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Radial artery

In human anatomy, the radial artery is the main artery of the lateral aspect of the forearm.

Structure
The radial artery arises from the bifurcation of the brachial artery in the antecubital fossa. It runs distally on the anterior part of the forearm. There, it serves as a landmark for the division between the anterior and posterior  compartments of the forearm, with the posterior compartment beginning just lateral to the artery. The artery winds laterally around the wrist, passing through the anatomical snuff box and between the heads of the first dorsal interosseous muscle. It passes anteriorly between the heads of the adductor pollicis, and becomes the deep palmar arch, which joins with the deep branch of the ulnar artery.

Along its course, it is accompanied by a similarly named vein, the radial vein.

Branches
The named branches of the radial artery may be divided into three groups, corresponding with the three regions in which the vessel is situated.

In the forearm

 * Radial recurrent artery - arises just after the radial artery comes off the brachial artery. It travels superiorly to anastomose with the radial collateral artery around the elbow joint
 * Palmar carpal branch of radial artery - a small vessel which arises near the lower border of the pronator quadratus
 * Superficial palmar branch of the radial artery - arises from the radial artery, just where this vessel is about to wind around the lateral side of the wrist.

At the wrist

 * Dorsal carpal branch of radial artery - a small vessel which arises beneath the extensor tendons of the thumb
 * First dorsal metacarpal artery - arises just before the radial artery passes between the two heads of the first dorsal interosseous muscle and divides almost immediately into two branches which supply the adjacent sides of the thumb and index finger; the lateral side of the thumb receives a branch directly from the radial artery.

In the hand

 * Princeps pollicis artery - arises from the radial artery just as it turns medially to the deep part of the hand.
 * Radialis indicis - arises close to the princeps pollicis. The two arteries may arise from a common trunk, the first palmar metacarpal artery.
 * Deep palmar arch - terminal part of radial artery.

Variations
In less than 1% of the population, the radial artery takes a superficial course in the anatomical snuff box. This arterial variation can be mistaken for the cephalic vein as accidental injection of this variant radial artery has been reported. Identifying arterial pulsation in the anatomical snuff box is therefore recommended.

Clinical significance
The radial artery lies superficially in front of the distal end of the radius, between the tendons of the brachioradialis and flexor carpi radialis; it is here that clinician takes the radial pulse. (where it is commonly used to assess the heart rate and cardiac rhythm). Presence of radial pulse was thought to indicate a systolic blood pressure of at least 70 mmHg, as estimated from the 50% percentile, although this was found to generally be an overestimation of a patient's true blood pressure. The radial artery can be less easily felt as it crosses the anatomical snuff box. The radial artery is used for coronary artery bypass grafting and is growing in popularity among cardiac surgeons. Recently, it has been shown to have a superior peri-operative and post-operative course when compared to saphenous vein grafts.

The radial artery is often punctured in a common procedure to obtain an arterial blood gas. Such a procedure may first involve an Allen's test.

The radial artery is also used to evaluate the collateral circulation of blood through the hands; applying pressure through palpating the palmar arches results in paleness over the area being compressed; adequate collateral circulation can be ascertained by how quickly normal colour returns after the pressure is removed.

The radial artery is a common site for the insertion of an arterial line, such as for blood pressure monitoring in an intensive care unit. It is also commonly used for cerebral angiograms for the treatment of cerebral pathologies, such as strokes, cerebral aneurysms It is selected because it is accessible, and because of the low incidence of complications such as thrombosis.

title: Radial artery


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Talk:Hernando de Soto (explorer)

Date of death
The date of de Soto's death is inconsistent within this article: at its head, the article states 21 May (as does Britannica), but the section "1542 – de Soto's Death" has it as 25 June.

Now, the date is probably not known with certainty, but we shouldn't have two different dates for the same event (particularly in the same article) without explanation. Does anyone have any information that could help? — John Mark Williams <⌂|☏> 29 June 2005 10:36 (UTC)

I see that this inconsistency has been copied across from the German version of the article. In addition to any other help anyone can give, perhaps a German speaker would like to ask there? — John Mark Williams <⌂|☏> 29 June 2005 10:48 (UTC)

A Good Man?
This article needs revision I dont think the folowing en-bolded should remain implemented.
 * The commonly assumed De Soto Trail runs in a west-northwest direction across the US states Mississippi, Arkansas and Oklahoma until Texas. Other opinions argue for a northern route across Kentucky and Indiana to the Great Lakes. He was a good manDryzen 16:47, 7 March 2006 (UTC)

Place of Birth
An anonymous editor posted the following, which is probably more properly put here than in the article mainspace, until one or the other can be properly cited ... "There is a dispute between Barcarrota, Spain and [Jerez de los Caballeros]], Spain for the bearth of Hernando de Soto, but there is a document where he expressed his desire of being buried in the Capilla de la Concepción (Chapel of the Conception) in the temple of San Miguel Arcángel (Saint Michael Archangel) in Jerez de los Caballeros, next to the rests of his mother, who is also buried there. This document seems to indicate that he was born in Jerez de los Caballeros." SkerHawx 19:49, 9 October 2006 (UTC)

 * This is an accurate assessment. It is unknown where he was born, with a couple likely candidates. Jerez de los Caballeros is the most common choice because that is where he wanted to be buried in his will and other family members are buried there, but not on really knows where he was born. -- Stbalbach 03:46, 2 November 2006 (UTC)

Place of death
There is some inconsistency in this article: "He is presumed to have died on a branch of the Mississippi River near present-day Lake Village, Arkansas." vs. "De Soto County, Mississippi (where he allegedly died)..."

