From 80326e3cc84b572b78c2dec8fce6197b654ef436 Mon Sep 17 00:00:00 2001 From: matt-graham Date: Tue, 10 Dec 2024 16:31:16 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20UCL/rmcm?= =?UTF-8?q?c@6d0808955a549a05695f30de02cb9ea1034e737e=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- articles/barker-proposal.html | 66 +++++----- .../figure-html/unnamed-chunk-19-1.png | Bin 36420 -> 34257 bytes .../figure-html/unnamed-chunk-20-1.png | Bin 44305 -> 34057 bytes .../figure-html/unnamed-chunk-22-1.png | Bin 105652 -> 81393 bytes .../figure-html/unnamed-chunk-23-1.png | Bin 90373 -> 71954 bytes .../figure-html/unnamed-chunk-25-1.png | Bin 138383 -> 123400 bytes .../figure-html/unnamed-chunk-26-1.png | Bin 129929 -> 63302 bytes index.html | 10 +- pkgdown.yml | 2 +- reference/covariance_shape_adapter.html | 24 +++- reference/dual_averaging_scale_adapter.html | 11 +- reference/index.html | 14 +- reference/sample_chain.html | 9 +- reference/scale_adapter.html | 33 ++++- reference/shape_adapter.html | 112 ++++++++++++++++ ...tochastic_approximation_scale_adapter.html | 123 ++++++++++++++++++ reference/variance_shape_adapter.html | 22 +++- search.json | 2 +- sitemap.xml | 4 +- 19 files changed, 371 insertions(+), 61 deletions(-) create mode 100644 reference/shape_adapter.html create mode 100644 reference/stochastic_approximation_scale_adapter.html diff --git a/articles/barker-proposal.html b/articles/barker-proposal.html index b3346ed..e3699d5 100644 --- a/articles/barker-proposal.html +++ b/articles/barker-proposal.html @@ -150,11 +150,11 @@

Setting up adaptation of tun distribution.

 adapters <- list(
-  simple_scale_adapter(
+  scale_adapter(
     initial_scale = dimension^(-1 / 6),
     target_accept_prob = 0.574
   ),
-  variance_shape_adapter()
+  shape_adapter("variance")
 )

Here we set the initial scale to π’ͺ(dimensionβˆ’16)\mathcal{O}(\text{dimension}^{-\frac{1}{6}}) @@ -237,7 +237,7 @@

Sampling a chain
 mean_accept_prob <- mean(barker_results$statistics[, "accept_prob"])
 cat(sprintf("Average acceptance probability is %.2f", mean_accept_prob))
-#> Average acceptance probability is 0.54
+#> Average acceptance probability is 0.61

This is close to the target acceptance rate of 0.574 indicating the scale adaptation worked as expected.

We can also inspect the shape parameter of the proposal to check the @@ -253,7 +253,7 @@

Sampling a chain sprintf("True target scales: %s", toString(scales[1:clipped_dimension])), sep = "\n" ) -#> Adapter scale est.: 0.00922080029766185, 0.995077611400515, 0.975164196791254, 0.938742004951002, 0.959131700160353 +#> Adapter scale est.: 0.0922872181053991, 1.8767157508315, 4.06222970407357, 2.47921441385872, 2.35568814672492 #> True target scales: 0.01, 1, 1, 1, 1

Again adaptation appears to have been successful with the adapted shape close to the true target scales.

@@ -289,17 +289,17 @@

Summarizing results using < #> # A tibble: 11 Γ— 10 #> variable mean median sd mad q5 q95 rhat ess_bulk #> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> -#> 1 position1 1.63e-4 3.51e-4 0.0102 0.0104 -0.0166 0.0169 1.00 1197. -#> 2 position2 -3.07e-2 -9.21e-3 1.01 0.990 -1.72 1.62 1.00 1405. -#> 3 position3 2.22e-2 1.54e-2 1.01 1.01 -1.61 1.64 1.00 1191. -#> 4 position4 2.13e-2 1.25e-2 1.02 1.04 -1.68 1.68 1.00 1250. -#> 5 position5 1.78e-2 2.02e-2 0.993 1.01 -1.63 1.62 1.00 1370. -#> 6 position6 -2.23e-2 -3.13e-2 1.01 0.996 -1.67 1.65 1.00 1157. -#> 7 position7 2.99e-2 4.19e-3 1.00 1.01 -1.59 1.69 1.00 1456. -#> 8 position8 2.38e-2 -4.45e-3 1.02 1.01 -1.63 1.75 1.00 1503. -#> 9 position9 -3.08e-2 -3.23e-2 1.01 1.02 -1.67 1.62 1.00 1478. -#> 10 position10 2.73e-2 1.43e-2 1.01 1.02 -1.61 1.67 1.00 1482. -#> 11 target_log_de… -5.11e+0 -4.71e+0 2.34 2.17 -9.43 -2.00 1.00 1188. +#> 1 position1 -1.46e-5 -8.54e-5 0.0101 0.0102 -0.0167 0.0165 1.00 4268. +#> 2 position2 -4.64e-2 -2.41e-2 0.952 0.937 -1.64 1.52 1.01 353. +#> 3 position3 4.44e-2 2.18e-2 0.992 0.988 -1.57 1.69 1.00 1468. +#> 4 position4 -1.65e-2 -2.96e-2 1.02 1.03 -1.69 1.68 1.00 553. +#> 5 position5 7.83e-3 -1.05e-2 1.03 1.03 -1.64 1.71 1.00 425. +#> 6 position6 -9.40e-2 -9.23e-2 0.996 0.956 -1.74 1.55 1.02 106. +#> 7 position7 -1.71e-2 -3.11e-2 1.02 1.00 -1.66 1.67 1.02 110. +#> 8 position8 -1.17e-2 -1.80e-2 1.02 1.03 -1.63 1.70 1.01 740. +#> 9 position9 -1.58e-1 -1.89e-1 0.945 0.868 -1.69 1.47 1.01 188. +#> 10 position10 3.43e-4 -1.10e-2 0.986 0.952 -1.63 1.67 1.00 316. +#> 11 target_log_de… -4.98e+0 -4.62e+0 2.29 2.11 -9.41 -1.95 1.01 427. #> # β„Ή 1 more variable: ess_tail <dbl>

