From 38057fe4478a71e6b7ba83e52eb34d3e4d8940f4 Mon Sep 17 00:00:00 2001 From: Allen Downey Date: Fri, 29 Dec 2023 12:33:39 -0500 Subject: [PATCH] Updates --- examples/bookstore.ipynb | 262 ++++++++++++++++++++------------------- 1 file changed, 135 insertions(+), 127 deletions(-) diff --git a/examples/bookstore.ipynb b/examples/bookstore.ipynb index 69c75e70..9f7c4632 100644 --- a/examples/bookstore.ipynb +++ b/examples/bookstore.ipynb @@ -25,7 +25,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -41,7 +41,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -55,7 +55,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -97,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -117,7 +117,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -126,7 +126,7 @@ "2.7952013319456332" ] }, - "execution_count": 78, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -134,17 +134,17 @@ "source": [ "from scipy.stats import norm\n", "\n", - "lambdas = np.linspace(0.01, 20, 50)\n", - "qs = np.log(lambdas)\n", + "λs = np.linspace(0.01, 20, 50)\n", + "qs = np.log(λs)\n", "\n", "mu, sigma = 0.3, 0.7\n", "ps = norm.pdf(qs, mu, sigma)\n", "\n", - "prior_lambda = Pmf(ps, lambdas)\n", - "prior_lambda.normalize()\n", - "prior_lambda.index.name = 'lambda'\n", + "prior_λ = Pmf(ps, λs)\n", + "prior_λ.normalize()\n", + "prior_λ.index.name = 'λ'\n", "\n", - "prior_lambda.mean()" + "prior_λ.mean()" ] }, { @@ -156,12 +156,12 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 22, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -171,8 +171,10 @@ } ], "source": [ - "prior_lambda.plot()\n", - "decorate()" + "prior_λ.plot()\n", + "decorate(xlabel='Book selling rate',\n", + " ylabel='PMF',\n", + " title='Prior')" ] }, { @@ -184,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -196,7 +198,7 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -205,14 +207,14 @@ "(10, 50, 21)" ] }, - "execution_count": 117, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "PK, PLAMBDA, PT = meshgrid(prior_k, prior_lambda, prior_t)\n", - "prior = PK * PLAMBDA * PT\n", + "PK, Pλ, PT = meshgrid(prior_k, prior_λ, prior_t)\n", + "prior = PK * Pλ * PT\n", "prior.shape" ] }, @@ -224,29 +226,27 @@ "\n", "Now for the update, we have to handle two cases:\n", "\n", - "* If we observe at least one book, `n`, the probability of the data is the probability of selling `k-n` book at rate `λ` over period `t`, which is given by the Poisson PMF.\n", + "* If we observe at least one book, `n`, the probability of the data is the probability of selling `k-n` books at rate `λ` over period `t`, which is given by the Poisson PMF.\n", "\n", - "* If we see that there are no copies left, we have to add in the probability that the number of books sold in this period could have exceeded `k`, which is given by the Poisson survival function.\n", + "* If there are no copies left, we have to add in the probability that the number of books sold in this period could have exceeded `k`, which is given by the Poisson survival function.\n", "\n", "The following function computes the probability of the data for all values of the parameters, multiplies by the prior, and normalizes the result." ] }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import poisson\n", "\n", - "def update(prior, data):\n", - " n = data\n", + "def update(prior, n):\n", + " K, λ, T = meshgrid(ks, λs, ts)\n", " \n", - " K, LAMBDA, T = meshgrid(ks, lambdas, ts)\n", - " \n", - " like = poisson(mu=LAMBDA*T).pmf(K-n)\n", + " like = poisson(mu=λ*T).pmf(K-n)\n", " if n == 0:\n", - " like += poisson(mu=LAMBDA*T).sf(K)\n", + " like += poisson(mu=λ*T).sf(K)\n", "\n", " posterior = prior * like\n", " posterior /= posterior.sum()\n", @@ -263,7 +263,7 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -280,7 +280,7 @@ }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -289,16 +289,16 @@ "(3.294088962095148, 2.720709517121936)" ] }, - "execution_count": 120, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior_k = Pmf(posterior.sum(axis=(1, 2)), ks)\n", - "posterior_lambda = Pmf(posterior.sum(axis=(0, 2)), lambdas)\n", + "posterior_λ = Pmf(posterior.sum(axis=(0, 2)), λs)\n", "\n", - "posterior_k.mean(), posterior_lambda.mean()" + "posterior_k.mean(), posterior_λ.mean()" ] }, { @@ -310,7 +310,7 @@ }, { "cell_type": "code", - "execution_count": 123, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -341,12 +341,12 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -356,11 +356,11 @@ } ], "source": [ - "prior_lambda.plot(label='prior', color='gray')\n", - "posterior_lambda.plot(label=f'n = {n}')\n", + "prior_λ.plot(label='prior', color='gray')\n", + "posterior_λ.plot(label=f'n = {n}')\n", "decorate(xlabel='Book-selling rate, λ',\n", " ylabel='PMF',\n", - " title='Posterior distribution of lambda')" + " title='Posterior distribution of λ')" ] }, { @@ -378,27 +378,34 @@ "\n", "Now let's consider the more general question, \"What number of books would you most like to see?