Did he die in Mississippi or Arkansas or is it completely unknown? -- Hestemand 18:52, 8 May 2006 (UTC)

 * He died on the western bank of the Mississippi, in the Indian town of Guachoya, near present-day McArthur, Arkansas. He was most likely buried in the middle of the Mississippi - wrapped in blankets loaded with sand to weigh his body down in the middle of the night so the Indians would not see that he was no an immortal Sun God - so I suppose the state of Mississippi could make a loose claim to his burial site on the state line - but he died in AR. The "Lake Village" thing is probably folklore/legend as there are a number of places that make that claim. -- Stbalbach 03:46, 2 November 2006 (UTC)

Birthplace (vandalism?)
User:71.52.247.107 changed de Soto's birthplace from Barcarota to Jellez de Caballeros without explanation. My Spanish isn't good enough. Is this a joke? Looks like vandalism to me, so I reverted the change.

--Richard 15:40, 17 May 2006 (UTC)

 * Jellez de Caballeros is probably correct (see above). -- Stbalbach 03:46, 2 November 2006 (UTC)

Jerez de Los Caballeros es un pueblo importante de la provincia de Cadiz el Xerry o vino de Jerez, debe su nombre a Jerez de Los caballeros. 212.97.182.180 18:25, 3 January 2007 (UTC)

October 2006 - vandals
Errors introduced:

This article seems to have been edited and some problems introduced. I have compared the text with cached versions, and this article needs to be checked to remove problems.

For example:

"Later, de Soto led the samllest expedition of both the 15th century and the 16th century through what would become the Southeastern coolstates and the Midwestern United States searching for gold and silver and other valuable goods."

"His only cool possessions then were a shield and his sword."

Probably someone thought they were being funny, or some vandalism.

Bob in MD, October 2, 2006

 * Thank you, corrected. -- Stbalbach 03:46, 2 November 2006 (UTC)

Death Of DeSoto
I corrected this but DeSoto died on may, 22 1522 not may, 22 1542

Cocoaguy 16:23, 14 November 2006 (UTC)

 * sorry he actualy died on may 21 1542 Cocoaguy 16:29, 14 November 2006 (UTC)

How De Soto died
I found that died of fever on may, 21 1542

Cocoaguy 15:59, 15 November 2006 (UTC)

Year of Birth
I don't think his actual birthdate is known, but an anonymous user just changed the year of his birth from 1500->1499. Granted it still has circa 1499, but does anyone have a good source for a consensus on this? Also, the article is in the category 1496 births... —The preceding unsigned comment was added by Prometheusg (talk • contribs) 00:20, 3 February 2007 (UTC).

 * This article has long been a constant target of vandalism, often the sneaky kind. Corrected the date and left a footnote to hopefully make it stick better. 1496/97 is correct, at least according to the latest Encyclopedia Britannica. -- Stbalbach 17:09, 3 February 2007 (UTC)

de Soto's befriending Atahualpa
In reading the history in this article, it strikes me that de Soto was not the most benevolent of people towards the indigenous population. Therefore, when Pizzaro took Atahualpa captive, why did de Soto strike an accord with him and befriend him? Was there an ulterior motive? Is there any research on their relationship? Cometstail 03:05, 22 February 2007 (UTC)

report vcVHCVh dvtydrv
cv d n aq GJBV —The preceding unsigned comment was added by 74.250.11.26 (talk) 01:19, 17 April 2007 (UTC).

Changes to article
There have been a lot of changes the article and some of it is good, and some of it is not. I'm not sure where to start because there is so much to cover. A lot of very good material was deleted with no explanation. I happy to work together, and I tried to make an integration of both the old and new in places where I thought the old material was better, going through it line by line, sentence by sentence. -- Stbalbach 14:25, 22 April 2007 (UTC)

Add An External Link?
I'm new to Wiki work, but not coding/designing. I'd like to add an external link, but this article seems locked to editing for me. Here's the link ... Thanks David Hager, M.D. 03:19, 13 November 2007 (UTC)
 * Boldly Onward - The Incredible Adventures of America's 'Adelantados' And Clues To Their Landing Places In Florida
 * Please see the policies at WP:EL and WP:COI. -- Donald Albury 03:44, 13 November 2007 (UTC)

Sorry!
I feel a little like an ignorant bull in a china shop.

Lin's years of research into Florida history and his writings, especially about south Florida history, might be useful somehow to Wikipedia. At age 87, though, he is not going to be the one to do the Wiki entries. Over the past couple of years I've thought of trying to integrate his work into Wikipedia somehow, but God only put 24 hours into each day.

