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@cshimmin
Created March 28, 2018 01:16
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import stats, optimize"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define the parameters of the experiment\n",
"For the purpose of illustration, we also assume we know the \"true\" value of the survival probability, p_s"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"N_well = 96\n",
"p_s = 0.4\n",
"n0 = 50"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Probability that a well will have zero surviving cells:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def p0(p_s, n0, N_well):\n",
" return np.exp(-p_s*n0/N_well)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Expected value of N_dead = 77.95\n"
]
}
],
"source": [
"N_dead_expected = N_well * p0(p_s, n0, N_well)\n",
"print(\"Expected value of N_dead = %.2f\"%N_dead_expected)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Randomly-chosen value for N_dead: 76\n"
]
}
],
"source": [
"N_dead = np.random.binomial(N_well, p0(p_s, n0, N_well))\n",
"print(\"Randomly-chosen value for N_dead: %d\"%N_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Randomly sample from the binomial distribution for this experiment\n",
"We have chosen one specific value at random to represent our actual \"observation\""
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993c673748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(np.random.binomial(N_well, p0(p_s, n0, N_well), size=1000), histtype='step', bins=40, range=(60,100));\n",
"plt.axvline(N_dead, linestyle='--', color='red', label='\"observed\" N_dead');\n",
"plt.axvline(N_dead_expected, color='black', label='expected N_dead');\n",
"plt.xlabel(\"$N_{dead}$\", fontsize=16);\n",
"plt.ylabel(\"number of occurances\", fontsize=16);\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Construct likelihood function\n",
"Note that in practice, one miniimzes the negative logarithm likelihood, rather than maximizing the lhood directly.\n",
"Also note that this is a function that takes the \"observed\" value and returns another function of the proposed survival probability."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def make_nll(N_dead):\n",
" def fn(p):\n",
" return -2*stats.binom.logpmf(N_dead, N_well, p0(p, n0, N_well))\n",
" return fn"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"observed_nll = make_nll(N_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minimize -2ln(L)\n",
"The value of p_s which minimizes -2ln(L) for our \"observation\" is the maximum likelihood estimate of this parameter for the experiment."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum likelihood estimate for p_s: 0.45\n"
]
}
],
"source": [
"result = optimize.minimize(observed_nll, x0=0.5, bounds=[(1e-2,1)])\n",
"p_s_estimate = result.x[0]\n",
"print(\"Maximum likelihood estimate for p_s: %.2f\"%p_s_estimate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot -2ln(L)\n",
"Vertical bars show our maximum likelihood estimate (red) along with the true value (black).\n",
"If you repeat the experiment by drawing a different random value of N_draw, this estimate will move around but on average should give the true value!\n",
"\n",
"Note that if you change the parameters of the experiment (e.g. n0, N_well), you can make the likelihood function \"steeper\", which gives greater precision in the final estimate."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993a4fb2b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_values = np.linspace(1e-2,1.0,50)\n",
"plt.plot(x_values, observed_nll(x_values));\n",
"plt.axvline(p_s_estimate, linestyle='--', color='red', label='estimated p_s');\n",
"plt.axvline(p_s, color='black', label='\"true\" p_s');\n",
"plt.xlabel(\"$p_s$\", fontsize=16);\n",
"plt.ylabel(\"$L(p_s | N_{dead})$\", fontsize=16);\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example combining two experiments, with different concentrations of cell A and B"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"p_A = 0.4\n",
"p_B = 0.1\n",
"\n",
"n0_A = 50*0.65\n",
"n0_B = 50*0.35\n",
"\n",
"n1_A = 0\n",
"n1_B = 50"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Probability that a well has no surviving cells\n",
"Note this now depends on more parameters of the experiment."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def p0_mix(p_A, p_B, n_A, n_B, N_well):\n",
" return np.exp(-(p_A*n_A + p_B*n_B)/N_well)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expected value of N_dead(0) = 82.33\n",
"expected value of N_dead(1) = 91.13\n"
]
}
],
"source": [
"N0_dead_expected = N_well * p0_mix(p_A, p_B, n0_A, n0_B, N_well)\n",
"print(\"expected value of N_dead(0) = %.2f\"%N0_dead_expected)\n",
"N1_dead_expected = N_well * p0_mix(p_A, p_B, n1_A, n1_B, N_well)\n",
"print(\"expected value of N_dead(1) = %.2f\"%N1_dead_expected)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Grab two values of N_dead\n",
"This represents doing the experiment twice, note that each experiment has its own, different parameters (i.e. the concentrations)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Randomly-chosen value of N_dead(0): 79\n",
