Download - 1.3.2 Teorema Bayes
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TEOREMA BAYES
Trihastuti Agustinah
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Pengantar
Teorema Bayes digunakan untuk mengestimasi suatu informasi atau hasil eksperimen
berdasarkan probabilitas event yang diketahui sebelum eksperimen tersebut dilakukan.
Aplikasi teorema Bayes banyak digunakan dalam sistem komunikasi.
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Konsep teorema Bayes Probabilitas bersyarat digunakan pada dua event
)()()(
APABPABP n
n∩
= )()()(
n
nn BP
BAPBAP ∩=
)()()(
)(AP
BPBAPABP nn
n =
)()()()()(
)(1 NN
nnn BPBAPBAP
BPBAPABP
++=
jadi
Subsitusi P(A) menggunakan rumus probabilitas total
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ContohDiagram ilustrasi sistem komunikasi
B2
B1 A1
A20.9
0.90.1
0.1
P(B2)=0.4
P(B1)=0.6B1: simbol ‘1’ dikirim
B2: simbol ‘0’ dikirim
A1: simbol ‘1’ diterima
A2: simbol ‘0’ diterima
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Probabilitas simbol ‘1’ diterima)()()()()( 2211111 BPBAPBPBAPAP +=
58.0)4.0(1.0)6.0(9.0 =+=
Probabilitas simbol ‘0’ diterima)()()()()( 2221122 BPBAPBPBAPAP +=
42.0)4.0(9.0)6.0(1.0 =+=
Probabilitas transisi9.0)( 11 =BAP 1.0)( 12 =BAP
9.0)( 22 =BAP 1.0)( 21 =BAP
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Probabilitas simbol yang diterima berasal dari simbol yang sama
)()()()(
1111
11 APBPBAPABP =
)()()()(
2222
22 APBPBAPABP =
857.042.036.0
42.0)4.0(9.0
≈==
931.058.054.0
58.0)6.0(9.0
≈==
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Probabilitas simbol yang diterima berbeda dengan simbol yang dikirim
)()()()(
2112
21 APBPBAPABP =
)()()()(
1221
12 APBPBAPABP =
143.042.006.0
42.0)6.0(1.0
≈==
069.058.004.0
58.0)4.0(1.0
≈==
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Ringkasan
• Probabilitas priori diketahui (diberikan) sebelumeksperimen dilakukan.
• Probabilitas posteriori dapat dihitung denganmenggunakan teorema Bayes bila eksperimentelah dilakukan dan terjadi event tertentu yangdiamati.