Any comments about this as a reference by those in the know? David Hager, M.D. 03:17, 14 November 2007 (UTC)
 * Boldly Onward
 * Table of Contents
 * Commentary by Reviewers

Cabeza de Vaca
Cabeza de Vaca's expedition came before de Soto. Several passages in this article state that de Soto was the first one to explore several of these areas and interact with its peoples. —Preceding unsigned comment added by 24.13.122.34 (talk • contribs)

 * First of all, Cabeza de Vaca was part of Pánfilo de Narváez's expedition. Vaca's name has come down to us because he was one of the very few survivors of that expedition, and wrote an account of it after finally returning to 'civilization'. Narváez followed a route that is believed to have been very close to the Gulf coast. While he entered into Apalachee territory, he did not reach the Apalachee capital of Anhaica before turning south to the Gulf coast and attempting to reach New Spain (Mexico) by sea. De Soto followed a more inland route, passing through what are now Marion and Alachua Counties, and he did reach Anhaica, where he spent the winter before moving up into what are now Georgis, Alabama, Mississippi and possibly, South Carolina and Tennessee. -- Donald Albury 22:27, 9 February 2008 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Hernando de Soto (explorer)


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User talk:Samantha45455

Hello and welcome to Wikipedia!

Here are some tips to help you get started:

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 * Eventually, read the Manual of Style and Policies and Guidelines.
 * If you need help, post a question at the Help Desk or ask me on my talk page.
 * Explore, be bold in editing pages, and, most importantly, have fun!

Good luck! Jrdioko

P.S. One last helpful hint. To sign your posts like I did above (on talk pages, for example) use the '~' symbol. To insert just your name, type ~~~ (3 tildes), or, to insert your name and timestamp, use ~~~~ (4 tildes).

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title: User talk:Samantha45455


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Canal Street (Manhattan)

Canal Street is a major east–west street of over 1 mi in Lower Manhattan, New York City, United States, running from East Broadway between Essex and Jefferson Streets in the east, to West Street between Watts and Spring Streets in the west. It runs through the neighborhood of Chinatown, and forms the southern boundaries of SoHo and Little Italy as well as the northern boundary of Tribeca. The street acts as a major connector between Jersey City, New Jersey, via the Holland Tunnel (I-78), and Brooklyn in New York City via the Manhattan Bridge. It is a two-way street for most of its length, with two unidirectional stretches between Forsyth Street and the Manhattan Bridge.

History

By 1800, Collect Pond, one of New York City's few natural sources of fresh water, had become completely polluted with sewage and run-off from the tanneries, breweries, and other workshops and factories around it. Run-off from the pond, including one "sluggish stream" which traveled part of the route of the future Canal Street, fed nearby swamps and marshes which prevented the city from continuing its northward growth. To deal with this, the city's Common Council ordered that the swamps be drained and, in 1803, that the pond itself be filled in. A drain was built continuing the path of the "sluggish stream" to the Hudson River, which redirected the underground springs which watered the swamps. The pond was successfully drained by 1813 or 1815.

The area was developed, but the springs remained and caused the "dry" land to be boggy and uneven. The Common Council then authorized a canal, in the form of a 40-foot wide, 8-foot deep ditch, which would continue carrying off the excess water. Because it was not efficient, and did not have sufficient flow, it, too, became an open sewer. The city covered it over in 1819, but as it had no air traps, the covered canal became a stinking covered sewer. Canal Street was completed in 1820, following the path of the covered canal and named for it. The historic townhouses and newer tenements that had been built along Canal Street quickly fell into disrepair, and the eastern stretch of Canal Street came within the ambit of the notorious Five Points slum as property values and living conditions plummeted.

Early in the 20th century, the jewelry trade centered on the corner of Canal Street and Bowery, but moved mid century to the modern Diamond District on 47th Street. In the 1920s, the Citizens Savings Bank built a notable domed headquarters at the intersection's southwest corner which remains a local landmark. The portion of Canal Street around Sixth Avenue was New York's principal market for electronics parts for a quarter-century after the closing of Radio Row to make way for the building of the World Trade Center.

Reputation as hawkers' haven
Canal Street is a bustling commercial district, crowded with comparatively low-rent open storefronts, and street vendors to the west; banks and jewelry shops to the east. For a generation after World War II, the former segment hosted many stores selling exotic high-tech components to would-be inventors and engineers. Canal Street is also the main Chinese jewelry business district of Chinatown. Tourists as well as locals pack its sidewalks every day to frequent the open-air stalls and bare-bones stores selling items such as perfume, purses, hardware, and industrial plastics at low prices. Many of these goods are grey market imports and many notoriously counterfeit, with fake trademarked brand names on electronics, clothing and personal accessories (including the fake Rolex watches that have become a Manhattan cliché). Bootleg CDs and DVDs were common, and were offered for sale on Canal Street—often before they were even officially released in stores or the theater—in makeshift stands and suitcases or simply laid out on bedsheets.

Widespread sale of these counterfeit goods persists along Canal Street and in its hidden back rooms despite frequent police raids. In addition, legislation was proposed in 2013 to try to make purchasing counterfeit items a crime; this would let the city's economy earn back at least $1 billion annually in taxes.

9/11 attack
After the 9/11 attack on the World Trade Center in 2001, Canal Street was the northern-most boundary of the area initially closed to everyone but residents and emergency personnel. When the 9/11 Victims Compensation Fund was established, Canal Street was again the northern cut-off for the World Trade Center Exposure Zone.