"Randomly-chosen value of N_dead(1): 94\n"
]
}
],
"source": [
"N0_dead = np.random.binomial(N_well, p0_mix(p_A, p_B, n0_A, n0_B, N_well))\n",
"N1_dead = np.random.binomial(N_well, p0_mix(p_A, p_B, n1_A, n1_B, N_well))\n",
"print(\"Randomly-chosen value of N_dead(0): %d\"%N0_dead)\n",
"print(\"Randomly-chosen value of N_dead(1): %d\"%N1_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combined likelihood\n",
"Note that in order to combine the results from two experiments, you just have to multiply the likelihoods together (or add the logarithms).\n",
"\n",
"Note also that the NLL depends on _two_ observations, one from each experiment."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def make_nll_mix(obs0, obs1):\n",
" def fn(p):\n",
" p_a = p[0]\n",
" p_b = p[1]\n",
" return -2*(\n",
" stats.binom.logpmf(obs0, N_well, p0_mix(p_a, p_b, n0_A, n0_B, N_well)) +\n",
" stats.binom.logpmf(obs1, N_well, p0_mix(p_a, p_b, n1_A, n1_B, N_well))\n",
" )\n",
" return fn"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"observed_nll_mix = make_nll_mix(N0_dead, N1_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minimize -2ln(L) in the 2-dimensional parameter space of (p_A,p_B)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum likelihood estimate for p_A: 0.55\n",
"Maximum likelihood estimate for p_B: 0.04\n"
]
}
],
"source": [
"result = optimize.minimize(observed_nll_mix, x0=(0.5, 0.5), bounds=[(1e-2,1), (1e-2, 1)])\n",
"p_A_estimate = result.x[0]\n",
"p_B_estimate = result.x[1]\n",
"print(\"Maximum likelihood estimate for p_A: %.2f\"%p_A_estimate)\n",
"print(\"Maximum likelihood estimate for p_B: %.2f\"%p_B_estimate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Contour plot of the 2-dimensional likelihood\n",
"Again, the \"steeper\" the bottom of this contour is (in both dimensions), the more precise the measurement.\n",
"Sometimes one variable is well defined while the other is not, giving an oblong contour lines."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993a590be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X, Y = np.meshgrid(np.linspace(1e-2,1), np.linspace(1e-2,1))\n",
"c = plt.contour(X,Y,observed_nll_mix([X,Y]), 25)\n",
"plt.scatter(p_A_estimate, p_B_estimate, marker='x', color='red', s=100, label='estimated (p_A,p_B)')\n",
"plt.scatter(p_A, p_B, marker='+', color='black', s=150, label='\"true\" (p_A,p_B)');\n",
"plt.xlabel(\"$p_A$\", fontsize=16)\n",
"plt.ylabel(\"$p_B$\", fontsize=16)\n",
"plt.legend();\n",
"plt.colorbar(c);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import stats, optimize"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define the parameters of the experiment\n",
"For the purpose of illustration, we also assume we know the \"true\" value of the survival probability, p_s"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"N_well = 96\n",
"p_s = 0.4\n",
"n0 = 50"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Probability that a well will have zero surviving cells:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def p0(p_s, n0, N_well):\n",
" return np.exp(-p_s*n0/N_well)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Expected value of N_dead = 77.95\n"
]
}
],
"source": [
"N_dead_expected = N_well * p0(p_s, n0, N_well)\n",
"print(\"Expected value of N_dead = %.2f\"%N_dead_expected)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Randomly-chosen value for N_dead: 76\n"
]
}
],
"source": [
"N_dead = np.random.binomial(N_well, p0(p_s, n0, N_well))\n",
"print(\"Randomly-chosen value for N_dead: %d\"%N_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Randomly sample from the binomial distribution for this experiment\n",
"We have chosen one specific value at random to represent our actual \"observation\""
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993c673748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(np.random.binomial(N_well, p0(p_s, n0, N_well), size=1000), histtype='step', bins=40, range=(60,100));\n",
"plt.axvline(N_dead, linestyle='--', color='red', label='\"observed\" N_dead');\n",
"plt.axvline(N_dead_expected, color='black', label='expected N_dead');\n",
"plt.xlabel(\"$N_{dead}$\", fontsize=16);\n",
"plt.ylabel(\"number of occurances\", fontsize=16);\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Construct likelihood function\n",
"Note that in practice, one miniimzes the negative logarithm likelihood, rather than maximizing the lhood directly.\n",
"Also note that this is a function that takes the \"observed\" value and returns another function of the proposed survival probability."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def make_nll(N_dead):\n",
" def fn(p):\n",
" return -2*stats.binom.logpmf(N_dead, N_well, p0(p, n0, N_well))\n",
" return fn"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"observed_nll = make_nll(N_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minimize -2ln(L)\n",
"The value of p_s which minimizes -2ln(L) for our \"observation\" is the maximum likelihood estimate of this parameter for the experiment."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum likelihood estimate for p_s: 0.45\n"
