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lectures/bayes_nonconj.md

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@@ -141,7 +141,8 @@ def simulate_draw(theta, n):
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def analytical_beta_posterior(data, alpha0, beta0):
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"""
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Computes analytically the posterior distribution with beta prior parametrized by (alpha, beta)
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Computes analytically the posterior distribution
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with beta prior parametrized by (alpha, beta)
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given # num observations
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Parameters
@@ -226,7 +227,8 @@ We will use the following priors:
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```{code-cell} ipython3
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def TruncatedLogNormal_trans(loc, scale):
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"""
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Obtains the truncated log normal distribution using numpyro's TruncatedNormal and ExpTransform
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Obtains the truncated log normal distribution
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using numpyro's TruncatedNormal and ExpTransform
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"""
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base_dist = ndist.TruncatedNormal(
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low=-jnp.inf, high=jnp.log(1), loc=loc, scale=scale
@@ -443,7 +445,8 @@ def show_prior(
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def set_model(model: BayesianInference, data):
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"""
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Define the probabilistic model by specifying prior, conditional likelihood, and data conditioning
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Define the probabilistic model by specifying prior,
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conditional likelihood, and data conditioning
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"""
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theta = sample_prior(model)
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output = numpyro.sample(
@@ -455,7 +458,8 @@ def MCMC_sampling(
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model: BayesianInference, data, num_samples, num_warmup=1000
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):
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"""
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Computes numerically the posterior distribution with beta prior parametrized by (alpha0, beta0)
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Computes numerically the posterior distribution
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with beta prior parametrized by (alpha0, beta0)
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given data using MCMC
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"""
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data = jnp.array(data, dtype=float)
@@ -476,7 +480,8 @@ def MCMC_sampling(
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# this is required by svi.run()
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def beta_guide(model: BayesianInference, data):
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"""
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Defines the candidate parametrized variational distribution that we train to approximate posterior with numpyro
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Defines the candidate parametrized variational distribution
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that we train to approximate posterior with numpyro
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Here we use parameterized beta
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"""
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alpha_q = numpyro.param("alpha_q", 10, constraint=nconstraints.positive)
@@ -488,7 +493,8 @@ def beta_guide(model: BayesianInference, data):
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# similar with beta_guide()
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def truncnormal_guide(model: BayesianInference, data):
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"""
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Defines the candidate parametrized variational distribution that we train to approximate posterior with numpyro
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Defines the candidate parametrized variational distribution
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that we train to approximate posterior with numpyro
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Here we use truncated normal on [0,1]
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"""
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loc = numpyro.param("loc", 0.5, constraint=nconstraints.interval(0.0, 1.0))
@@ -638,10 +644,8 @@ class BayesianInferencePlot:
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a list of sample size
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BayesianInferenceClass : class.
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a class initiated using BayesianInference()
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"""
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"""Enter Parameters for data generation and plotting"""
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theta: float
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N_list: list
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BayesianInferenceClass: BayesianInference

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