Transportation
Canal Street is served by the New York City Subway at seven stations, west to east:

 * Canal Street (IRT Broadway–Seventh Avenue Line) at Varick Street, served by the
 * Canal Street (IND Eighth Avenue Line) at Sixth Avenue, served by the
 * Canal Street (BMT Broadway, Manhattan Bridge, and Nassau Street Lines, and IRT Lexington Avenue Line) at Broadway, Lafayette Street, and Centre Street, served by the at four separate sets of platforms
 * East Broadway (IND Sixth Avenue Line) at East Broadway, served by the

Canal Street is also served by the New York City Bus system, though no routes actually run on Canal Street. Routes intersecting with the street include M20 at Hudson Street (northbound) and at Varick Street (southbound); M55 at Sixth Avenue (northbound) and Broadway (southbound); M103 at Bowery; M15 at Allen Street; and M9 (at East Broadway).

title: Canal Street (Manhattan)


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Liquid Television

Liquid Television was an animation showcase that appeared on MTV from 1991 to 1995. It served as the launching point for several high-profile original cartoons, including Beavis and Butt-Head and Æon Flux. Independent animators and artists created the bulk of Liquid Television ' s material specifically for the show, and some previously produced segments were compiled from festivals such as Spike and Mike's Festival of Animation.

The first season of Liquid Television also aired on BBC Two in co-production with MTV. Ultimately, MTV commissioned three seasons of the show, produced by Colossal Pictures. The show was eventually succeeded by Cartoon Sushi. Mark Mothersbaugh composed the show's theme music.

The show was broadcast in Canada on MuchMusic, in Asia on Channel V, in Australia on SBS and in New Zealand on TV3.

History
There were also a large number of animation pieces adapted from the work of Art Spiegelman's comic compilation, RAW. RAW featured underground cartoonists such as Mark Beyer, Richard Sala, and Peter Bagge. In particular, Dog-Boy by Charles Burns was based on the artist's series from RAW.

Due to the extensive use of licensed music throughout the series (episodes often began with a contemporary music video being "liquified"), full episodes of Liquid Television have not been seen in any form since their original run. Selected segments from the series, including the first appearances of Æon Flux, were released on two VHS tapes in the late 1990s as The Best of Liquid Television parts one and two. A collection volume, titled Wet Shorts (The Best of Liquid Television), comprising the two VHS tapes, was released on DVD in 1997.

Series credits

 * 1) Japhet Asher – Executive Producer/Creative Director
 * 2) Prudence Fenton – Executive Producer/Story Editor
 * 3) Mark Mothersbaugh – Composer, Theme Music
 * 4)  XAOS Inc.  – Title Sequences, Liquid Lips, Liquid Eyes, End Credits Bed
 * 5) A BIG Pictures &  Noyes & Laybourne Collaboration
 * 6) Produced by (Colossal) Pictures for MTV & BBC-TV

Recurring segments

 * Winter Steele – A puppet show about a biker chick searching for her long-lost love (see below).
 * Soap Opera – A parody of daytime soaps, with bars of soap as the actors.
 * Cut-Up Camera – A parody of Candid Camera involving outrageous situations.
 * Miss Lidia's Makeover to the Stars – A short about an unseen makeup artist (with live-action hands) who gives celebrities mock make-overs via her computer.
 * Invisible Hands – About a turban-clad sleuth who solves murders.
 * Buzz Box – A short with changing patterns set to rock music.
 * Stick Figure Theatre – A series of shorts recreating scenes from popular movies using stick-figures drawn on 3 × 5 cards.
 * Dangerous Puppets – About two puppets who violently destroy each other.
 * The Art School Girls of Doom – A live-action short in the early 1990s about two art school girls. Codie Field and Gina Varla Vetro, transgender actresses, played the girls in an animated environment.
 * Footworks – Stories featuring footprints as the characters.
 * Æon Flux – About a scantily-clad female secret agent (later spun off into its own series; also adapted into a 2005 live-action film starring Charlize Theron). The series later became part of Liquid Television's online version in 2012.
 * Beavis and Butt-Head – About two adolescent morons who cause their own trouble; later spun off into its own series.
 * Psychogram – A series of stories told with postcards and voiceover narration.
 * The Specialists – A 10-episode series about three private detectives.
 * Dog Boy – A live-action, comic book-style story about the adventures of a young man who received a dog's heart in a medical transplant.
 * The Adventures of Thomas and Nardo – A computer-animated series about a man and his anthropomorphic house done in a 3D paper-style, created by Mark Beyer. It had an original soundtrack composed by The Residents.
 * Speedbump the Roadkill Possum – About a possum who often gets run over.
 * Was (Not Was) – A series of fast-paced chalk animations to the tune of songs by the titular band.
 * Uncle Louie – A series of cut-out animations about an older yet jovial uncle and his young nephew in various adventures.
 * Bobby & Billy – A series of cut-out animations, drawn similar to Norman Rockwell paintings, about two younger boys who display malevolence and immoral behavior in various situations. The cartoon often satirizes indecency set in the 1960s.
 * Brickface & Stucco – A live-action series about two grease monkeys and their custom hot rod gear head adventures.
 * Brad Dharma: Psychedelic Detective – An animated series about a psychic private detective in the future megacity of Timbuktu. It mixed cyberpunk and fantasy tropes.

Winter Steele
Winter Steele is a puppet television series created by Cintra Wilson that aired as a segment of Liquid Television during its first two seasons, 1991–1993. Wilson wrote the series, created the puppets, did the voice of the main character and even did some live action body double work.

