UNR, MATH/STAT 352, Spring 2007 Predictable, certain, deterministic Unpredictable, uncertain Gravity...

UNR, MATH/STAT 352, Spring 2007

Predictable, certain,deterministic

Unpredictable, uncertain

Gravity accelerationg ~ 9.8 m/s2

h = ½ gt2

E = mgh=mv2/2

A black hole


Coin as a rigid body obeys classicalgravitation laws, and its fall is deterministic & predictable…

… it is well described by physical laws

Coin as a gambling tool (also obeyinggravitation laws) is unpredictable…

TAIL?

HEAD?h = ½ gt2

… so its fall is better described by probabilistic laws


TAIL?

HEAD?h = ½ gt2

Level of detail may turn deterministic phenomena into random and vice versa…


Life time of a device (computer chip)

Time

Failure

Shooting a target with a fixed riffle

micro-defects, change in temperature condition, transportation, storage, energy power,…

Origin of randomness:

Origin of randomness:defects in bullets masses, density inhomogeneities,changing atmospheric-conditions, …


Max Born

(December 11, 1882 – January 5, 1970)

Angular momentum

Ene

rgy

Electron position measurements

High probability

Low probability


1954 Nobel Prize in Physics"for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction"

Max Born

(December 11, 1882 – January 5, 1970)


Albert Einstein

(March 14, 1879 – April 18, 1955)

Quantum mechanics is certainly imposing. But an inner voice tells me it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the Old One. I, at any rate, am convinced that He does not throw dice.

(Letter to Max Born,1926)


1: Single out a set of primary factors

2: Determine their interrelationships

3: Choose appropriate mathematical apparatus

4: Determine outcome given primary factors

5: Add new primary factors


20th century has witnessed the Science revolution that demonstrated a limited power of the classical approach, its

inability to predict evolution of many natural phenomena.

This happens because many processes crucially depend on a countless number of uncontrolled parameters and their interplay.

Insignificant and undetectable changes in initial conditions may (and do) lead to different result of an entire experiment.

Say, try to figure out what controls the position (head vs. tail) of a coin.


There should be a principal difference in methods and approaches applied to description of a small

number of well controlled primary factors and a large number of uncontrollable secondary factors.

TP & S are among sciences targeted at solving this problem (other are theory of deterministic chaos,

theory of complexity, etc.)


Da Vinci (1452-1519)


Weather = Dynamics of atmosphere = Turbulence !


Hurricane Floyd, 1999

Andrei Kolmogorov (1903-1987):A founder of modern theory of

probabilities (1933)

Da Vinci (1452-1519)

Claude Louise Mary Henry

Navier (1821)

George Gabriel Stokes

Turbulence

Phenomenon

Classical (deterministic) approach

Probabilistic approach

Navier-Stokes EQsUNR, MATH/STAT 352, Spring 2007

Possible outcomes of coin tossing:

HEAD

TAIL

RIB

LOSTRelevant, interesting, most probable outcomes:

HEAD

TAILModel: { H, T }


( ) ( ) ( )k kE g g x F x

( ) ( ) ( )k kE g g x F x ObservationsModel

Probability (a fair coin will show about 50% of tails)

Statistics (a coin that shows 90 tails out of 100 throws is probably not fair)

( ) ( ) ( )k kE g g x F x

TABLE 2.1.1 Data on Male Heart Attack PatientsSYS- DIA- OUT-

ID EJEC VOL VOL OCCLU STEN TIME COME AGE SMOKE BETA CHOLaSURG

390 72 36 131 0 0 143 0 49 2 2 59 0279 52 74 155 37 63 143 0 54 2 2 68 1391 62 52 137 33 47 16 2 56 2 2 52 0201 50 165 329 33 30 143 0 42 2 2 39 0202 50 47 95 0 100 143 0 46 2 2 74 1

69 27 124 170 77 23 143 0 57 2 2 NA 2310 60 86 215 7 50 40 0 51 2 2 58 0392 72 37 132 40 10 9 5 56 2 2 75 0311 60 65 163 0 40 142 0 45 2 2 72 0393 63 52 140 0 10 142 0 46 2 2 90 0

70 29 117 164 50 0 142 0 48 2 2 72 0203 48 69 133 0 27 142 0 54 2 2 NA 0394 59 54 133 30 13 142 0 39 2 1 NA 0204 50 67 135 37 63 141 0 49 2 2 86 2280 53 65 138 0 33 140 0 58 2 1 49 0

55 17 184 221 57 13 5 1 50 2 2 70 279 37 88 140 37 47 118 5 58 2 2 NA 0

205 45 106 193 33 43 140 0 47 1 1 38 1206 43 85 150 0 50 23 5 51 2 2 61 0312 60 59 149 7 37 139 0 43 2 1 56 0

