to Kepler’smost important domain: Earth-size planets orbiting far enoughfrom Sun-like stars to receive a similar intensity of light energyas Earth.

Planet SurveyWe performed an independent search of Kepler photometry fortransiting planets with the goal of measuring the underlying oc-currence distribution of planets as a function of orbital period,P, and planet radius, RP. We restricted our survey to a set of Sun-like stars (GK type) that are the most amenable to the detectionof Earth-size planets. We define GK-type stars as those with sur-face temperatures Teff = 4,100–6,100 K and gravities logg = 4.0–4.9(logg is the base 10 logarithm of a star’s surface gravity measured incm s−2) (8). Our search for planets was further restricted to thebrightest Sun-like stars observed by Kepler (Kp = 10–15 mag). These42,557 stars (Best42k) have the lowest photometric noise, makingthem amenable to the detection of Earth-size planets. Whena planet crosses in front of its star, it causes a fractional dimmingthat is proportional to the fraction of the stellar disk blocked,δF = ðRP=RpÞ2, where Rp is the radius of the star. As viewed bya distant observer, the Earth dims the Sun by ∼100 parts permillion (ppm) lasting 12 h every 365 d.

We searched for transiting planets in Kepler brightness mea-surements using our custom-built TERRA software packagedescribed in previous works (6, 9) and in SI Appendix. In brief,TERRA conditions Kepler photometry in the time domain, re-moving outliers, long timescale variability (>10 d), and systematicerrors common to a large number of stars. TERRA then searchesfor transit signals by evaluating the signal-to-noise ratio (SNR) ofprospective transits over a finely spaced 3D grid of orbital period,P, time of transit, t0, and transit duration, ΔT. This grid-basedsearch extends over the orbital period range of 0.5–400 d.TERRA produced a list of “threshold crossing events” (TCEs)

that meet the key criterion of a photometric dimming SNR ratioSNR > 12. Unfortunately, an unwieldy 16,227 TCEs met this cri-terion, many of which are inconsistent with the periodic dimmingprofile from a true transiting planet. Further vetting was performedby automatically assessing which light curves were consistent withtheoretical models of transiting planets (10). We also visuallyinspected each TCE light curve, retaining only those exhibiting aconsistent, periodic, box-shaped dimming, and rejecting thosecaused by single epoch outliers, correlated noise, and other dataanomalies. The vetting process was applied homogeneously to allTCEs and is described in further detail in SI Appendix.To assess our vetting accuracy, we evaluated the 235 Kepler

objects of interest (KOIs) among Best42k stars having P > 50 d,which had been found by the Kepler Project and identified as planetcandidates in the official Exoplanet Archive (exoplanetarchive.ipac.caltech.edu; accessed 19 September 2013). Among them, wefound four whose light curves are not consistent with beingplanets. These four KOIs (364.01, 2,224.02, 2,311.01, and 2,474.01)have long periods and small radii (SI Appendix). This exercisesuggests that our vetting process is robust and that careful scrutinyof the light curves of small planets in long period orbits is useful toidentify false positives.

Significance

A major question is whether planets suitable for biochemistryare common or rare in the universe. Small rocky planets withliquid water enjoy key ingredients for biology. We used theNational Aeronautics and Space Administration Kepler tele-scope to survey 42,000 Sun-like stars for periodic dimmingsthat occur when a planet crosses in front of its host star. Wefound 603 planets, 10 of which are Earth size and orbit in thehabitable zone, where conditions permit surface liquid water.We measured the detectability of these planets by injectingsynthetic planet-caused dimmings into Kepler brightness mea-surements. We find that 22% of Sun-like stars harbor Earth-sizeplanets orbiting in their habitable zones. The nearest such planetmay be within 12 light-years.

Author contributions: E.A.P., A.W.H., and G.W.M. designed research, performed research,analyzed data, and wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.

Data deposition: The Kepler photometry is available at the Milkulski Archive for SpaceTelescopes (archive.stsci.edu). All spectra are available to the public on the CommunityFollow-up Program website (cfop.ipac.caltech.edu).1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1319909110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1319909110 PNAS | November 26, 2013 | vol. 110 | no. 48 | 19273–19278

AST

RONOMY

Bootcamp/Seminar Alum

Python

DOE/NERSC computation

PNAS [2014]

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Dangers+of+a+Cursory+Training/Teaching+Curriculum

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first-this... ...then-this.