Winter Steele is depicted as a female biker who is in hot pursuit of her childhood friend, lover and sometime nemesis David "Crow" Dickerson, himself a biker. The two met as children in a repressive orphanage and bonded. Separated, the two vowed to find each other, with Winter criss-crossing the land on a motorcycle. In this course Winter breaks many laws - robbing a crossdresser at gunpoint, credit card fraud, etc. As it transpires, Crow is also desperately looking for Winter, he has gotten a career as a stunt performer a la Evel Knievel and a cape he uses in his act bears the inscription "Winter, where are you?" At one point Winter even meets up with Crow's mother, who abandoned her son to an orphanage. Asked if she regretted sending Crow there, she tersely replies "Hell no!"

Winter eventually learns of Crow's career as a daredevil, but despairs of reaching him when she can't get his attention at a show. Defeated, Winter attempts suicide by immolation, wrecking her motorcycle, tearing off her clothes and setting them on fire. She is stopped when a private detective hired by Crow recognizes her. But before he can bring her to Crow, he sees Winter's burnt belongings and assumes she has committed suicide. He attempts suicide himself by ramming his chopper into a brick wall, but though seriously injured he is not killed. Winter finally catches up with Crow at the intensive care unit at the hospital, but is taken away by the police on various charges before she can stay long. After the police have taken her away, we see Crow raise a thumb towards Winter.

Revival
On October 13, 2011, MTVX, MTV's cross media group, announced the return of Liquid Television. It is now a network that is available on the internet and social media. The first content to debut on the network was "F**KING BEST SONG EVERRR" by Wallpaper, available on the website. Full-length episodes featuring the online content and all-new material were released in 2013.

Shows on LiquidTelevision.com

 * The Head - Animated series about the adventures of a young man who has an alien hatch out of his head.
 * The Maxx - Animated adaptation of comic book series The Maxx, the story follows the dual-reality adventures and struggles of the Maxx and his social worker Julie. Aired on MTV's Oddities, which was a sub-category of Liquid Television in the 1990s.
 * Daria - Focuses on Daria Morgendorffer, a smart, acerbic, and somewhat misanthropic teenage girl who observes the world around her. Spin-off of Beavis and Butt-Head.
 * Wonder Showzen - Live-action/animated sketch comedy series about a darkly perverse kids' show modeled after Sesame Street.
 * Celebrity Deathmatch - Clay animation series featuring overly violent wrestling matches between celebrities. Originally part of LT's follow-up, Cartoon Sushi.

title: Liquid Television


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Akaike information criterion

The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.

AIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process. AIC estimates the relative amount of information lost by a given model: the less information a model loses, the higher the quality of that model.

In estimating the amount of information lost by a model, AIC deals with the trade-off between the goodness of fit of the model and the simplicity of the model. In other words, AIC deals with both the risk of overfitting and the risk of underfitting.

The Akaike information criterion is named after the Japanese statistician Hirotsugu Akaike, who formulated it. It now forms the basis of a paradigm for the foundations of statistics and is also widely used for statistical inference.

Definition
Suppose that we have a statistical model of some data. Let $k$ be the number of estimated parameters in the model. Let $$\hat L$$ be the maximized value of the likelihood function for the model. Then the AIC value of the model is the following.

 * $$\mathrm{AIC} \, = \, 2k - 2\ln(\hat L)$$

Given a set of candidate models for the data, the preferred model is the one with the minimum AIC value. Thus, AIC rewards goodness of fit (as assessed by the likelihood function), but it also includes a penalty that is an increasing function of the number of estimated parameters. The penalty discourages overfitting, which is desired because increasing the number of parameters in the model almost always improves the goodness of the fit.

AIC is founded in information theory. Suppose that the data is generated by some unknown process f. We consider two candidate models to represent f: g1 and g2. If we knew f, then we could find the information lost from using g1 to represent f by calculating the Kullback–Leibler divergence, DKL(f ‖ g1); similarly, the information lost from using g2 to represent f could be found by calculating DKL(f ‖ g2). We would then, generally, choose the candidate model that minimized the information loss.

We cannot choose with certainty, because we do not know f. showed, however, that we can estimate, via AIC, how much more (or less) information is lost by g1 than by g2. The estimate, though, is only valid asymptotically; if the number of data points is small, then some correction is often necessary (see AICc, below).

Note that AIC tells nothing about the absolute quality of a model, only the quality relative to other models. Thus, if all the candidate models fit poorly, AIC will not give any warning of that. Hence, after selecting a model via AIC, it is usually good practice to validate the absolute quality of the model. Such validation commonly includes checks of the model's residuals (to determine whether the residuals seem like random) and tests of the model's predictions. For more on this topic, see statistical model validation.

How to use AIC in practice
To apply AIC in practice, we start with a set of candidate models, and then find the models' corresponding AIC values. There will almost always be information lost due to using a candidate model to represent the "true model," i.e. the process that generated the data. We wish to select, from among the candidate models, the model that minimizes the information loss. We cannot choose with certainty, but we can minimize the estimated information loss.

Suppose that there are R candidate models. Denote the AIC values of those models by AIC1, AIC2, AIC3, ..., AICR. Let AICmin be the minimum of those values. Then the quantity exp((AICmin − AICi)/2) can be interpreted as being proportional to the probability that the ith model minimizes the (estimated) information loss.