80 38 103 168 47 43 100 1 55 2 2 62 1281 57 53 124 0 57 140 0 58 2 1 93 0207 44 68 121 27 60 139 0 55 2 2 63 1282 51 53 109 0 77 139 0 41 2 2 45 4396 63 58 157 0 73 139 0 51 2 2 60 0208 49 81 157 13 13 139 0 49 2 2 60 0209 48 58 112 0 0 72 1 56 2 2 57 0283 58 71 167 27 0 138 0 45 2 1 46 0210 42 92 159 0 0 139 0 57 2 2 58 0397 68 50 156 0 100 138 0 51 2 1 NA 0211 43 146 259 47 33 3 1 56 2 2 70 0398 67 43 130 0 70 138 0 49 2 2 NA 3284 52 70 146 0 23 137 0 47 1 2 NA 0399 63 73 195 27 0 136 0 36 1 1 61 0285 54 62 133 33 23 137 0 38 2 2 NA 0

71 37 93 148 47 0 137 0 59 2 2 NA 0286 51 65 133 43 7 136 0 54 2 2 NA 0212 42 95 163 40 10 109 3 57 2 2 NA 4400 66 49 144 10 50 65 1 52 2 2 55 0287 54 66 145 7 40 136 0 47 2 2 62 0

81 39 144 237 13 87 136 0 39 2 2 56 3813 63 52 141 0 47 43 3 48 2 2 NA 0

68 30 219 314 33 45 76 1 53 1 2 NA 0288 59 39 94 0 0 135 0 47 1 2 63 0407 67 39 117 0 73 53 1 57 2 2 62 2

a NA = Not Available(missing data code).


ID EJEC VOL VOL OCCLU STEN TIME COME AGE SMOKE BETA CHOLaSURG

390 72 36 131 0 0 143 0 49 2 2 59 0279 52 74 155 37 63 143 0 54 2 2 68 1391 62 52 137 33 47 16 2 56 2 2 52 0201 50 165 329 33 30 143 0 42 2 2 39 0202 50 47 95 0 100 143 0 46 2 2 74 1

69 27 124 170 77 23 143 0 57 2 2 NA 2310 60 86 215 7 50 40 0 51 2 2 58 0392 72 37 132 40 10 9 5 56 2 2 75 0311 60 65 163 0 40 142 0 45 2 2 72 0393 63 52 140 0 10 142 0 46 2 2 90 0

70 29 117 164 50 0 142 0 48 2 2 72 0203 48 69 133 0 27 142 0 54 2 2 NA 0394 59 54 133 30 13 142 0 39 2 1 NA 0204 50 67 135 37 63 141 0 49 2 2 86 2280 53 65 138 0 33 140 0 58 2 1 49 0

55 17 184 221 57 13 5 1 50 2 2 70 279 37 88 140 37 47 118 5 58 2 2 NA 0

205 45 106 193 33 43 140 0 47 1 1 38 1206 43 85 150 0 50 23 5 51 2 2 61 0312 60 59 149 7 37 139 0 43 2 1 56 0

80 38 103 168 47 43 100 1 55 2 2 62 1281 57 53 124 0 57 140 0 58 2 1 93 0207 44 68 121 27 60 139 0 55 2 2 63 1282 51 53 109 0 77 139 0 41 2 2 45 4396 63 58 157 0 73 139 0 51 2 2 60 0208 49 81 157 13 13 139 0 49 2 2 60 0209 48 58 112 0 0 72 1 56 2 2 57 0283 58 71 167 27 0 138 0 45 2 1 46 0210 42 92 159 0 0 139 0 57 2 2 58 0397 68 50 156 0 100 138 0 51 2 1 NA 0211 43 146 259 47 33 3 1 56 2 2 70 0398 67 43 130 0 70 138 0 49 2 2 NA 3284 52 70 146 0 23 137 0 47 1 2 NA 0399 63 73 195 27 0 136 0 36 1 1 61 0285 54 62 133 33 23 137 0 38 2 2 NA 0

71 37 93 148 47 0 137 0 59 2 2 NA 0286 51 65 133 43 7 136 0 54 2 2 NA 0212 42 95 163 40 10 109 3 57 2 2 NA 4400 66 49 144 10 50 65 1 52 2 2 55 0287 54 66 145 7 40 136 0 47 2 2 62 0