Undergraduate$&$Graduate$Training$MissionThinking$Data'Literacy$before$Thinking$Big'Data'Proficiency

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34 Fitting a straight line to data

0 50 100 150 200 250 300x

0

100

200

300

400

500

600

700

y

y = 1.33 x + 164

0 50 100 150 200 250 300x

0

100

200

300

400

500

600

700

y

0.0

1.0

1.0

1.0

0.0

0.0

0.00.00.0

0.00.0

0.0

0.00.0

0.0

0.0

0.0

0.0

0.0

0.0

Figure 10.— Partial solution to Exercise 14: On the left, the same as Figure 9but including the outlier points. On the right, the same as in Figure 4but applying the outlier (mixture) model to the case of two-dimensionaluncertainties.

0 50 100 150 200 250 300x

0

100

200

300

400

500

600

700

y

forward � � � y = (2.24 ± 0.11) x + (34 ± 18)reverse � · � y = (2.64 ± 0.12) x + (�50 ± 21)

Figure 11.— Partial solution to Exercise 15: Results of “forward and reverse”fitting. Don’t ever do this.

Data analysis recipes:

Fitting a model to data

David W. HoggCenter for Cosmology and Particle Physics, Department of Physics, New York University

Max-Planck-Institut fur Astronomie, Heidelberg

Jo BovyCenter for Cosmology and Particle Physics, Department of Physics, New York University

Dustin LangDepartment of Computer Science, University of Toronto

Princeton University Observatory

Abstract

We go through the many considerations involved in fitting a modelto data, using as an example the fit of a straight line to a set of pointsin a two-dimensional plane. Standard weighted least-squares fittingis only appropriate when there is a dimension along which the datapoints have negligible uncertainties, and another along which all theuncertainties can be described by Gaussians of known variance; theseconditions are rarely met in practice. We consider cases of general,heterogeneous, and arbitrarily covariant two-dimensional uncertain-ties, and situations in which there are bad data (large outliers), un-known uncertainties, and unknown but expected intrinsic scatter inthe linear relationship being fit. Above all we emphasize the impor-tance of having a “generative model” for the data, even an approx-imate one. Once there is a generative model, the subsequent fittingis non-arbitrary because the model permits direct computation of thelikelihood of the parameters or the posterior probability distribution.Construction of a posterior probability distribution is indispensible ifthere are “nuisance parameters” to marginalize away.

It is conventional to begin any scientific document with an introductionthat explains why the subject matter is important. Let us break with tra-dition and observe that in almost all cases in which scientists fit a straightline to their data, they are doing something that is simultaneously wrong

and unnecessary. It is wrong because circumstances in which a set of two

⇤The notes begin on page 39, including the license1 and the acknowledgements2.

1

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v1 [

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010

Dataanalysisrecipes:

Fittingamodeltodata

David

W.H

oggCenter

forCosm

ologyan

dParticle

Physics,

Departm

entof

Physics,

New

York

University

Max-P

lanck-In

stitutfurAstron

omie,

Heid

elberg

JoB

ovyCenter

forCosm

ologyan

dParticle

Physics,

Departm

entof

Physics,

New

York

University

Dustin

Lan

gDepartm

entof

Com

puter

Scien

ce,University

ofToronto

Prin

cetonUniversity

Observatory

Abstra

ct

We

goth

rough

the

man

ycon

sideration

sin

volvedin

fittin

ga

model

todata,

usin

gas

anex

ample

the

fit

ofa

straight

line

toa

setof

poin

tsin

atw

o-dim

ension

alplan

e.Stan

dard

weigh

tedleast-sq

uares

fittin

gis

only

approp

riatew

hen

there

isa

dim

ension

along

which

the

data

poin

tshave

negligib

leuncertain

ties,an

dan

other

along

which

allth

euncertain

tiescan

be

describ

edby

Gau

ssians

ofknow

nvarian

ce;th

esecon

dition

sare

rarelym

etin

practice.

We

consid

ercases

ofgen

eral,heterogen

eous,

and

arbitrarily

covariant

two-d

imen

sional

uncertain

-ties,

and

situation

sin

which

there

arebad

data

(largeou

tliers),un-

know

nuncertain

ties,an

dunknow

nbut

expected

intrin

sicscatter

inth

elin

earrelation

ship

bein

gfit.

Above

allw

eem

phasize

the

impor-

tance

ofhav

ing

a“gen

erativem

odel”

forth

edata,

evenan

approx

-im

ateon

e.O

nce

there

isa

generative

model,

the

subseq

uen

tfittin

gis

non

-arbitrary

becau

seth

em

odel

perm

itsdirect

computation

ofth

elikelih

ood

ofth

eparam

etersor

the

posterior

prob

ability

distrib

ution

.C

onstru

ctionof

aposterior

prob

ability

distrib

ution

isin

disp

ensib

leif

there

are“n

uisan

ceparam

eters”to

margin

alizeaw

ay.