As an example, suppose that there are three candidate models, whose AIC values are 100, 102, and 110. Then the second model is $exp((100 − 102)/2) = 0.368$ times as probable as the first model to minimize the information loss. Similarly, the third model is $exp((100 − 110)/2) = 0.007$ times as probable as the first model to minimize the information loss.

In this example, we would omit the third model from further consideration. We then have three options: (1) gather more data, in the hope that this will allow clearly distinguishing between the first two models; (2) simply conclude that the data is insufficient to support selecting one model from among the first two; (3) take a weighted average of the first two models, with weights proportional to 1 and 0.368, respectively, and then do statistical inference based on the weighted multimodel.

The quantity $exp((AIC_{min} − AIC_{i})/2)$ is known as the relative likelihood of model i. It is closely related to the likelihood ratio used in the likelihood-ratio test. Indeed, if all the models in the candidate set have the same number of parameters, then using AIC might at first appear to be very similar to using the likelihood-ratio test. There are, however, important distinctions. In particular, the likelihood-ratio test is valid only for nested models, whereas AIC (and AICc) has no such restriction.

Hypothesis testing
Every statistical hypothesis test can be formulated as a comparison of statistical models. Hence, every statistical hypothesis test can be replicated via AIC. Two examples are briefly described in the subsections below. Details for those examples, and many more examples, are given by and.

Replicating Student's t-test
As an example of a hypothesis test, consider the t-test to compare the means of two normally-distributed populations. The input to the t-test comprises a random sample from each of the two populations.

To formulate the test as a comparison of models, we construct two different models. The first model models the two populations as having potentially different means and standard deviations. The likelihood function for the first model is thus the product of the likelihoods for two distinct normal distributions; so it has four parameters: $μ_{1}, σ_{1}, μ_{2}, σ_{2}$. To be explicit, the likelihood function is as follows (denoting the sample sizes by $n_{1}$ and $n_{2}$).

\mathcal{L}(\mu_1,\sigma_1,\mu_2,\sigma_2) \, = \, $$

\prod_{i=1}^{n_1} \frac{1}{\sqrt{2 \pi}\sigma_1} \exp\left( -\frac{(x_i-\mu_1)^2}{2\sigma_1^2}\right) \; \, \boldsymbol\cdot \, \prod_{i=n_1+1}^{n_1+n_2} \frac{1}{\sqrt{2 \pi}\sigma_2} \exp\left( -\frac{(x_i-\mu_2)^2}{2\sigma_2^2}\right) $$

The second model models the two populations as having the same means but potentially different standard deviations. The likelihood function for the second model thus sets $μ_{1} = μ_{2}$ in the above equation; so it has three parameters.

We then maximize the likelihood functions for the two models (in practice, we maximize the log-likelihood functions); after that, it is easy to calculate the AIC values of the models. We next calculate the relative likelihood. For instance, if the second model was only 0.01 times as likely as the first model, then we would omit the second model from further consideration: so we would conclude that the two populations have different means.

The t-test assumes that the two populations have identical standard deviations; the test tends to be unreliable if the assumption is false and the sizes of the two samples are very different (Welch's t-test would be better). Comparing the means of the populations via AIC, as in the example above, has an advantage by not making such assumptions.

Comparing categorical data sets
For another example of a hypothesis test, suppose that we have two populations, and each member of each population is in one of two categories—category #1 or category #2. Each population is binomially distributed. We want to know whether the distributions of the two populations are the same. We are given a random sample from each of the two populations.

Let $m$ be the size of the sample from the first population. Let $m_{1}$ be the number of observations (in the sample) in category #1; so the number of observations in category #2 is $m − m_{1}$. Similarly, let $n$ be the size of the sample from the second population. Let $n_{1}$ be the number of observations (in the sample) in category #1.

Let $p$ be the probability that a randomly-chosen member of the first population is in category #1. Hence, the probability that a randomly-chosen member of the first population is in category #2 is $1 − p$. Note that the distribution of the first population has one parameter. Let $q$ be the probability that a randomly-chosen member of the second population is in category #1. Note that the distribution of the second population also has one parameter.

To compare the distributions of the two populations, we construct two different models. The first model models the two populations as having potentially different distributions. The likelihood function for the first model is thus the product of the likelihoods for two distinct binomial distributions; so it has two parameters: $p$, $q$. To be explicit, the likelihood function is as follows.

\mathcal{L}(p,q) \, = \, \frac{m!}{m_1! (m-m_1)!} p^{m_1} (1-p)^{m-m_1} \; \, \boldsymbol\cdot \; \; \frac{n!}{n_1! (n-n_1)!} q^{n_1} (1-q)^{n-n_1} $$

The second model models the two populations as having the same distribution. The likelihood function for the second model thus sets $p = q$ in the above equation; so the second model has one parameter.

We then maximize the likelihood functions for the two models (in practice, we maximize the log-likelihood functions); after that, it is easy to calculate the AIC values of the models. We next calculate the relative likelihood. For instance, if the second model was only 0.01 times as likely as the first model, then we would omit the second model from further consideration: so we would conclude that the two populations have different distributions.