\" There are two ways we might answer:\n", "\n", - "* The observation that leads to the highest estimate of `λ` might seem to be the best. However, that ignore an interaction between `k` and ``\n", - " `" + "* One answer might be the observation that leads to the highest estimate of `λ`. But if the book-selling rate is high, relative to `k`, the book will sometimes be out of stock, leading to lost sales.\n", + "\n", + "* So an alternative is to choose the observation that implies the highest number of books sold per cycle.\n", + "\n", + "To compute the second one, we'll need the following function, which makes a `Pmf` that represents the distribution of books sold during one cycle with rate `λ` and upper bound `k`." ] }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ - "def make_poisson(lam, k):\n", + "def make_poisson(λ, k):\n", + " \"\"\"Make a truncated Poisson distribution.\n", + " \"\"\"\n", " qs = np.arange(k+1)\n", - " ps = poisson.pmf(qs, lam)\n", + " ps = poisson.pmf(qs, λ)\n", " pmf = Pmf(ps, qs)\n", - " pmf[k] += poisson.sf(k, lam)\n", + " \n", + " # assign the total probability mass above `k` to `k`.\n", + " pmf[k] += poisson.sf(k, λ)\n", " return pmf" ] }, { "cell_type": "code", - "execution_count": 88, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -418,74 +425,49 @@ ] }, { - "cell_type": "code", - "execution_count": 91, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "def compute_sales(posterior):\n", - " posterior_joint = posterior.sum(axis=2)\n", - " posterior_joint.shape\n", - "\n", - " K, LAMBDA = meshgrid(ks, lambdas)\n", - " K.shape\n", - "\n", - " SALES = posterior_joint * np.minimum(K, LAMBDA)\n", - " return np.sum(SALES)" + "Now if we are given a posterior distribution, we can compute the expected sales for each pair of parameters and make a Pmf that maps from each expectation to its probability." ] }, { "cell_type": "code", - "execution_count": 92, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2.449169695342132" - ] - }, - "execution_count": 92, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "compute_sales(posterior)" - ] - }, - { - "cell_type": "code", - "execution_count": 100, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def compute_sales(posterior):\n", + " \"\"\"Expected number of books sold per cycle.\n", + " \n", + " posterior: array of posterior probabilities for k, λ, t\n", + " \"\"\"\n", + " # make the marginal joint posterior of k, λ\n", " posterior_joint = pd.DataFrame(posterior.sum(axis=2), \n", - " index=ks, columns=lambdas)\n", + " index=ks, columns=λs)\n", "\n", " res = []\n", " for (k, lam), p in posterior_joint.stack().items():\n", " exp_sales = make_poisson(lam, k).mean()\n", - " res.append((exp_sales, p))\n", + " res.append((p, exp_sales))\n", " \n", - " qs, ps = np.transpose(res)\n", + " ps, qs = np.transpose(res)\n", " pmf = Pmf(ps, qs)\n", " return pmf.mean()" ] }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "2.2695775366862856" + "2.0364396231583672" ] }, - "execution_count": 101, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -495,26 +477,15 @@ ] }, { - "cell_type": "code", - "execution_count": 103, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "res = []\n", - "\n", - "for n in range(11):\n", - " posterior = update(prior, n)\n", - " posterior_k = Pmf(posterior.sum(axis=(1, 2)), ks)\n", - " posterior_lambda = Pmf(posterior.sum(axis=(0, 2)), lambdas)\n", - "\n", - " k, lam = posterior_k.mean(), posterior_lambda.mean()\n", - " sales = compute_sales(posterior)\n", - " res.append((n, k, lam, sales))" + "Finally, let's loop over possible values of `n` and compute for each one the posterior mean values of `k` and `λ`." ] }, { "cell_type": "code", - "execution_count": 104, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -540,7 +511,7 @@ " \n", " n\n", " mean k\n", - " mean lambda\n", + " mean λ\n", " exp sales\n", " \n", " \n", @@ -627,38 +598,57 @@ "" ], "text/plain": [ - " n mean k mean lambda exp sales\n", - "0 0 2.409571 4.361937 2.025360\n", - "1 1 2.322331 2.740616 1.643844\n", - "2 2 3.294089 2.720710 2.036440\n", - "3 3 4.254728 2.693604 2.269578\n", - "4 4 5.199590 2.656726 2.393205\n", - "5 5 6.122093 2.606749 2.441859\n", - "6 6 7.013147 2.539618 2.435680\n", - "7 7 7.860703 2.450961 2.384995\n", - "8 8 8.649959 2.337343 2.295145\n", - "9 9 9.365430 