Translation examples
Prezentare Thomas Bayes' father, Joshua Bayes, was one of the first six Nonconformist ministers to be ordained in England.
Thomas Bayes-isä, Joshua Bayes, oli yksi kuuden ensimmäisen Nonconformist ministereitä on vihitty Englanti.
A naive Bayes classifier is a term in Bayesian statistics dealing with a simple probabilistic classifier based on applying Bayes' theorem with strong (naive) independence assumptions.
Naiivi Bayes-valitsin on termi Bayes tilastot käsitellessään yksinkertainen todennäköisyyspohjaisen valitsimeen perust
Several of Bayes 's papers were therefore given to Price.
Monet Bayes' s paperit olivat sen vuoksi hintaa.
This seems to have come about through his friendship with Bayes .
Tämä vaikuttaa ovat syntyneet kautta hänen ystävyyttä Bayes.
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
Bayesin teoreema (myös Bayesin sääntö tai Bayesin laki) on ehdolliseen todennäköisyyteen liittyvä matemaattinen teoreema.
A central rule of Bayesian inference is Bayes' theorem.
Bayesilainen roskapostisuodatus soveltaa Bayesin teoreemaa.
This contribution is called the posterior probability and is computed using Bayes' theorem.
Tätä vaikutusta kutsutaan posteriori-todennäköisyydeksi ja se lasketaan Bayesin teoreemaa soveltaen.
He is known to have published two works in his lifetime, one theological and one mathematical: Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731) An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (published anonymously in 1736), in which he defended the logical foundation of Isaac Newton's calculus ("fluxions") against the criticism of George Berkeley, author of The Analyst It is speculated that Bayes was elected as a Fellow of the Royal Society in 1742 on the strength of the Introduction to the Doctrine of Fluxions, as he is not known to have published any other mathematical works during his lifetime.
Bayesin tiedetään julkaisseen kaksi teosta: Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731) ja An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst (1736), jossa hän puolustaa Isaac Newtonin laskentaoppia George Berkeleyn hyökkäystä vastaan.
Given our current estimate of the parameters θ(t), the conditional distribution of the Zi is determined by Bayes theorem to be the proportional height of the normal density weighted by τ: T j , i ( t ) := P ( Z i = j | X i = x i ; θ ( t ) ) = τ j ( t ) f ( x i ; μ j ( t ) , Σ j ( t ) ) τ 1 ( t ) f ( x i ; μ 1 ( t ) , Σ 1 ( t ) ) + τ 2 ( t ) f ( x i ; μ 2 ( t ) , Σ 2 ( t ) ) {\displaystyle T_{j,i}^{(t)}:=\operatorname {P} (Z_{i}=j|X_{i}=\mathbf {x} _{i};\theta ^{(t)})={\frac {\tau _{j}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{j}^{(t)},\Sigma _{j}^{(t)})}{\tau _{1}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{1}^{(t)},\Sigma _{1}^{(t)})+\tau _{2}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{2}^{(t)},\Sigma _{2}^{(t)})}}} .
Tällöin Zi:n ehdollinen jakauma voidaan kirjoittaa todennäköisyytenä Bayesin kaavan mukaisesti: T j , i ( t ) := P ( Z i = j | X i = x i ; θ ( t ) ) = τ j ( t ) f ( x i ; μ j ( t ) , Σ j ( t ) ) τ 1 ( t ) f ( x i ; μ 1 ( t ) , Σ 1 ( t ) ) + τ 2 ( t ) f ( x i ; μ 2 ( t ) , Σ 2 ( t ) ) {\displaystyle T_{j,i}^{(t)}:=\operatorname {P} (Z_{i}=j|X_{i}=\mathbf {x} _{i};\theta ^{(t)})={\frac {\tau _{j}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{j}^{(t)},\Sigma _{j}^{(t)})}{\tau _{1}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{1}^{(t)},\Sigma _{1}^{(t)})+\tau _{2}^{(t)}\ f(\mathbf {x} _{i};{\boldsymbol {\mu }}_{2}^{(t)},\Sigma _{2}^{(t)})}}} .
Call A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} the events that the corresponding prisoner will be pardoned, and b {\displaystyle b} the event that the warden tells A that prisoner B is to be executed, then, using Bayes' theorem, the posterior probability of A being pardoned, is: P ( A | b ) = P ( b | A ) P ( A ) P ( b | A ) P ( A ) + P ( b | B ) P ( B ) + P ( b | C ) P ( C ) = {\displaystyle P(A|b)={\frac {P(b|A)P(A)}{P(b|A)P(A)+P(b|B)P(B)+P(b|C)P(C)}}=} = 1 2 × 1 3 1 2 × 1 3 + 0 × 1 3 + 1 × 1 3 = 1 3 . {\displaystyle ={\frac {{\tfrac {1}{2}}\times {\tfrac {1}{3}}}{{\tfrac {1}{2}}\times {\tfrac {1}{3}}+0\times {\tfrac {1}{3}}+1\times {\tfrac {1}{3}}}}={\tfrac {1}{3}}.} The probability of C being pardoned, on the other hand, is: P ( C | b ) = P ( b | C ) P ( C ) P ( b | A ) P ( A ) + P ( b | B ) P ( B ) + P ( b | C ) P ( C ) = {\displaystyle P(C|b)={\frac {P(b|C)P(C)}{P(b|A)P(A)+P(b|B)P(B)+P(b|C)P(C)}}=} = 1 × 1 3 1 2 × 1 3 + 0 × 1 3 + 1 × 1 3 = 2 3 . {\displaystyle ={\frac {1\times {\tfrac {1}{3}}}{{\tfrac {1}{2}}\times {\tfrac {1}{3}}+0\times {\tfrac {1}{3}}+1\times {\tfrac {1}{3}}}}={\tfrac {2}{3}}.} The crucial difference making A and C unequal is that P ( b | A ) = 1 2 {\displaystyle P(b|A)={\tfrac {1}{2}}} but P ( b | C ) = 1 {\displaystyle P(b|C)=1} .
Tapahtumat A = ”vanki A armahdetaan” B = ”vanki B armahdetaan” C = ”vanki C armahdetaan” b = ”vartija nimeää vangin B joutuvan teloitettavaksi (ei armahdettu)” Nyt Bayesin teoreemaa käyttäen saadaan, että vangin A mahdollisuus tulla armahdetuksi on: P ( A | b ) = P ( b | A ) P ( A ) P ( b | A ) P ( A ) + P ( b | B ) P ( B ) + P ( b | C ) P ( C ) = {\displaystyle P(A|b)={\frac {P(b|A)P(A)}{P(b|A)P(A)+P(b|B)P(B)+P(b|C)P(C)}}=} = 1 2 × 1 3 1 2 × 1 3 + 0 × 1 3 + 1 × 1 3 = 1 3 . {\displaystyle ={\frac {{\tfrac {1}{2}}\times {\tfrac {1}{3}}}{{\tfrac {1}{2}}\times {\tfrac {1}{3}}+0\times {\tfrac {1}{3}}+1\times {\tfrac {1}{3}}}}={\tfrac {1}{3}}.} Jokaisella vangilla on 1/3 mahdollisuus tulla armahdetuksi.
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