Foundations of statistics
Statistical inference is generally regarded as comprising hypothesis testing and estimation. Hypothesis testing can be done via AIC, as discussed above. Regarding estimation, there are two types: point estimation and interval estimation. Point estimation can be done within the AIC paradigm: it is provided by maximum likelihood estimation. Interval estimation can also be done within the AIC paradigm: it is provided by likelihood intervals. Hence, statistical inference generally can be done within the AIC paradigm.

The most commonly used paradigms for statistical inference are frequentist inference and Bayesian inference. AIC, though, can be used to do statistical inference without relying on either the frequentist paradigm or the Bayesian paradigm: because AIC can be interpreted without the aid of significance levels or Bayesian priors. In other words, AIC can be used to form a foundation of statistics that is distinct from both frequentism and Bayesianism.

Modification for small sample size
When the sample size is small, there is a substantial probability that AIC will select models that have too many parameters, i.e. that AIC will overfit. To address such potential overfitting, AICc was developed: AICc is AIC with a correction for small sample sizes.

The formula for AICc depends upon the statistical model. Assuming that the model is univariate, is linear in its parameters, and has normally-distributed residuals (conditional upon regressors), then the formula for AICc is as follows.

 * $$\mathrm{AICc} \, = \, \mathrm{AIC} + \frac{2k^2 + 2k}{n - k - 1}$$

—where $n$ denotes the sample size and $k$ denotes the number of parameters. Thus, AICc is essentially AIC with an extra penalty term for the number of parameters. Note that as $n → ∞$, the extra penalty term converges to 0, and thus AICc converges to AIC.

If the assumption that the model is univariate and linear with normal residuals does not hold, then the formula for AICc will generally be different from the formula above. For some models, the formula can be difficult to determine. For every model that has AICc available, though, the formula for AICc is given by AIC plus terms that includes both $k$ and $k$2. In comparison, the formula for AIC includes $k$ but not $k$2. In other words, AIC is a first-order estimate (of the information loss), whereas AICc is a second-order estimate.

Further discussion of the formula, with examples of other assumptions, is given by and by. In particular, with other assumptions, bootstrap estimation of the formula is often feasible.

To summarize, AICc has the advantage of tending to be more accurate than AIC (especially for small samples), but AICc also has the disadvantage of sometimes being much more difficult to compute than AIC. Note that if all the candidate models have the same $k$ and the same formula for AICc, then AICc and AIC will give identical (relative) valuations; hence, there will be no disadvantage in using AIC, instead of AICc. Furthermore, if $n$ is many times larger than $k$2, then the extra penalty term will be negligible; hence, the disadvantage in using AIC, instead of AICc, will be negligible.

History
The Akaike information criterion was formulated by the statistician Hirotsugu Akaike. It was originally named "an information criterion". It was first announced in English by Akaike at a 1971 symposium; the proceedings of the symposium were published in 1973. The 1973 publication, though, was only an informal presentation of the concepts. The first formal publication was a 1974 paper by Akaike.

The initial derivation of AIC relied upon some strong assumptions. showed that the assumptions could be made much weaker. Takeuchi's work, however, was in Japanese and was not widely known outside Japan for many years. (Translated in )

AICc was originally proposed for linear regression (only) by. That instigated the work of, and several further papers by the same authors, which extended the situations in which AICc could be applied.

The first general exposition of the information-theoretic approach was the volume by. It includes an English presentation of the work of Takeuchi. The volume led to far greater use of AIC, and it now has more than 64,000 citations on Google Scholar.

Akaike called his approach an "entropy maximization principle", because the approach is founded on the concept of entropy in information theory. Indeed, minimizing AIC in a statistical model is effectively equivalent to maximizing entropy in a thermodynamic system; in other words, the information-theoretic approach in statistics is essentially applying the Second Law of Thermodynamics. As such, AIC has roots in the work of Ludwig Boltzmann on entropy. For more on these issues, see and.

Counting parameters
A statistical model must account for random errors. A straight line model might be formally described as yi = b0 + b1xi + εi. Here, the εi are the residuals from the straight line fit. If the εi are assumed to be i.i.d. Gaussian (with zero mean), then the model has three parameters: b0, b1, and the variance of the Gaussian distributions. Thus, when calculating the AIC value of this model, we should use k=3. More generally, for any least squares model with i.i.d. Gaussian residuals, the variance of the residuals' distributions should be counted as one of the parameters.

As another example, consider a first-order autoregressive model, defined by xi = c + φxi−1 + εi, with the εi being i.i.d. Gaussian (with zero mean). For this model, there are three parameters: c, φ, and the variance of the εi. More generally, a pth-order autoregressive model has $p + 2$ parameters. (If, however, c is not estimated from the data, but instead given in advance, then there are only $p + 1$ parameters.)

Transforming data
The AIC values of the candidate models must all be computed with the same data set. Sometimes, though, we might want to compare a model of the response variable, $y$, with a model of the logarithm of the response variable, $log(y)$. More generally, we might want to compare a model of the data with a model of transformed data. Following is an illustration of how to deal with data transforms (adapted from : "Investigators should be sure that all hypotheses are modeled using the same response variable").