2.199540 2.172083\n", - "10 10 10.000000 2.056530 2.037294" + " n mean k mean λ exp sales\n", + "0 0 2.409571 4.361937 2.025360\n", + "1 1 2.322331 2.740616 1.643844\n", + "2 2 3.294089 2.720710 2.036440\n", + "3 3 4.254728 2.693604 2.269578\n", + "4 4 5.199590 2.656726 2.393205\n", + "5 5 6.122093 2.606749 2.441859\n", + "6 6 7.013147 2.539618 2.435680\n", + "7 7 7.860703 2.450961 2.384995\n", + "8 8 8.649959 2.337343 2.295145\n", + "9 9 9.365430 2.199540 2.172083\n", + "10 10 10.000000 2.056530 2.037294" ] }, - "execution_count": 104, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "df = pd.DataFrame(res, columns=['n', 'mean k', 'mean lambda', 'exp sales'])\n", + "res = []\n", + "\n", + "for n in range(11):\n", + " posterior = update(prior, n)\n", + " posterior_k = Pmf(posterior.sum(axis=(1, 2)), ks)\n", + " posterior_λ = Pmf(posterior.sum(axis=(0, 2)), λs)\n", + "\n", + " k, λ = posterior_k.mean(), posterior_λ.mean()\n", + " sales = compute_sales(posterior)\n", + " res.append((n, k, λ, sales))\n", + "\n", + "df = pd.DataFrame(res, columns=['n', 'mean k', 'mean λ', 'exp sales'])\n", "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the implied sales rate as a function of the observed number of books.\n", + "By this metric, the best number of books to see is `0`." + ] + }, { "cell_type": "code", - "execution_count": 105, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { - "image/png": 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SOgFk5FdJXQ4RERHZCAY7K6XvjuXWYkRERHSlGOysVGIIZ8YSERGRaRjsrFRCS4tdGveMJSIioivEYGel9F2xJwqrUNeolbgaIiIisgUMdlYqRO0KHzdnNOkEsgo5gYKIiIguj8HOSslkskvWs2N3LBEREV0eg50VS2jZgSKdM2OJiIjoCjDYWTH9nrFHOTOWiIiIrgCDnRXT7xmbUVCFRq1O4mqIiIjI2jHYWbFwXzd4Kp3Q0KTDyaJqqcshIiIiK8dgZ8XkchniuVAxERERXSEGOyt3cWsxzowlIiIi4xjsrJx+AgVb7IiIiOhyGOysnH4CxbF8DbQ6IXE1REREZM0Y7KxclL8HXJ3lqG3QIrukRupyiIiIyIox2Fk5hVyG+OCW9ey4UDEREREZwWBnAy5uLcZgR0RERB1jsLMB+nF23DOWiIiIjGGwswEJ+pmxeZUQghMoiIiIqH0MdjYgJsATLgo5quqakFN2QepyiIiIyEox2NkAFyc5YoM8ATS32hERERG1h8HORnChYiIiIrocBjsbkaCfQMGtxYiIiKgDDHY2wrBnbC4nUBAREVH7GOxsRFyQJxRyGUprGlCgqZO6HCIiIrJCDHY2wtVZgZgADwBcz46IiIjax2BnQwzj7DiBgoiIiNrBYGdD9DNjuWcsERERtYfBzoZc3DOWXbFERETUFoOdDekV7AWZDCjQ1KG4ql7qcoiIiMjKMNjZEA+lEyK7uQNgdywRERG1xWBnYxJbJlAc5ULFRERE9CcMdjaGW4sRERFRRxjsbEyiYWsxBjsiIiJqjcHOxujXssspu4DK2kaJqyEiIiJrwmBnY9RuzgjzVQHgBAoiIiJq7aqC3f/+9z8MGzYMISEhOHv2LABg4cKFWLt2rVmLo/axO5aIiIjaY3KwW7x4MZ544gnccsstqKiogFarBQB4e3tj4cKF5q6P2sGFiomIiKg9Jge7999/H0uXLsUzzzwDhUJhOD5gwACkpaWZtThqX0JIy8xYttgRERHRJUwOdtnZ2ejbt2+b40qlEjU1NWYpiozTT6DILqlBdX2TxNUQERGRtTA52EVGRiI1NbXN8Z9++gm9evUyR010Gf6eSgR5uUIIICOf3bFERETUzMnUFzzxxBOYOXMm6urqIITAH3/8gS+//BIpKSn45JNPLFEjtSMx1AsFmjqk51ZiYA9fqcshIiIiK2BysHvooYegUqnw7LPPora2Fvfeey9CQkKwaNEi/PWvf7VEjdSOhBA1fs0o4gQKIiIiMjA52AHAlClTMGXKFNTW1qK6uhoBAQHmrosuQz8zlmvZERERkZ7JY+xGjx6NiooKAICbm5sh1Gk0GowePdqsxVHH9HvGniiqRl2jVuJqiIiIyBqYHOy2bNmChoaGNsfr6uqwfft2sxRFlxfk5Qo/dxdodQLHC6qkLoeIiIiswBV3xR45csTw92PHjqGgoMDwXKvV4qeffkJoaKh5q6MOyWQyJISqsS2rGOm5legT5i11SURERCSxKw52ffr0gUwmg0wma7fLVaVS4f333zdrcWRcYogXtmUVc5wdERERATChKzY7OxunTp0yLHGSnZ1teOTm5kKj0eCBBx4w6eaLFy9GUlISvLy84OXlhSFDhmDjxo0dXr98+XJDuNQ/XF1dTbqnPeHWYkRERHSpK26xi4iIAADodDqz3bx79+547bXXEBMTAyEEPvvsM0yYMAGHDh1CQkJCu6/x8vJCZmam4blMJjNbPbamd0uwyyyoQkOTDi5OJg+ZJCIiIjtyVcudAM3j7M6dO9dmIsXtt99+xe8xfvz4Vs8XLFiAxYsXY8+ePR0GO5lMhqCgINMLtkPdfVTwcnWCpq4JJ4qqDFuNERERkWMyOdidPn0ad9xxB9LS0iCTySCEAHCx5UyrvbqlN7RaLb755hvU1NRgyJAhHV5XXV2NiIgI6HQ69OvXD6+++mqHIdDeyWQyJIaqsetUKY7mahjsiIiIHJzJfXezZ89GZGQkioqK4ObmhqNHj2Lbtm0YMGAAtmzZYnIBaWlp8PDwgFKpxCOPPILVq1cjPj6+3WtjY2Px3//+F2vXrsUXX3wBnU6HoUOH4vz58x2+f319PTQaTauHPTGMs+MECiIiIodncrDbvXs3XnrpJXTr1g1yuRxyuRzDhw9HSkoKHn/8cZMLiI2NRWpqKvbu3YtHH30U06ZNw7Fjx9q9dsiQIZg6dSr69OmDUaNG4fvvv4e/vz8+/vjjDt8/JSUFarXa8AgLCzO5RmuWENK8UHF6LoMdERGRozM52Gm1Wnh6egIAunXrhry8PADNkysundRwpVxcXBAdHY3+/fsjJSUFycnJWLRo0RW91tnZGX379sXJkyc7vGb+/PmorKw0PHJyckyu0ZrpW+yO5Wug1QmJqyEiIiIpmTzGLjExEYcPH0ZkZCQGDRqEN954Ay4uLliyZAmioqI6XZBOp0N9ff0VXavVapGWloZbbrmlw2uUSiWUSmWn67JWkX7ucHdRoKZBi9PF1YgJ9JS6JCIiIpKIycHu2WefRU1NDQDgpZdewm233YYRI0bAz88PX331lUnvNX/+fIwbNw7h4eGoqqrCypUrsWXLFvz8888AgKlTpyI0NBQpKSmG+w0ePBjR0dGoqKjAm2++ibNnz+Khhx4y9WPYDblchvgQL+w7U470vEoGOyIiIgdmcrAbO3as4e/R0dE4fvw4ysrK4OPjY/KackVFRZg6dSry8/OhVquRlJSEn3/+GTfeeCMA4Ny5c5DLL/YWl5eXY8aMGSgoKICPjw/69++PXbt2dTjZwlEkhKibg12uBnf0lboaIiIikopM6NcruQKNjY1QqVRITU1FYmKiJeuyGI1GA7VajcrKSnh5eUldjll8e+A85n1zGIMiffHVwx0vFUNERES2x5TsYtLkCWdnZ4SHh1/1WnVkGYmhzV/ysTwNdJxAQURE5LBMnhX7zDPP4Omnn0ZZWZkl6qGrEO3vAaWTHFX1TThXVit1OURERCQRk8fYffDBBzh58iRCQkIQEREBd3f3VucPHjxotuLoyjgp5IgL9sLhnAqk51WiRzf3y7+IiIiI7I7JwW7ixIkWKIM6KzGkJdjlanBbUojU5RAREZEETA52L7zwgiXqoE7SL1R8lFuLEREROSyTx9iRdUoMadkzNrcSJkx0JiIiIjvCYGcnegZ5wEkuQ3ltI/Iq66Quh4iIiCTAYGcnlE4K9GzZdSI9l92xREREjojBzo7o17M7ymBHRETkkDod7LRaLVJTU1FeXm6OeqgT9BMo0vM0EldCREREUjA52M2ZMweffvopgOZQN2rUKPTr1w9hYWHYsmWLuesjEyRcMoGCiIiIHI/Jwe7bb79FcnIyAGDdunXIzs7G8ePHMXfuXDzzzDNmL5CuXK9gT8hlQFFVPYo0nEBBRETkaEwOdiUlJQgKCgIAbNiwAZMmTULPnj3xwAMPIC0tzewF0pVzc3HCNf4eAICj7I4lIiJyOCYHu8DAQBw7dgxarRY//fQTbrzxRgBAbW0tFAqF2Qsk0+jH2aWxO5aIiMjhmBzspk+fjrvvvhuJiYmQyWQYM2YMAGDv3r2Ii4sze4FkmoSQ5pmxHGdHRETkeEzeUuzf//43EhMTkZOTg0mTJkGpVAIAFAoFnnrqKbMXSKa5uLUYu2KJiIgcjcnBDgD+8pe/AADq6i4O0J82bZp5KqJOiW9pscutuICymgb4urtIXBERERF1FZO7YrVaLV5++WWEhobCw8MDp0+fBgA899xzhmVQSDpers7o4ecGADiax+5YIiIiR2JysFuwYAGWL1+ON954Ay4uF1uDEhMT8cknn5i1OLo6CfqFinPZHUtERORITA52n3/+OZYsWYIpU6a0mgWbnJyM48ePm7U4ujqJ+oWK2WJHRETkUEwOdrm5uYiOjm5zXKfTobGx0SxFUedwz1giIiLHZHKwi4+Px/bt29sc//bbb9G3b1+zFEWdo99a7ExpLTR1DNtERESOwuRZsc8//zymTZuG3Nxc6HQ6fP/998jMzMTnn3+O9evXW6JGMpGvuwtCvVXIrbiAY3kaDI7yk7okIiIi6gImt9hNmDAB69atw6+//gp3d3c8//zzyMjIwLp16wy7UJD0uFAxERGR47mqdexGjBiBTZs2mbsWMqPEUDV+OVbIhYqJiIgciMktdmQb9BMo2GJHRETkOK6oxc7HxwcymeyK3rCsrKxTBZF56Jc8OVVcjdqGJri5XFXjLBEREdmQK/ptv3DhQguXQeYW4OUKf08liqvqkZFfhf4RPlKXRERERBZ2RcGO+8DapsQQL/yeWYyjeZUMdkRERA6gU2Ps6urqoNFoWj3IeiQathbjODsiIiJHYHKwq6mpwaxZsxAQEAB3d3f4+Pi0epD10C9UzD1jiYiIHIPJwe7//u//8Ntvv2Hx4sVQKpX45JNP8OKLLyIkJASff/65JWqkq6SfGZtVWIX6Jq3E1RAREZGlmRzs1q1bh//85z+466674OTkhBEjRuDZZ5/Fq6++ihUrVliiRrpKod4qeLs5o0knkFVQLXU5REREZGEmB7uysjJERUUBALy8vAzLmwwfPhzbtm0zb3XUKTKZzLDsSXoex9kRERHZO5ODXVRUFLKzswEAcXFx+PrrrwE0t+R5e3ubtTjqvAQuVExEROQwTA5206dPx+HDhwEATz31FD788EO4urpi7ty5ePLJJ81eIHXOxRY7TqAgIiKydyZvRzB37lzD38eMGYPjx4/jwIEDiI6ORlJSklmLo87TL3mSka9Bo1YHZwV3kSMiIrJXnd5nKiIiAmq1mt2wVirC1w0eSidU1zfhVHE14oK8pC6JiIiILMTk5pvXX38dX331leH53XffDT8/P4SGhhq6aMl6yOUyxIfox9mxO5aIiMiemRzsPvroI4SFhQEANm3ahE2bNmHjxo0YN24cx9hZKcM4O06gICIismsmd8UWFBQYgt369etx991346abbkKPHj0waNAgsxdInadfqPgolzwhIiKyaya32Pn4+CAnJwcA8NNPP2HMmDEAACEEtFrubmCN9BMojuZpoNMJiashIiIiSzG5xe7OO+/Evffei5iYGJSWlmLcuHEAgEOHDiE6OtrsBVLnRXVzh6uzHLUNWmSX1uAafw+pSyIiIiILMLnF7t1338WsWbMQHx+PTZs2wcOjOSTk5+fjH//4h9kLpM5zUsjRK5gLFRMREdk7k1vsnJ2dMW/evDbHL13fjqxPYogah85V4GieBhP6hEpdDhEREVkAV6t1EIncWoyIiMjuMdg5iIRLljwRghMoiIiI7BGDnYPoGegJZ4UMmromnC+/IHU5REREZAEMdg7CxUmO2CBPAOyOJSIisldXFewqKirwySefYP78+SgrKwMAHDx4ELm5uWYtjszLsAMFFyomIiKySybPij1y5AjGjBkDtVqNM2fOYMaMGfD19cX333+Pc+fO4fPPP7dEnWQGCaFqYF8O94wlIiKyUya32D3xxBO4//77ceLECbi6uhqO33LLLdi2bZtZiyPz6h3KCRRERET2zORgt2/fPjz88MNtjoeGhqKgoMAsRZFlxAV5QiGXobSmAYWaeqnLISIiIjMzOdgplUpoNG278rKysuDv72+WosgyXJ0ViAlo3imEEyiIiIjsj8nB7vbbb8dLL72ExsZGAIBMJsO5c+fwr3/9C3fddZfZCyTzSuAECiIiIrtlcrB7++23UV1djYCAAFy4cAGjRo1CdHQ0PD09sWDBAkvUSGZ0cQcKTqAgIiKyNybPilWr1di0aRN27NiBI0eOoLq6Gv369cOYMWMsUR+ZWWLLBIqjbLEjIiKyOyYHO73hw4dj+PDh5qyFukCvYC/IZEB+ZR1KquvRzUMpdUlERERkJiYHu/fee6/d4zKZDK6uroiOjsbIkSOhUCg6XRyZn4fSCZHd3HG6uAZH8zQY1ZMTXoiIiOyFycHu3XffRXFxMWpra+Hj4wMAKC8vh5ubGzw8PFBUVISoqCj8/vvvCAsLM3vB1HmJIWqcLq5Bem4lgx0REZEdMXnyxKuvvoqBAwfixIkTKC0tRWlpKbKysjBo0CAsWrQI586dQ1BQEObOnWuJeskM9BMoOM6OiIjIvpjcYvfss8/iu+++wzXXXGM4Fh0djbfeegt33XUXTp8+jTfeeINLn1gxw56xnBlLRERkV0xuscvPz0dTU1Ob401NTYadJ0JCQlBVVdX56sgi9GvZnSurRWVto8TVEBERkbmYHOyuv/56PPzwwzh06JDh2KFDh/Doo49i9OjRAIC0tDRERkaar0oyK7WbM8J8VQCAo/nsjiUiIrIXJge7Tz/9FL6+vujfvz+USiWUSiUGDBgAX19ffPrppwAADw8PvP3222YvlsxH3x17lN2xREREdsPkMXZBQUHYtGkTjh8/jqysLABAbGwsYmNjDddcf/315quQLCIxVI2N6QXcWoyIiMiOXPUCxXFxcYiLizNnLdSFEkL0W4sx2BEREdmLqwp258+fxw8//IBz586hoaGh1bl33nnHLIWRZeknUJwuqUFNfRPclVed8YmIiMhKmPzbfPPmzbj99tsRFRWF48ePIzExEWfOnIEQAv369bNEjWQB/p5KBHm5okBTh4x8DQb08JW6JCIiIuokkydPzJ8/H/PmzUNaWhpcXV3x3XffIScnB6NGjcKkSZNMeq/FixcjKSkJXl5e8PLywpAhQ7Bx40ajr/nmm28QFxcHV1dX9O7dGxs2bDD1I1AL/ULF7I4lIiKyDyYHu4yMDEydOhUA4OTkhAsXLsDDwwMvvfQSXn/9dZPeq3v37njttddw4MAB7N+/H6NHj8aECRNw9OjRdq/ftWsXJk+ejAcffBCHDh3CxIkTMXHiRKSnp5v6MQgXu2PT8zgzloiIyB6YHOzc3d0N4+qCg4Nx6tQpw7mSkhKT3mv8+PG45ZZbEBMTg549e2LBggXw8PDAnj172r1+0aJFuPnmm/Hkk0+iV69eePnll9GvXz988MEHpn4MQvPMWIAtdkRERPbC5GA3ePBg7NixAwBwyy234J///CcWLFiABx54AIMHD77qQrRaLVatWoWamhoMGTKk3Wt2796NMWPGtDo2duxY7N69+6rv68j0XbEniqpR16iVuBoiIiLqLJMnT7zzzjuorq4GALz44ouorq7GV199hZiYmKuaEZuWloYhQ4agrq4OHh4eWL16NeLj49u9tqCgAIGBga2OBQYGGrYya099fT3q6+sNzzUadjvqBXm5ws/dBaU1DcgsqEJymLfUJREREVEnmBTstFotzp8/j6SkJADN3bIfffRRpwqIjY1FamoqKisr8e2332LatGnYunVrh+HOVCkpKXjxxRfN8l72RiaTISFUjW1ZxUjPq2SwIyIisnEmdcUqFArcdNNNKC8vN1sBLi4uiI6ORv/+/ZGSkoLk5GQsWrSo3WuDgoJQWFjY6lhhYSGCgoI6fP/58+ejsrLS8MjJyTFb7fYg0bBQMVsyiYiIbJ3JY+wSExNx+vRpS9QCANDpdK26Ti81ZMgQbN68udWxTZs2dTgmDwCUSqVhORX9gy7ST6A4yq3FiIiIbJ7JY+xeeeUVzJs3Dy+//DL69+8Pd3f3VudNCU7z58/HuHHjEB4ejqqqKqxcuRJbtmzBzz//DACYOnUqQkNDkZKSAgCYPXs2Ro0ahbfffhu33norVq1ahf3792PJkiWmfgxqkdiy5Mnx/Co0anVwVpic9YmIiMhKmBzsbrnlFgDA7bffDplMZjguhIBMJoNWe+WzK4uKijB16lTk5+dDrVYjKSkJP//