]
}
],
"source": [
"result = optimize.minimize(observed_nll, x0=0.5, bounds=[(1e-2,1)])\n",
"p_s_estimate = result.x[0]\n",
"print(\"Maximum likelihood estimate for p_s: %.2f\"%p_s_estimate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot -2ln(L)\n",
"Vertical bars show our maximum likelihood estimate (red) along with the true value (black).\n",
"If you repeat the experiment by drawing a different random value of N_draw, this estimate will move around but on average should give the true value!\n",
"\n",
"Note that if you change the parameters of the experiment (e.g. n0, N_well), you can make the likelihood function \"steeper\", which gives greater precision in the final estimate."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993a4fb2b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_values = np.linspace(1e-2,1.0,50)\n",
"plt.plot(x_values, observed_nll(x_values));\n",
"plt.axvline(p_s_estimate, linestyle='--', color='red', label='estimated p_s');\n",
"plt.axvline(p_s, color='black', label='\"true\" p_s');\n",
"plt.xlabel(\"$p_s$\", fontsize=16);\n",
"plt.ylabel(\"$L(p_s | N_{dead})$\", fontsize=16);\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example combining two experiments, with different concentrations of cell A and B"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"p_A = 0.4\n",
"p_B = 0.1\n",
"\n",
"n0_A = 50*0.65\n",
"n0_B = 50*0.35\n",
"\n",
"n1_A = 0\n",
"n1_B = 50"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Probability that a well has no surviving cells\n",
"Note this now depends on more parameters of the experiment."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def p0_mix(p_A, p_B, n_A, n_B, N_well):\n",
" return np.exp(-(p_A*n_A + p_B*n_B)/N_well)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expected value of N_dead(0) = 82.33\n",
"expected value of N_dead(1) = 91.13\n"
]
}
],
"source": [
"N0_dead_expected = N_well * p0_mix(p_A, p_B, n0_A, n0_B, N_well)\n",
"print(\"expected value of N_dead(0) = %.2f\"%N0_dead_expected)\n",
"N1_dead_expected = N_well * p0_mix(p_A, p_B, n1_A, n1_B, N_well)\n",
"print(\"expected value of N_dead(1) = %.2f\"%N1_dead_expected)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Grab two values of N_dead\n",
"This represents doing the experiment twice, note that each experiment has its own, different parameters (i.e. the concentrations)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Randomly-chosen value of N_dead(0): 79\n",
"Randomly-chosen value of N_dead(1): 94\n"
]
}
],
"source": [
"N0_dead = np.random.binomial(N_well, p0_mix(p_A, p_B, n0_A, n0_B, N_well))\n",
"N1_dead = np.random.binomial(N_well, p0_mix(p_A, p_B, n1_A, n1_B, N_well))\n",
"print(\"Randomly-chosen value of N_dead(0): %d\"%N0_dead)\n",
"print(\"Randomly-chosen value of N_dead(1): %d\"%N1_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combined likelihood\n",
"Note that in order to combine the results from two experiments, you just have to multiply the likelihoods together (or add the logarithms).\n",
"\n",
"Note also that the NLL depends on _two_ observations, one from each experiment."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def make_nll_mix(obs0, obs1):\n",
" def fn(p):\n",
" p_a = p[0]\n",
" p_b = p[1]\n",
" return -2*(\n",
" stats.binom.logpmf(obs0, N_well, p0_mix(p_a, p_b, n0_A, n0_B, N_well)) +\n",
" stats.binom.logpmf(obs1, N_well, p0_mix(p_a, p_b, n1_A, n1_B, N_well))\n",
" )\n",
" return fn"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"observed_nll_mix = make_nll_mix(N0_dead, N1_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minimize -2ln(L) in the 2-dimensional parameter space of (p_A,p_B)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum likelihood estimate for p_A: 0.55\n",
"Maximum likelihood estimate for p_B: 0.04\n"
]
}
],
"source": [
"result = optimize.minimize(observed_nll_mix, x0=(0.5, 0.5), bounds=[(1e-2,1), (1e-2, 1)])\n",
"p_A_estimate = result.x[0]\n",
"p_B_estimate = result.x[1]\n",
"print(\"Maximum likelihood estimate for p_A: %.2f\"%p_A_estimate)\n",
"print(\"Maximum likelihood estimate for p_B: %.2f\"%p_B_estimate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Contour plot of the 2-dimensional likelihood\n",
"Again, the \"steeper\" the bottom of this contour is (in both dimensions), the more precise the measurement.\n",
"Sometimes one variable is well defined while the other is not, giving an oblong contour lines."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f993a590be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X, Y = np.meshgrid(np.linspace(1e-2,1), np.linspace(1e-2,1))\n",
"c = plt.contour(X,Y,observed_nll_mix([X,Y]), 25)\n",
"plt.scatter(p_A_estimate, p_B_estimate, marker='x', color='red', s=100, label='estimated (p_A,p_B)')\n",
"plt.scatter(p_A, p_B, marker='+', color='black', s=150, label='\"true\" (p_A,p_B)');\n",
"plt.xlabel(\"$p_A$\", fontsize=16)\n",
"plt.ylabel(\"$p_B$\", fontsize=16)\n",
"plt.legend();\n",
"plt.colorbar(c);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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