Suppose that we want to compare two models: one with a normal distribution of $y$ and one with a normal distribution of $log(y)$. We should not directly compare the AIC values of the two models. Instead, we should transform the normal cumulative distribution function to first take the logarithm of $y$. To do that, we need to perform the relevant integration by substitution: thus, we need to multiply by the derivative of the (natural) logarithm function, which is $1/y$. Hence, the transformed distribution has the following probability density function:
 * $$y \mapsto \, \frac{1}{y} \frac{1}{\sqrt{2\pi\sigma^2}}\,\exp \left(-\frac{\left(\ln y-\mu\right)^2}{2\sigma^2}\right)$$

—which is the probability density function for the log-normal distribution. We then compare the AIC value of the normal model against the AIC value of the log-normal model.

For misspecified model, Takeuchi's Information Criterion (TIC) might be more appropriate. However, TIC often suffers from instability caused by estimation errors.

Comparisons with other model selection methods
The critical difference between AIC and BIC (and their variants) is the asymptotic property under well-specified and misspecified model classes. Their fundamental differences have been well-studied in regression variable selection and autoregression order selection problems. In general, if the goal is prediction, AIC and leave-one-out cross-validations are preferred. If the goal is selection, inference, or interpretation, BIC or leave-many-out cross-validations are preferred. A comprehensive overview of AIC and other popular model selection methods is given by Ding et al. (2018)

Comparison with BIC
The formula for the Bayesian information criterion (BIC) is similar to the formula for AIC, but with a different penalty for the number of parameters. With AIC the penalty is $2k$, whereas with BIC the penalty is $ln(n)k$.

A comparison of AIC/AICc and BIC is given by, with follow-up remarks by. The authors show that AIC/AICc can be derived in the same Bayesian framework as BIC, just by using different prior probabilities. In the Bayesian derivation of BIC, though, each candidate model has a prior probability of 1/R (where R is the number of candidate models). Additionally, the authors present a few simulation studies that suggest AICc tends to have practical/performance advantages over BIC.

A point made by several researchers is that AIC and BIC are appropriate for different tasks. In particular, BIC is argued to be appropriate for selecting the "true model" (i.e. the process that generated the data) from the set of candidate models, whereas AIC is not appropriate. To be specific, if the "true model" is in the set of candidates, then BIC will select the "true model" with probability 1, as $n → ∞$; in contrast, when selection is done via AIC, the probability can be less than 1. Proponents of AIC argue that this issue is negligible, because the "true model" is virtually never in the candidate set. Indeed, it is a common aphorism in statistics that "all models are wrong"; hence the "true model" (i.e. reality) cannot be in the candidate set.

Another comparison of AIC and BIC is given by. Vrieze presents a simulation study—which allows the "true model" to be in the candidate set (unlike with virtually all real data). The simulation study demonstrates, in particular, that AIC sometimes selects a much better model than BIC even when the "true model" is in the candidate set. The reason is that, for finite $n$, BIC can have a substantial risk of selecting a very bad model from the candidate set. This reason can arise even when $n$ is much larger than $k$2. With AIC, the risk of selecting a very bad model is minimized.

If the "true model" is not in the candidate set, then the most that we can hope to do is select the model that best approximates the "true model". AIC is appropriate for finding the best approximating model, under certain assumptions. (Those assumptions include, in particular, that the approximating is done with regard to information loss.)

Comparison of AIC and BIC in the context of regression is given by. In regression, AIC is asymptotically optimal for selecting the model with the least mean squared error, under the assumption that the "true model" is not in the candidate set. BIC is not asymptotically optimal under the assumption. Yang additionally shows that the rate at which AIC converges to the optimum is, in a certain sense, the best possible.

Comparison with least squares
Sometimes, each candidate model assumes that the residuals are distributed according to independent identical normal distributions (with zero mean). That gives rise to least squares model fitting.

With least squares fitting, the maximum likelihood estimate for the variance of a model's residuals distributions is
 * $$\hat\sigma^2 = \mathrm{RSS}/n$$,

where the residual sum of squares is
 * $$\textstyle \mathrm{RSS} = \sum_{i=1}^n (y_i-f(x_i;\hat{\theta}))^2$$

Then, the maximum value of a model's log-likelihood function is (see Normal distribution):
 * $$\ln(\hat L)=

-\frac{n}{2}\ln(2\pi) - \frac{n}{2}\ln(\hat\sigma^2) - \frac{1}{2\hat\sigma^2}\mathrm{RSS} \, = \, - \frac{n}{2}\ln(\hat\sigma^2) + C $$ where $C$ is a constant independent of the model, and dependent only on the particular data points, i.e. it does not change if the data does not change.

That gives:
 * $$\mathrm{AIC} = 2k - 2\ln(\hat L) = 2k + n\ln(\hat\sigma^2) - 2C$$

Because only differences in AIC are meaningful, the constant $C$ can be ignored, which allows us to conveniently take the following for model comparisons:
 * $$\Delta \mathrm{AIC} = 2k + n\ln(\hat\sigma^2)$$

Note that if all the models have the same $k$, then selecting the model with minimum AIC is equivalent to selecting the model with minimum $RSS$—which is the usual objective of model selection based on least squares.

Comparison with cross-validation
Leave-one-out cross-validation is asymptotically equivalent to AIC, for ordinary linear regression models. Asymptotic equivalence to AIC also holds for mixed-effects models.

Comparison with Mallows's Cp
Mallows's Cp is equivalent to AIC in the case of (Gaussian) linear regression.

title: Akaike information criterion