8M2688UYAwLlz5yCXXwwaQ4cOxcqVK/Hss8/i6aefRkxMDNasWYPExERTPwa1CPNVwdPVCVV1TThRWI34ELZoEhER2SqZEEKY8oKtW7caPT9q1KhOFWRpGo0GarUalZWV7JZtMXnJHuw+XYo3/pKEuweESV0OERERXcKU7GJyi521BzcyXWKoF3afLsXR3EqAwY6IiMhmXdWAqu3bt+Nvf/sbhg4ditzcXADA//73P8PCxWRbDDtQcGsxIiIim2ZysPvuu+8wduxYqFQqHDx40DCDtbKyEq+++qrZCyTL0+8ZeyxPA63OpJ55IiIisiImB7tXXnkFH330EZYuXQpnZ2fD8WHDhuHgwYNmLY66RmQ3d7i5KHChUYvTxdVSl0NERERXyeRgl5mZiZEjR7Y5rlarUVFRYY6aqIsp5DLEB7csVMz17IiIiGyWycEuKCgIJ0+ebHN8x44diIqKMktR1PUM4+y4AwUREZHNMjnYzZgxA7Nnz8bevXshk8mQl5eHFStWYN68eXj00UctUSN1gQTD1mJssSMiIrJVJi938tRTT0Gn0+GGG25AbW0tRo4cCaVSiXnz5uGxxx6zRI3UBfQtdsfyNNDpBORy2WVeQURERNbG5AWK9RoaGnDy5ElUV1cjPj4eHh4e5q7NIrhAcfsatTokvPAzGpp02DLvOvTo5n75FxEREZHFmZJdTO6K/eKLL1BbWwsXFxfEx8fj2muvtZlQRx1zVsjRK8gTACdQEBER2SqTg93cuXMREBCAe++9Fxs2bDBpb1iybgmcQEFERGTTTA52+fn5WLVqFWQyGe6++24EBwdj5syZ2LVrlyXqoy6U2LJQ8VG22BEREdkkk4Odk5MTbrvtNqxYsQJFRUV49913cebMGVx//fW45pprLFEjdZHE0IszY69y6CURERFJyORZsZdyc3PD2LFjUV5ejrNnzyIjI8NcdZEEegZ6wkkuQ3ltI/Iq6xDqrZK6JCIiIjKByS12AFBbW4sVK1bglltuQWhoKBYuXIg77rgDR48eNXd91IVcnRWICWyZQMH17IiIiGyOyS12f/3rX7F+/Xq4ubnh7rvvxnPPPYchQ4ZYojaSQGKIFzLyNTiaW4mxCUFSl0NEREQmMDnYKRQKfP311xg7diwUCkWrc+np6UhMTDRbcdT1EkPV+ObAeaTncWYsERGRrTE52K1YsaLV86qqKnz55Zf45JNPcODAAS5/YuMunUBBREREtuWqxtgBwLZt2zBt2jQEBwfjrbfewujRo7Fnzx5z1kYS6BXsBZkMKKqqR5GmTupyiIiIyAQmtdgVFBRg+fLl+PTTT6HRaHD33Xejvr4ea9asQXx8vKVqpC7k5uKEa/w9cLKoGkfzNAjwcpW6JCIiIrpCV9xiN378eMTGxuLIkSNYuHAh8vLy8P7771uyNpJIYgi7Y4mIiGzRFbfYbdy4EY8//jgeffRRxMTEWLImklhiqBprUvO4ZywREZGNueIWux07dqCqqgr9+/fHoEGD8MEHH6CkpMSStZFEEkK4ZywREZEtuuJgN3jwYCxduhT5+fl4+OGHsWrVKoSEhECn02HTpk2oqqqyZJ3UheJbumJzKy6gvKZB4mqIiIjoSpk8K9bd3R0PPPAAduzYgbS0NPzzn//Ea6+9hoCAANx+++2WqJG6mFrljAg/NwDAUa5nR0REZDOuerkTAIiNjcUbb7yB8+fP48svvzRXTWQFEvXdsRxnR0REZDM6Fez0FAoFJk6ciB9++MEcb0dWIIELFRMREdkcswQ7sj/6Fjt2xRIREdkOBjtqV0LLBIrskhpU1TVKXA0RERFdCQY7apefhxIh6uZdJ46x1Y6IiMgmMNhRhxJC9RMoGOyIiIhsAYMddcgwzo4TKIiIiGwCgx11qHf3lpmxXPKEiIjIJjDYUYf0LXYni6pxoUErcTVERER0OU5SF0DWK8DLFf6eShRX1ePdX7MQ1c0dXipneLk6w0vl1PKnMzxdneCs4P8jEBERSY3BjoxK7q7GrxlFWLLttNHr3FwUULcT+rxcndoNg/rnapUzPJROcGIwJCIi6jQGOzLq6Vt6IdzXHRW1DdDUNUJzoanlz0Zo6ppQXd8EAKht0KK2QYv8yrqruo+H0slICPzT8Za/64Okh6sTFHKZOT82ERGRTZIJIYTURXQljUYDtVqNyspKeHl5SV2OzWvS6lBV19RO6GsbAjUXGlH5p3O1Zhq756l0MnQLdxQO1armMOjnoUQ3Dxf4eSjh7qKATMZQSERE1suU7MIWO+oUJ4UcPu4u8HF3uarXN+qDYbthsCUIthMQ9ddeaGwOhlX1TahqaT00hdJJjm4eSvh5uMDP3QW+7vrQ5wI/9+bj+vO+7i5QOimu6nMSERF1BQY7kpSzQg5f9+bQdDUamnSoquu4RfDPgbG8pgGlNQ0oq2lAbYMW9U065FZcQG7FhSu6n6erU3PQc3dpCXstQdC9uQXQEATdXeDt5sIuYiIi6lIMdmTTXJzkLYFKafJraxuaUFrdHPRKq+tRWt2AkprmP0ur61Fa04CSlr+X1TSgSSdQVdeEqromZJfUXPb95TLA1/1iy5+fPhC2CoEXz3sondgtTEREncJgRw7LzcUJbr5OCPN1u+y1QghoLjS1Cn4llwTC0pp6QwgsrWlARW0jdAIoqW4Ohyi8fD0uTnJ0uyT0GQLhpUHQ/WK3sKszu4WJiKg1BjuiKyCTyaB2c4bazRnX+F/++katDuW1DS0h8E/B79LnLUGxtkGLhiYd8irrkHeFM4vVKmeEeKsQ6u2KEG8VgtUqhHi7ItRbhRBvFQI8lVxGhojIwTDYEVmAs0KOAE9XBHi6XtH1Fxq0hpB3MQRe2iV88VxpdXO3cGXLmMKMfE2776mQyxDoqURIS9DTh8DmAKhCqLcKXip2/xIR2RMGOyIroHJRoLuLG7r7XFm3cOWFRhRq6pFXeQF5FfpHHXIrLiC/8gLyK+rQpBMXWwDPlrf7Xu4uiubWPn3Ln1p1SRB0RZDalTOBiYhsCIMdkY2RyWTwdmuedRsb5NnuNVqdQEl1PXJbQl9+S+jLq7jQEgbrUFbTgJoGLU4UVeNEUXWH9/NvafVr3drnagiAfu4ubPUjIrISDHZEdkghlyHQyxWBXq7oF+7T7jUXGrTIbwl5eS1Lvvz5eX2TDsVV9SiuqsfhnPbv5eIkR4jatVWXb+vnrnBz4X9qiIi6Av9rS+SgVC4KRPl7IMrfo93zQgiU1TQgv/KS1r4/dfkWVdWjoUmHM6W1OFNa2+G9fNyc27T2BV/y90BPV8i55h8RUacx2BFRu2QymWGNwMRQdbvXNDTpUKi5GPzaC4HV9U0or21EeW0jjnUw0cPVWY7Ibh6IDvDANf7uLX96ILKbO5d1ISIyAYMdEV01Fyc5wnzdjK4FqKlrNAS93JZu3vxLWv4KNHWoa9QhI1/TZoavTAaE+bi1CnvXBHgg2t/jqrexIyKyZzIhhJC6iK5kyka6RGR5TVodcsov4FRRNU4WVxv+PFlUjaq6jvf/9XV3aTfwhXqr2K1LRHbFlOzCYEdEVkkIgZLqBpwsqsap4ubHyaJqnC6uMbq3r9JJjij/1l261/h7IMqf3bpEZJsY7IxgsCOyfTX1zfv16sOe/s8zJbVo0OrafY1MBnT3USHa/5IWvpbg58tuXSKyYgx2RjDYEdmvJq0O58svtAp7+j81V9Cte43/xbAXHeCBEG8VFOzWJSKJMdgZwWBH5Hj03bqXdumeKq7BqaLqy3brRnZrO46P3bpE1JVMyS6cFUtEdk8mk8HfUwl/TyUGR/m1Olfb0ITTxc3duhcncNQgu6QG9U06HC+owvGCqj+9X3O3rn783qWtfOzWJSIpscWOiKgdWp1ATlltm1a+k0XVqLzQ2OHrQtSu6BPujeTu3kgO80bvUDXclfx/aCK6euyKNYLBjog6QwiB0pqGVq17+mVa2uvWlcuAnoGehqCXHKZGbKAnnBRyCaonIlvEYGcEgx0RWUp1fRPSzlfi8PkKpJ6rwOHzFcivrGtznauzHL1D1Yaw1yfMG919VJDJOFGDiNpisDOCwY6IulKhpg6HcyqQmtMc9I7kVKKqvu0MXT93l+YWve7NrXp9wrzh7cbxekTEYGcUgx0RSUmnEzhdUtMc9FrCXka+Bo3atv8p7uHnZgh7fcK9ER/sxdm4RA6Iwc4IBjsisjZ1jVocy9c0B72cChw+X4nskpo21znJZegV7NXSoueDPmFqRHXz4BZqRHaOwc4IBjsisgUVtQ04fL7SEPZScypQWtPQ5jpPpRN6d2/uutWP1wv0cpWgYiKyFAY7IxjsiMgWCSFwvvwCDp+/GPTScitR19h2C7UgL1dD0EsOUyOpuzc8uOQKkc1isDOCwY6I7EWTVoeswupWs3CzCqug+9N/1WUyICbAo9Us3NggTzhzyRUim8BgZwSDHRHZs5r6JqTnVhpm4R7OqWx3fT2lkxyJhiVXmrtyw33duOQKkRVisDOCwY6IHE1RVR0O51QaZuGm5lSgqq7tkis+bs6tZuEOivSFmwu7cImkxmBnBIMdETk6nU4gu7Tm4sSM85XIyNOgQdt6vJ6LQo6BkT4YGeOPUbH+iA30ZIsekQQY7IxgsCMiaqu+SYuM/