81 39 144 237 13 87 136 0 39 2 2 56 3813 63 52 141 0 47 43 3 48 2 2 NA 0

68 30 219 314 33 45 76 1 53 1 2 NA 0288 59 39 94 0 0 135 0 47 1 2 63 0407 67 39 117 0 73 53 1 57 2 2 62 2



ID EJEC VOL VOL OCCLU STEN TIME COME AGE SMOKE BETA CHOLa SURG390 72 36 131 0 0 143 0 49 2 2 59 0279 52 74 155 37 63 143 0 54 2 2 68 1391 62 52 137 33 47 16 2 56 2 2 52 0201 50 165 329 33 30 143 0 42 2 2 39 0202 50 47 95 0 100 143 0 46 2 2 74 1

69 27 124 170 77 23 143 0 57 2 2 NA 2310 60 86 215 7 50 40 0 51 2 2 58 0392 72 37 132 40 10 9 5 56 2 2 75 0311 60 65 163 0 40 142 0 45 2 2 72 0393 63 52 140 0 10 142 0 46 2 2 90 0

70 29 117 164 50 0 142 0 48 2 2 72 0203 48 69 133 0 27 142 0 54 2 2 NA 0394 59 54 133 30 13 142 0 39 2 1 NA 0204 50 67 135 37 63 141 0 49 2 2 86 2280 53 65 138 0 33 140 0 58 2 1 49 0

55 17 184 221 57 13 5 1 50 2 2 70 279 37 88 140 37 47 118 5 58 2 2 NA 0

205 45 106 193 33 43 140 0 47 1 1 38 1206 43 85 150 0 50 23 5 51 2 2 61 0312 60 59 149 7 37 139 0 43 2 1 56 0

80 38 103 168 47 43 100 1 55 2 2 62 1281 57 53 124 0 57 140 0 58 2 1 93 0207 44 68 121 27 60 139 0 55 2 2 63 1282 51 53 109 0 77 139 0 41 2 2 45 4396 63 58 157 0 73 139 0 51 2 2 60 0208 49 81 157 13 13 139 0 49 2 2 60 0209 48 58 112 0 0 72 1 56 2 2 57 0283 58 71 167 27 0 138 0 45 2 1 46 0210 42 92 159 0 0 139 0 57 2 2 58 0397 68 50 156 0 100 138 0 51 2 1 NA 0211 43 146 259 47 33 3 1 56 2 2 70 0398 67 43 130 0 70 138 0 49 2 2 NA 3284 52 70 146 0 23 137 0 47 1 2 NA 0399 63 73 195 27 0 136 0 36 1 1 61 0285 54 62 133 33 23 137 0 38 2 2 NA 0

71 37 93 148 47 0 137 0 59 2 2 NA 0286 51 65 133 43 7 136 0 54 2 2 NA 0212 42 95 163 40 10 109 3 57 2 2 NA 4400 66 49 144 10 50 65 1 52 2 2 55 0287 54 66 145 7 40 136 0 47 2 2 62 0

81 39 144 237 13 87 136 0 39 2 2 56 3813 63 52 141 0 47 43 3 48 2 2 NA 0

68 30 219 314 33 45 76 1 53 1 2 NA 0288 59 39 94 0 0 135 0 47 1 2 63 0407 67 39 117 0 73 53 1 57 2 2 62 2



… work when we can describe possible outcomesof experiment, but can not predict its specific outcome

… deal with appropriate mathematical model ofa physical phenomenon, not with phenomenon itself


Q1: What % of bullets will on average hit the target?

Q2: How many bullets should be spent to hit the target almost surely?

Q3: 14 bullets out of 100 hit the target: Was it riffle A?

A: 75% A: from 60% to 90%

sample population

A: 3 bullets

Riffle A hit the target with75 bullets out of 100

A: Most probably not

Point estimation

Interval estimation

Hypothesis testingUNR, MATH/STAT 352, Spring 2007

% newborn boys(about 51%)

TP & S use the phenomenon of stability of frequencies: Observing a large number of uniform random events, we often detect amazing regularities

# tails# bets

1/2% quality goods

Car

accident

s

Car

accident

s Street

traumatism Street

traumatism Crim

e

rates Crime

rates


Earthquakes: the most unpredictable Natural disaster

Gutenberg-Richter law

Prediction: In 2007 there will be about 1000 EQs with magnitude 5, and 10 EQs with M7


$$$ = ???

$$$ = !!!


Luggage = ???


TP&S do not cancel randomness, unpredictability of individual experiment. They allow to predict in some approximation an average result of a mass of uniform random phenomena.

The goal of TP&S is to overpass a difficult (and often practically impossible) exploration of a single random phenomena and jump to collective behavior.

Probabilistic predictions are different from exact statementof what, when, and where to expect. They establish boundarywithin which, with a high degree of reliability one will observeinteresting phenomenon. The larger the number of individual events, the sharper the possible probabilistic prediction.


UNR, MATH/STAT 352, Spring 2007 Predictable, certain, deterministic Unpredictable, uncertain Gravity...

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