Itis

conventional

tobegin

anyscientifi

cdocu

ment

with

anintrod

uction

that

explain

sw

hyth

esu

bject

matter

isim

portant.

Let

us

break

with

tra-dition

and

observe

that

inalm

ostall

casesin

which

scientistsfit

astraight

line

toth

eirdata,

they

aredoin

gsom

ethin

gth

atis

simultan

eously

wrong

andunnecessary.

Itis

wron

gbecau

secircu

mstan

cesin

which

aset

oftw

o

⇤The

notes

begin

onpage

39,in

cludin

gth

elicen

se1

and

the

acknow

ledgem

ents

2.

1

arXiv:1008.4686v1 [astro-ph.IM] 27 Aug 2010

Sta8s8cal+Inference

Undergraduate$&$Graduate$Training$MissionThinking$Data'Literacy$before$Thinking$Big'Data'Proficiency

Page 30: Data Science at Berkeley

Versioning+&+Reproducibility

“Recently, the scientific community was shaken by reports that a troubling proportion of peer-reviewed preclinical studies are not reproducible.” McNutt, 2014

http://www.sciencemag.org/content/343/6168/229.summary

K'Git'has'emerged'as'the'de'facto'versioning'toolK'Berkeley'Common'Environment'(BCE)'Sonware'StackK'“Reproducible'and'CollaboraHve'StaHsHcal'Data'Science”'(StaHsHcs'157:'P.'Stark)

Undergraduate$&$Graduate$Training$MissionThinking$Data'Literacy$before$Thinking$Big'Data'Proficiency

Page 31: Data Science at Berkeley

The'IPython'Notebook'–'SupporHng'Research'at'Berkeley

•Designing'nuclear'reactor'cores

•SimulaHng'electron'flow'in'plasmas

•CompuHng'supernovae'spectra

•Analyzing'brain'acHvity

•Modeling'neural'networks

•CalculaHng'quantum'dynamics'and'spectroscopy

•Visualizing'MRI'results

Page 32: Data Science at Berkeley

Berkeley Data Analytics Stack A Comprehensive Big Data Reference Architecture

AMP!Alpha or

Soon!

AMP!Released!

BSD/Apache!

3rd Party Open Source!

Apache Mesos! YARN Resource Manager! Resource!

HDFS / Hadoop Storage!

Tachyon!Storage!

!Apache Spark!

Spark Streaming! ML-lib! Processing!

and Data !Management!

Applications: Traffic, Carat, Genomics, 3rd Party!Tools: Visualization, Data Cleaning, …!

Shark (SQL)!

BlinkDB! GraphX! MLBase! Analytics!Frameworks!Spark-R!

Berkeley$Data$Analy;cs$StackA,Comprehensive,Big,Data,Reference,Architecture

Methodology'innovaHon:'InvenHng'What’s'Next'in'Big'Data'AnalyHcs

Testing the Vision/Early Adopters/Momentum 2010+

Page 33: Data Science at Berkeley

(Recent)'Data'Science'Industry'Spinoffs'at'Berkeley

http://berkeleystartupcluster.com/

Page 34: Data Science at Berkeley

Data'Science'growing'organically'everywhere

Feb'15,'2013

AMP'LabIon$Stoica,$CSMichael$Franklin,$CS

Adam$Arkin,$Bioengineering

Emmanuel$Saez,$Economics

Reconstruc;ng$the$moviesin$your$mind

Bin$Yu,$Sta;s;csJack$Gallant,$Neuroscience

Earthquake

Strong Shaking

in

11seconds

Richard$Allen$Earth&$Plan.$ScienceGeospa;al$Lab

Fernando$Perez,$Brain$Imaging$CenteriPython$tools$and$community Charles$Marshall

Rosie$GillespieIntegra;ve$BiologyDigi;zed$Museum

Page 35: Data Science at Berkeley

Created by Natalia Bilenko.Data source: PubMed Central. http://sciencereview.berkeley.edu/bsr_design/Issue26/datascience/cover/

Page 36: Data Science at Berkeley

Established-CS/Stats/Math-in,Serviceof-novelty-in-domain-science

vs.