CpD2NubXdamCzfQS2kIecOju3EBZaIuwmBnBIMdEdHlCdG8kPK2rGJszSrGntOlrWbgymVAcpg3RvX0x8ie/kju7g0F19MjsgibCXYpKSn4/vvvcfz4cahUKgwdOhSvv/46YmNjO3zN8uXLMX369FbHlEol6ura7sfYHgY7IiLT1TVqse9MGbZmNge9E0XVrc57uzljeHQ3jOzpj1E9/bmWHpEZmZJdJB0Vu3XrVsycORMDBw5EU1MTnn76adx00004duwY3N3dO3ydl5cXMjMzDc855oOIyLJcnRUYEeOPETH+eBZAXsUFQ2vejpMlqKhtxPoj+Vh/JB8AEBfkiVEtIa9/Dx8onbgVGlFXsKqu2OLiYgQEBGDr1q0YOXJku9csX74cc+bMQUVFxVXdgy12RETm1aTVITWnAluzirEtqxhHcitx6W8WNxcFhkT5YVRsc9CL8Ov4f9yJqC2babH7s8rKSgCAr6+v0euqq6sREREBnU6Hfv364dVXX0VCQkK719bX16O+vt7wXKPRmK9gIiKCk0KOAT18MaCHL/55UyzKahqw/URxS9ArQUl1PTYfL8Lm40UAgAg/t+axeTH+GHKNH9y5KwaR2VhNi51Op8Ptt9+OiooK7Nixo8Prdu/ejRMnTiApKQmVlZV46623sG3bNhw9ehTdu3dvc/2///1vvPjii22Os8WOiMjydDqBjAINtmYVY2tmMQ6cLUfTJVtjOCtkGNjD1zAJIy6IS6oQ/ZnNTJ641KOPPoqNGzdix44d7Qa0jjQ2NqJXr16YPHkyXn755Tbn22uxCwsLY7AjIpJAVV0jdp8qbQ56WcU4X97+kioje/pjRAyXVCECbDDYzZo1C2vXrsW2bdsQGRlp8usnTZoEJycnfPnll5e9lmPsiIisgxAC2SU1hrF5u9tZUiWpe/OSKqNiuaQKOS6bCXZCCDz22GNYvXo1tmzZgpiYGJPfQ6vVIiEhAbfccgveeeedy17PYEdEZJ30S6roZ9tmFbZeUkWtcsbwmG6G2bZcUoUchc0Eu3/84x9YuXIl1q5d22rtOrVaDZVKBQCYOnUqQkNDkZKSAgB46aWXMHjwYERHR6OiogJvvvkm1qxZgwMHDiA+Pv6y92SwIyKyDfmVlyypcqIEmj/tb6tfUmVkT38M4JIqZMdsZlbs4sWLAQDXXXddq+PLli3D/fffDwA4d+4c5HK54Vx5eTlmzJiBgoIC+Pj4oH///ti1a9cVhToiIrIdwWoV7hkYjnsGhqNJq8Ph8xXNCySfKMGR8xU4XlCF4wVV+HjbaaicFRh6jZ9hgeQe3bikCjkmqxhj15XYYkdEZPv0S6psyyrB1qxilFTXtzof7utm6LLlkipk62ymK1YKDHZERPZFv6RKc8grwv4zrZdUUTrJMSY+EBP7hGJUT3+4OMmNvBuR9WGwM4LBjojIvlXXN7UsqVKErVnFyCm7uKSKt5szbksKxh19Q9Ev3Idr5pFNYLAzgsGOiMhxCCFwNE+D1Ydy8cPhPBRXXeyyDfNVYWKfUEzoE4roAA8JqyQyjsHOCAY7IiLHpNUJ7DpVgtWHcvFTegFqG7SGc0nd1ZjYJxTjk0Pg76mUsEqithjsjGCwIyKi2oYmbDpWiDWHcrHtRAm0LWPy5DJgeIw/7ugbgpvigzjpgqwCg50RDHZERHSpkup6/HgkH6sP5SI1p8JwXOWswNiEQEzsG4rh0d3gpOCkC5IGg50RDHZERNSR7JIarDmUizWpuThbWms43s3DBbclheCOvqFI6q7mpAvqUgx2RjDYERHR5QghcCinAmsP5WLdkXyU1TQYzkV1c8fEvqGY2CcU4X5uElZJjoLBzggGOyIiMkWjVoftJ4qx+lAeNh0rQF2jznCuX7g37ugbiluTQuDr7iJhlWTPGOyMYLAjIqKrVV3fhJ/TC7AmNRc7T5ZAvw6yk1yG62L9MbFvKMb0CoSrM/etJfNhsDOCwY6IiMyhUFOHdYfzsPpQLo7maQzHPZROuDkxCHf0DcXgKD8o5ByPR53DYGcEgx0REZnbicIqrEnNxZpDecituLjTRaCXEhP6hGJCnxDEB3tx0gVdFQY7IxjsiIjIUnQ6gf1ny7H6UC42pOWj8kKj4VzPQA9M7Nu800Wot0rCKsnWMNgZwWBHRERdob5Jiy2ZxVhzKBebM4rQoL046WJQpC8m9g3FLYnBULs5S1gl2QIGOyMY7IiIqKtV1jZiY3rzIsh7s8sMx10UcoyOC8DEvqG4Ps4fSidOuqC2GOyMYLAjIiIp5VZcwA+peVh96DyyCqsNx71cnXBrUggm9gnBwB6+kHPSBbVgsDOCwY6IiKyBEAIZ+c2TLtam5qJQU284F+qtwoQ+zTtdxAR6SlglWQMGOyMY7IiIyNpodQJ7TpdizaFcbEwvQHV9k+FcQogXJvYJxe19QhDo5SphlSQVBjsjGOyIiMia1TVq8WtGIdYcysWWzGI0tayCLJMBI2P8cf+wHhgV48+uWgfCYGcEgx0REdmKspoG/JiWjzWHcnHgbLnheFQ3d9w/rAfu6tcd7konCSukrsBgZwSDHRER2aIzJTX4356z+GpfjqGr1tPVCX8dGIapQ3ogzNdN4grJUhjsjGCwIyIiW1Zd34Rv9+dg+a4zOFNaCwCQy4Cb4oMwfVgPXBvpyx0u7AyDnREMdkREZA90OoHfM4uwbOcZ7DhZYjieEOKF6cMiMT45mOvi2QkGOyMY7IiIyN5kFlRh+a5sfH8wF/VNzTtcdPNwwZRBEZgyOBwBnpxNa8sY7IxgsCMiIntVVtOAL/84h//tPosCTR2A5t0tbksOxgPDIpEYqpa4QroaDHZGMNgREZG9a9TqsDG9AMt2ZuPQuQrD8YE9fPDAsEjcGB8IJ4VcugLJJAx2RjDYERGRIzl0rhzLdp7BhrR8w5p4od4qTBsagXsGhEPt5ixxhXQ5DHZGMNgREZEjKqiswxd7zmLF3rMor20EAKicFbirfyjuHxqJ6AAPiSukjjDYGcFgR0REjqyuUYu1qblYtvMMjhdUGY6P6umPB4ZHYmRMNy6XYmUY7IxgsCMiIgKEENh9qhT/3XkGm48XQp8GrvF3x/RhkbizXyjcXLirhTVgsDOCwY6IiKi1s6U1WL7rDL7Zf96wq4WXqxMmXxuOqUN7INRbJXGFjo3BzggGOyIiovZV1TXi2wPnsXzXGZxt2dVCIZdhbEIgpg+LxIAIH3bTSoDBzggGOyIiIuO0OoHfjxdh2a5s7DxZajjeO1SN6cN64LakELg4cbmUrsJgZwSDHRER0ZU7XqDB8p1nsPrQxV0t/D2V+FvLrhbdPJQSV2j/GOyMYLAjIiIynX5Xi893n0Ghph5A864Wt/cJwfRhPZAQwl0tLIXBzggGOyIioqvXqNVhQ1o+lu08g9ScCsPxayN9DbtaKOQch2dODHZGMNgRERGZx8GWXS02XrKrRXcfFe4f2gOTBoRBreKuFubAYGcEgx0REZF5FVTW4X97zmDl3nOGXS3cXBSY1L87pg3tgSh/7mrRGQx2RjDYERERWUZdoxZrDuXivzuzkVVYbTh+faw/pg+LxAjuanFVGOyMYLAjIiKyLCEEdp0qxbKd2dh8vMiwq0VMgAfuH9YDd/btDpWLQtoibQiDnREMdkRERF3nTIl+V4sc1DRoAQDebs6YfG047h/aA4FerhJXaP0Y7IxgsCMiIup6mrpGfLP/PD7bdQbnypp3tXBWyDChTygeGhGJuCD+Tu4Ig50RDHZERETS0eoENmcU4pPt2fjjTJnh+Mie/pgxIhLDozkO788Y7IxgsCMiIrIOqTkVWLr9NDam5aNltRTEBXlixogojE/mtmV6DHZGMNgRERFZl5yyWny6Ixtf789Bbcs4vEAvJe4fGol7B4U7/Hp4DHZGMNgRERFZp8raRqz44yyW7zyDoqrmbcvcXRS4Z2A4pg/rgTBfN4krlAaDnREMdkRERNatoUmHHw7nYem208gsrAIAyGXALb2DMWNEFJLDvKUtsIsx2BnBYEdERGQbhBDYfqIES7efxvYTJYbj10b64u8jojA6LgByB9iXlsHOCAY7IiIi23MsT4NPdpzGusN5aNQ2R5cof3c8NDwKd/YLhauz/S54zGBnBIMdERGR7SqorMPyXWewYu9ZVNU1AQD83F1w35AI3Dc4An4eSokrND8GOyMY7IiIiGxfdX0Tvt6Xg093ZCO34gIAQOkkx139u+PB4ZG4xt9D4grNh8HOCAY7IiIi+9Gk1eGnowVYuu00Dp+vBADIZMANcYH4+8goDOzhY/MLHjPYGcFgR0REZH+EEPgjuwxLt2fj14xCw/Hk7mrMGBmFmxOC4KSwzQWPGeyMYLAjIiKyb6eKq/Hpjmx8d+A86pt0AIDuPio8MCwSdw8Mg4fSSeIKTcNgZwSDHRERkWMora7H//acxee7z6KspgEA4OXqhHsHReD+oT0QpHaVuMIrw2BnBIMdERGRY6lr1OK7g+fx6fZsnC6pAQA4K2QYnxyCGSOi0CvYuvMAg50RDHZERESOSacT2Hy8CEu3n8Yf2WWG4yNiumHGiCiMiOlmlRMtGOyMYLAjIiKi1JwKLN1+GhvT8qFrSUJxQZ54aEQUbk8OgYuT9Uy0YLAzgsGOiIiI9HLKavHfndn4al8Oahu0AIBALyWmDe2BKddGQO3mLHGFDHZGMdgRERHRn1XWNmLlH+ewfFc2CjX1AAA3FwXuHhCGB4dHIszXTbLaGOyMYLAjIiKijjQ06bDucB6Wbj+N4wVVAAC5DBiXGIwZI6PQJ8y7y2tisDOCwY6IiIguRwiBHSdLsGTbaWw/UWI4fm0PXzw0IhJjegVCLu+aiRYMdkYw2BEREZEpMvI1+GR7Nn44nItGbXNsiurmjgeGR+Iv/bvD1Vlh0fsz2BnBYEdERERXo1BTh+W7zmDFnrPQ1DUBAHzdXfDg8EjMvD7aYvc1JbtYz1xeIiIiIisW6OWKf90ch93zb8AL4+PR3UeFspoGZLcsemwNbGuzNCIiIiKJuSudMH1YJO4bHIGfjxYiNshT6pIMGOyIiIiIroKTQo5bk4KlLqMVdsUSERER2QkGOyIiIiI7IWmwS0lJwcCBA+Hp6YmAgABMnDgRmZmZl33dN998g7i4OLi6uqJ3797YsGFDF1RLREREZN0kDXZbt27FzJkzsWfPHmzatAmNjY246aabUFPT8eySXbt2YfLkyXjwwQdx6NAhTJw4ERMnTkR6enoXVk5ERERkfaxqHbvi4mIEBARg69atGDlyZLvX3HPPPaipqcH69esNxwYPHow+ffrgo48+uuw9uI4dERER2RKbXceusrISAODr69vhNbt378aYMWNaHRs7dix2797d7vX19fXQaDStHkRERET2yGqCnU6nw5w5czBs2DAkJiZ2eF1BQQECAwNbHQsMDERBQUG716ekpECtVhseYWFhZq2biIiIyFpYTbCbOXMm0tPTsWrVKrO+7/z581FZWWl45OTkmPX9iYiIiKyFVSxQPGvWLKxfvx7btm1D9+7djV4bFBSEwsLCVscKCwsRFBTU7vVKpRJKpdJstRIRERFZK0lb7IQQmDVrFlavXo3ffvsNkZGRl33NkCFDsHnz5lbHNm3ahCFDhliqTCIiIiKbIGmL3cyZM7Fy5UqsXbsWnp6ehnFyarUaKpUKADB16lSEhoYiJSUFADB79myMGjUKb7/9Nm699VasWrUK+/fvx5IlSyT7HERERETWQNIWu8WLF6OyshLXXXcdgoODDY+vvvrKcM25c+eQn59veD506FCsXLkSS5YsQXJyMr799lusWbPG6IQLIiIiIkdgVevYdQWuY0dERES2xGbXsSMiIiKiq8dgR0RERGQnrGK5k66k73nmDhRERERkC/SZ5UpGzzlcsKuqqgIA7kBBRERENqWqqgpqtdroNQ43eUKn0yEvLw+enp6QyWQWu49Go0FYWBhycnI4ScNK8DuxTvxerA+/E+vE78U6dcX3IoRAVVUVQkJCIJcbH0XncC12crn8srtbmJOXlxf/BbQy/E6sE78X68PvxDrxe7FOlv5eLtdSp8fJE0RERER2gsGOiIiIyE4w2FmIUqnECy+8AKVSKXUp1ILfiXXi92J9+J1YJ34v1snavheHmzxBREREZK/YYkdERERkJxjsiIiIiOwEgx0RERGRnWCws4APP/wQPXr0gKurKwYNGoQ//vhD6pIcWkpKCgYOHAhPT08EBARg4sSJyMzMlLosusRrr70GmUyGOXPmSF2Kw8vNzcXf/vY3+Pn5QaVSoXfv3ti/f7/UZTk0rVaL5557DpGRkVCpVLjmmmvw8ssvX9H2UmQe27Ztw/jx4xESEgKZTIY1a9a0Oi+EwPPPP4/g4GCoVCqMGTMGJ06ckKRWBjsz++qrr/DEE0/ghRdewMGDB5GcnIyxY8eiqKhI6tIc1tatWzFz5kzs2bMHmzZtQmNjI2666SbU1NRIXRoB2LdvHz7++GMkJSVJXYrDKy8vx7Bhw+Ds7IyNGzfi2LFjePvtt+Hj4yN1aQ7t9ddfx+LFi/HBBx8gIyMDr7/+Ot544w28//77UpfmMGpqapCcnIwPP/yw3fNvvPEG3nvvPXz00UfYu3cv3N3dMXbsWNTV1XVxpZwVa3aDBg3CwIED8cEHHwBo3sIsLCwMjz32GJ566imJqyMAKC4uRkBAALZu3YqRI0dKXY5Dq66uRr9+/fCf//wHr7zyCvr06YOFCxdKXZbDeuqpp7Bz505s375d6lLoErfddhsCAwPx6aefGo7dddddUKlU+OKLLySszDHJZDKsXr0aEydOBNDcWhcSEoJ//vOfmDdvHgCgsrISgYGBWL58Of761792aX1ssTOjhoYGHDhwAGPGjDEck8vlGDNmDHbv3i1hZXSpyspKAICvr6/EldDMmTNx6623tvp3hqTzww8/YMCAAZg0aRICAgLQt29fLF26VOqyHN7QoUOxefNmZGVlAQAOHz6MHTt2YNy4cRJXRgCQnZ2NgoKCVv8dU6vVGDRokCS/+x1ur1hLKikpgVarRWBgYKvjgYGBOH78uERV0aV0Oh3mzJmDYcOGITExUepyHNqqVatw8OBB7Nu3T+pSqMXp06exePFiPPHEE3j66aexb98+PP7443BxccG0adOkLs9hPfXUU9BoNIiLi4NCoYBWq8WCBQswZcoUqUsjAAUFBQDQ7u9+/bmuxGBHDmXmzJlIT0/Hjh07pC7FoeXk5GD27NnYtGkTXF1dpS6HWuh0OgwYMACvvvoqAKBv375IT0/HRx99xGAnoa+//horVqzAypUrkZCQgNTUVMyZMwchISH8XqgNdsWaUbdu3aBQKFBYWNjqeGFhIYKCgiSqivRmzZqF9evX4/fff0f37t2lLsehHThwAEVFRejXrx+cnJzg5OSErVu34r333oOTkxO0Wq3UJTqk4OBgxMfHtzrWq1cvnDt3TqKKCACefPJJPPXUU/jrX/+K3r1747777sPcuXORkpIidWkEGH6/W8vvfgY7M3JxcUH//v2xefNmwzGdTofNmzdjyJAhElbm2IQQmDVrFlavXo3ffvsNkZGRUpfk8G644QakpaUhNTXV8BgwYACmTJmC1NRUKBQKqUt0SMOGDWuzFFBWVhYiIiIkqogAoLa2FnJ561/XCoUCOp1OooroUpGRkQgKCmr1u1+j0WDv3r2S/O5nV6yZPfHEE5g2bRoGDBiAa6+9FgsXLkRNTQ2mT58udWkOa+bMmVi5ciXWrl0LT09Pw5gHtVoNlUolcXWOydPTs80YR3d3d/j5+XHso4Tmzp2LoUOH4tVXX8Xdd9+NP/74A0uWLMGSJUukLs2hjR8/HgsWLEB4eDgSEhJw6NAhvPPOO3jggQekLs1hVFdX4+TJk4bn2dnZSE1Nha+vL8LDwzFnzhy88soriImJQWRkJJ577jmEhIQYZs52KUFm9/7774vw8HDh4uIirr32WrFnzx6pS3JoANp9LFu2TOrS6BKjRo0Ss2fPlroMh7du3TqRmJgolEqliIuLE0uWLJG6JIen0WjE7NmzRXh4uHB1dRVRUVHimWeeEfX19VKX5jB+//33dn+PTJs2TQghhE6nE88995wIDAwUSqVS3HDDDSIzM1OSWrmOHREREZGd4Bg7IiIiIjvBYEdERERkJxjsiIiIiOwEgx0RERGRnWCwIyIiIrITDHZEREREdoLBjoiIiMhOMNgRERER2QkGOyJCjx49sHDhQqnLMBtr/jz333+/NNsMGfHvf/8bgYGBkMlkWLNmTZvzW7ZsgUwmQ0VFhUXrWL58Oby9vS16DyJ7x2BHZMdycnLwwAMPICQkBC4uLoiIiMDs2bNRWloqdWlkJTIyMvDiiy/i448/Rn5+PsaNGyd1SUTUCQx2RHbq9OnTGDBgAE6cOIEvv/wSJ0+exEcffYTNmzdjyJAhKCsrk6w2rVYLnU4n2f3tjRACTU1NV/XaU6dOAQAmTJiAoKAgKJVKc5ZGRF2MwY7ITs2cORMuLi745ZdfMGrUKISHh2PcuHH49ddfkZubi2eeeabV9VVVVZg8eTLc3d0RGhqKDz/80HBOCIF///vfCA8Ph1KpREhICB5//HHD+fr6esybNw+hoaFwd3fHoEGDsGXLFsN5fRfbDz/8gPj4eCiVSnzyySdwdXVt0703e/ZsjB492vB8x44dGDFiBFQqFcLCwvD444+jpqbGcL6oqAjjx4+HSqVCZGQkVqxYcdmfjb479K233kJwcDD8/Pwwc+ZMNDY2Gq5pr1vS29sby5cvBwCcOXMGMpkMX3/9taG+gQMHIisrC/v27cOAAQPg4eGBcePGobi4uE0NL774Ivz9/eHl5YVHHnkEDQ0NhnM6nQ4pKSmIjIyESqVCcnIyvv32W8N5fdfoxo0b0b9/fyiVSuzYsaPdz5qWlobRo0dDpVLBz88Pf//731FdXQ2guQt2/PjxAAC5XA6ZTGb057Zz504kJSXB1dUVgwcPRnp6eqvz3333HRISEqBUKtGjRw+8/fbbrc6Xl5dj6tSp8PHxgZubG8aNG4cTJ050eL/i4mIMGDAAd9xxB+rr61FeXo4pU6bA398fKpUKMTExWLZsmdGaiRyOICK7U1paKmQymXj11VfbPT9jxgzh4+MjdDqdEEKIiIgI4enpKVJSUkRmZqZ47733hEKhEL/88osQQohvvvlGeHl5iQ0bNoizZ8+KvXv3iiVLlhje76GHHhJDhw4V27ZtEydPnhRvvvmmUCqVIisrSwghxLJly4Szs7MYOnSo2Llzpzh+/Liorq4WgYGB4pNPPjG8T1NTU6tjJ0+eFO7u7uLdd98VWVlZYufOnaJv377i/vvvN7xm3LhxIjk5WezevVvs379fDB06VKhUKvHuu+92+POZNm2a8PLyEo888ojIyMgQ69atE25ubq0+EwCxevXqVq9Tq9Vi2bJlQgghsrOzBQARFxcnfvrpJ3Hs2DExePBg0b9/f3HdddeJHTt2iIMHD4ro6GjxyCOPtLq3h4eHuOeee0R6erpYv3698Pf3F08//bThmldeecXwvqdOnRLLli0TSqVSbNmyRQghxO+//y4AiKSkJPHLL7+IkydPitLS0jafs7q6WgQHB4s777xTpKWlic2bN4vIyEgxbdo0IYQQVVVVYtmyZQKAyM/PF/n5+e3+vPT369Wrl/jll1/EkSNHxG233SZ69OghGhoahBBC7N+/X8jlcvHSSy+JzMxMsWzZMqFSqQw/LyGEuP3220WvXr3Etm3bRGpqqhg7dqyIjo42vMeyZcuEWq0WQghx7tw5ERsbK6ZNmyaampqEEELMnDlT9OnTR+zbt09kZ2eLTZs2iR9++KHD75nIETHYEdmhPXv2tBtM9N555x0BQBQWFgohmoPdzTff3Oqae+65R4wbN04IIcTbb78tevbsafgFfKmzZ88KhUIhcnNzWx2/4YYbxPz584UQwhAeUlNTW10ze/ZsMXr0aMPzn3/+WSiVSlFeXi6EEOLBBx8Uf//731u9Zvv27UIul4sLFy6IzMxMAUD88ccfhvMZGRkCwGWDXUREhCEwCCHEpEmTxD333GN4fqXB7tJg+uWXXwoAYvPmzYZjKSkpIjY2ttW9fX19RU1NjeHY4sWLhYeHh9BqtaKurk64ubmJXbt2tbr3gw8+KCZPniyEuBi01qxZ0+FnFEKIJUuWCB8fH1FdXW049uOPPwq5XC4KCgqEEEKsXr1aXO7/8fX3W7VqleFYaWmpUKlU4quvvhJCCHHvvfeKG2+8sdXrnnzySREfHy+EECIrK0sAEDt37jScLykpESqVSnz99ddCiIvB7vjx4yIsLEw8/vjjhv/5EEKI8ePHi+nTpxutlcjRsSuWyI4JIa742iFDhrR5npGRAQCYNGkSLly4gKioKMyYMQOrV682jOlKS0uDVqtFz5494eHhYXhs3brVMH4LAFxcXJCUlNTqHlOmTMGWLVuQl5cHAFixYgVuvfVWw8zIw4cPY/ny5a3ed+zYsdDpdMjOzkZGRgacnJzQv39/w3vGxcVd0czKhIQEKBQKw/Pg4GAUFRVd8c9L79LPFBgYCADo3bt3q2N/ft/k5GS4ubkZng8ZMgTV1dXIycnByZMnUVtbixtvvLHV5/78889b/TwBYMCAAUZry8jIQHJyMtzd3Q3Hhg0bBp1Oh8zMTJM/66X/jPj6+iI2Ntbwz0hGRgaGDRvW6vphw4bhxIkT0Gq1hu9q0KBBhvN+fn6t3gMALly4gBEjRuDOO+/EokWLWnUPP/roo1i1ahX69OmD//u//8OuXbtM/gxE9s5J6gKIyPyio6Mhk8mQkZGBO+64o835jIwM+Pj4wN/f/4reLywsDJmZmfj111+xadMm/OMf/8Cbb76JrVu3orq6GgqFAgcOHGgVlADAw8PD8HeVStVmDNfAgQNxzTXXYNWqVXj00UexevVqwxg2AKiursbDDz/cajyfXnh4OLKysq6o/vY4Ozu3ei6TyVpN6JDJZG2C8aVj8Np7H/3n+/MxUyaK6Me//fjjjwgNDW117s8TGy4NbPZCqVRizJgxWL9+PZ588slWP4Nx48bh7Nmz2LBhAzZt2oQbbrgBM2fOxFtvvSVhxUTWhS12RHbIz88PN954I/7zn//gwoULrc4VFBRgxYoVuOeee1oFrT179rS6bs+ePejVq5fhuUqlwvjx4/Hee+9hy5Yt2L17N9LS0tC3b19otVoUFRUhOjq61SMoKOiytU6ZMgUrVqzAunXrIJfLceuttxrO9evXD8eOHWvzvtHR0XBxcUFcXByamppw4MABw2syMzPNst6av78/8vPzDc9PnDiB2traTr8v0NwSeen3smfPHnh4eCAsLMwwueTcuXNtPnNYWJhJ9+nVqxcOHz7carLJzp07IZfLERsba3Ldl/4zUl5ejqysLMM/I7169cLOnTtbXb9z50707NkTCoUCvXr1QlNTE/bu3Ws4X1paiszMTMTHxxuOyeVy/O9//0P//v1x/fXXG1pz9fz9/TFt2jR88cUXWLhwIZYsWWLy5yCyZwx2RHbqgw8+QH19PcaOHYtt27YhJycHP/30E2688UaEhoZiwYIFra7fuXMn3njjDWRlZeHDDz/EN998g9mzZwNontX66aefIj09HadPn8YXX3wBlUqFiIgI9OzZE1OmTMHUqVPx/fffIzs7G3/88QdSUlLw448/XrbOKVOm4ODBg1iwYAH+8pe/tGqV+te//oVdu3Zh1qxZSE1NxYkTJ7B27VrMmjULABAbG4ubb74ZDz/8MPbu3YsDBw7goYcegkql6vTPb/To0fjggw9w6NAh7N+/H4888kibVr6r1dDQgAcffBDHjh3Dhg0b8MILL2DWrFmQy+Xw9PTEvHnzMHfuXHz22Wc4deoUDh48iPfffx+fffaZSfeZMmUKXF1dMW3aNKSnp+P333/HY489hvvuu8/QbWyKl156CZs3b0Z6ejruv/9+dOvWzbDY8j//+U9s3rwZL7/8MrKysvDZZ5/hgw8+wLx58wAAMTExmDBhAmbMmIEdO3bg8OHD+Nvf/obQ0FBMmDCh1X0UCgVWrFiB5ORkjB49GgUFBQCA559/HmvXrsXJkydx9OhRrF+/vtX/fBAROCuWyJ6dOXNGTJs2TQQGBgpnZ2cRFhYmHnvsMVFSUtLquoiICPHiiy+KSZMmCTc3NxEUFCQWLVpkOL969WoxaNAg4eXlJdzd3cXgwYPFr7/+ajjf0NAgnn/+edGjRw/h7OwsgoODxR133CGOHDkihGg927E91157rQAgfvvttzbn/vjjD3HjjTcKDw8P4e7uLpKSksSCBQsM5/Pz88Wtt94qlEqlCA8PF59//rmIiIi47OSJCRMmtDo2e/ZsMWrUKMPz3NxccdNNNwl3d3cRExMjNmzY0O7kiUOHDhleo59koJ/80d5n19/7+eefF35+fsLDw0PMmDFD1NXVGa7R6XRi4cKFIjY2Vjg7Owt/f38xduxYsXXr1g7v05EjR46I66+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" ] @@ -668,14 +658,21 @@ } ], "source": [ - "df['mean lambda'].plot()\n", + "df['mean λ'].plot()\n", "decorate(xlabel='Observed number of books',\n", " ylabel='Average sales rate')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's the implied number of books sold per cycle." + ] + }, { "cell_type": "code", - "execution_count": 106, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -684,7 +681,7 @@ "5" ] }, - "execution_count": 106, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, @@ -707,22 +704,33 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "This result is a little more interesting.\n", + "Seeing `0` books is still good, but the optimal value is around `5`.\n", + "\n", + "Now, we should not take this value too seriously, as it is based on a very small amount of data and a lot of assumptions -- both in the model and in the priors.\n", + "But it is interesting that the optimal point is neither many nor none." + ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Thanks to Aubrey Clayton for [this tweet], which gave me the idea for this article.\n", + "Thanks to Aubrey Clayton for [this tweet](https://twitter.com/aubreyclayton/status/1735467931490734251), which gave me the idea for this article.\n", "\n", "Copyright 2023 Allen B. Downey\n", "\n", "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": {