Dirichlet processes

distributions.ipynb

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    "Link: http://www.cs.cmu.edu/~epxing/Class/10701-08s/recitation/dirichlet.pdf"
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   "source": [
    "## Binomial Distribution"
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    "Represents the number of successes in a sequence of independent yes / no experiments"
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   "source": [
    "$$ P(X = x\\, |\\, n, p) = {n\\choose k}\\, p^k (1-p)^{n-k}$$\n"
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   "source": [
    "## Multinomial Distribution"
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   "source": [
    "Extension of the binomial distribution to k possible outcomes"
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   "source": [
    "$$P(x_1, \\ldots, x_k\\, |\\, n, p_1, . . . , p_k) \n",
    "= \\frac{N!}{\\Pi_{i=1}^{k} p_i^{xi} {x_i!}}$$\n",
    "$$\\sum_i x_i = N, x_i \\geq 0$$"
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   "source": [
    "## Beta Distribution"
   ]
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   "source": [
    "- ein\n",
    "- zwei\n",
    "- drei"
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   "source": [
    "$$\\frac{x^{\\alpha-1}(1-x)^{\\beta-1}} { B (\\alpha,\\beta)}\\!$$"
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   "source": [
    "import scipy as sp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import beta"
   ]
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formulas.md

http://www.cs.cmu.edu/~epxing/Class/10701-08s/recitation/dirichlet.pdf

• Binomial

$ x = x + 1$

P(X=