Novelty-in-domain-science-driving-&-informing-novelty-in-CS/Stats/Math

“novelty2$problem”an'extra'Burden'for'Forefront'ScienHsts

hhps://medium.com/techKtalk/dd88857f662

Page 37: Data Science at Berkeley

Berkeley Institute for

Data Science

Berkeley Institute for

Data Science

http://bitly.com/bundles/fperezorg/1

“Bold new partnership launches to harness potential of data scientists and big data”

Founded'in'December'2013'as'a'result'of'a'year+'long'naHonal'selecHon'process$37.8M'over'5'years,'along'with'University'of'Washington'&'NYU

‣ An'accelerator'for'dataKdriven'discovery‣ An'agent$of$change'in'the'modern'university'as'Data'Science'takes'hold‣ An'incubator'for'the'next'generaHon'of'Data'Science'technology'and'pracHce

Page 38: Data Science at Berkeley

Leadership$from$across$the$spectrum

Joshua$Bloom,'Professor,'Astronomy;'Director,'Center'for'Time'Domain'InformaHcs''''

Henry$Brady,'Dean,'Goldman'School'of'Public'Policy''''''

Cathryn$Carson,'Associate'Dean,'Social'Sciences;'AcHng'Director'of'Social'Sciences'Data'Laboratory'"DKLab”''''''

David$Culler,'Chair,'EECS'''''''

Michael$Franklin,'Professor;'EECS,'CoKDirector,'AMP'Lab'''''''''

Erik$Mitchell,'Associate'University'Librarian'''''''''

Faculty'Lead/PI:'Saul$PerlmuXer,'Physics,'Berkeley'Center'for'Cosmological'Physics

Fernando$Perez,'Researcher,'Henry'H.'Wheeler'Jr.'Brain'Imaging'Center

Jasjeet$Sekhon,'Professor,'PoliHcal'Science'and'StaHsHcs;'Center'for'Causal'Inference'and'Program'EvaluaHon''''''

Jamie$Sethian,'Professor,'MathemaHcs''''''

Kimmen$Sjölander,'Professor,'Bioengineering,'Plant'and'Microbial'Biology''''''

Philip$Stark,'Chair,'StaHsHcs'''''

Ion$Stoica,'Professor,'EECS;'CoKDirector,'AMP'Lab

Page 39: Data Science at Berkeley

BIDS goals

‣ Support$meaningful$and$sustained$interac;ons$and$collabora;ons$between'Methodology'fields'&'Science'domains'to'recognize'what'it'takes'to'move'these'fields'forward

‣ Establish$new$Data$Science$career$paths$that$are$longAterm$and$sustainable• A'generaHon'of'mulHKdisciplinary'scienHsts'in'dataKintensive'science• A'generaHon'of'data'scienHsts'focused'on'tool'development

‣ Build$an$ecosystem$of$analy;cal$tools,$teaching,$&$research$prac;ces• Sustainable,'reusable,'extensible,'easy'to'learn'and'to'translate'across'research'domains

• Enables'scienHsts'to'spend'more'Hme'focusing'on'their'science

37

Page 40: Data Science at Berkeley

A'place'to'bring'it'all'together'at'the'Center

Vibrant'nexus'in'the'heart'of'campus

Doe-Library

Enhancing'strengths'of:

•Simons-InsFtute-for-the-Theory-of-CompuFng•-AMP-Lab•-CITRIS•etc.

Page 41: Data Science at Berkeley

Doe'Memorial'Library@'the'center'of'UC'Berkeley

Page 42: Data Science at Berkeley

Berkeley Institute for Data Science Opening

Page 43: Data Science at Berkeley

Berkeley Institute for Data Science Opening

Page 44: Data Science at Berkeley

Berkeley/UW/NYU$Working$Groups$as$Bridges$

Applied'Math

/

Page 45: Data Science at Berkeley

Towards+an+Inclusive+EcosystemExpanding+Par8cipa8on+Among+Underrepresented+Groups

11%

56%

33% female maledecline'to'state

2013'Python'bootcamp

K'2013'AMP'Camp:'''<'5%'women

K'Today'@'PyData:'''''1'women'out'of'18'speakers

K'2013'Python'Seminar:''36%'women

Page 46: Data Science at Berkeley

Chris-MentzelMoore-FoundaFon

@NYU,-on-Monday

Josh-GreenbergSloan-FoundaFon

Yann-LeCunNYU/Facebook

Page 47: Data Science at Berkeley

Summary

Data+science+at+Berkeley+is+thriving+and+is+geJng+an+intellectual+home---D-incubaFng-novel-science-&-methodologies---D-teaching-&-training---D-innovate-environments,-interacFons,-&-networks

A+data+scien8st+is+a+unicorn,+but...

Looking-for-founda8onal+industry+partners-to-parFcipate-and-help-us-grow

Page 48: Data Science at Berkeley

@pro{sb

Thank+you.

PyData,'May'4.'2014