We can also first explicit convert the traces matrix to a posterior draws object using the @@ -311,17 +311,17 @@

Summarizing results using < #> # A tibble: 11 Γ— 10 #> variable mean median sd mad q5 q95 rhat ess_bulk #> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> -#> 1 position1 1.63e-4 3.51e-4 0.0102 0.0104 -0.0166 0.0169 1.00 1197. -#> 2 position2 -3.07e-2 -9.21e-3 1.01 0.990 -1.72 1.62 1.00 1405. -#> 3 position3 2.22e-2 1.54e-2 1.01 1.01 -1.61 1.64 1.00 1191. -#> 4 position4 2.13e-2 1.25e-2 1.02 1.04 -1.68 1.68 1.00 1250. -#> 5 position5 1.78e-2 2.02e-2 0.993 1.01 -1.63 1.62 1.00 1370. -#> 6 position6 -2.23e-2 -3.13e-2 1.01 0.996 -1.67 1.65 1.00 1157. -#> 7 position7 2.99e-2 4.19e-3 1.00 1.01 -1.59 1.69 1.00 1456. -#> 8 position8 2.38e-2 -4.45e-3 1.02 1.01 -1.63 1.75 1.00 1503. -#> 9 position9 -3.08e-2 -3.23e-2 1.01 1.02 -1.67 1.62 1.00 1478. -#> 10 position10 2.73e-2 1.43e-2 1.01 1.02 -1.61 1.67 1.00 1482. -#> 11 target_log_de… -5.11e+0 -4.71e+0 2.34 2.17 -9.43 -2.00 1.00 1188. +#> 1 position1 -1.46e-5 -8.54e-5 0.0101 0.0102 -0.0167 0.0165 1.00 4268. +#> 2 position2 -4.64e-2 -2.41e-2 0.952 0.937 -1.64 1.52 1.01 353. +#> 3 position3 4.44e-2 2.18e-2 0.992 0.988 -1.57 1.69 1.00 1468. +#> 4 position4 -1.65e-2 -2.96e-2 1.02 1.03 -1.69 1.68 1.00 553. +#> 5 position5 7.83e-3 -1.05e-2 1.03 1.03 -1.64 1.71 1.00 425. +#> 6 position6 -9.40e-2 -9.23e-2 0.996 0.956 -1.74 1.55 1.02 106. +#> 7 position7 -1.71e-2 -3.11e-2 1.02 1.00 -1.66 1.67 1.02 110. +#> 8 position8 -1.17e-2 -1.80e-2 1.02 1.03 -1.63 1.70 1.01 740. +#> 9 position9 -1.58e-1 -1.89e-1 0.945 0.868 -1.69 1.47 1.01 188. +#> 10 position10 3.43e-4 -1.10e-2 0.986 0.952 -1.63 1.67 1.00 316. +#> 11 target_log_de… -4.98e+0 -4.62e+0 2.29 2.11 -9.41 -1.95 1.01 427. #> # β„Ή 1 more variable: ess_tail <dbl>

The draws object can also be manipulated and subsetted with various functions provided by posterior. For example the extract_variable @@ -337,7 +337,7 @@

Summarizing results using < ess_mean(extract_variable(draws, "target_log_density")) ) ) -#> Effective sample size of mean(target_log_density) is 1206 +#> Effective sample size of mean(target_log_density) is 408

Sampling using a Langevin proposal @@ -346,9 +346,9 @@

Sampling using a Langevin proposallangevin_proposal in place of baker_proposal.

Here we create a new set of adapters using the default arguments to -simple_scale_adapter which will set the target acceptance -rate to the Langevin proposal optimal value of 0.574 following the -results in Roberts and Rosenthal (2001).

+scale_adapter which will set the target acceptance rate to +the Langevin proposal optimal value of 0.574 following the results in +Roberts and Rosenthal (2001).

 mala_results <- sample_chain(
   target_distribution = target_distribution,
@@ -356,7 +356,7 @@ 

Sampling using a Langevin proposal initial_state = initial_state, n_warm_up_iteration = n_warm_up_iteration, n_main_iteration = n_main_iteration, - adapters = list(simple_scale_adapter(), variance_shape_adapter()), + adapters = list(scale_adapter(), shape_adapter("variance")), trace_warm_up = TRUE )

We can again check the average acceptance rate of the main chain @@ -368,7 +368,7 @@

Sampling using a Langevin proposal mean(mala_results$statistics[, "accept_prob"]) ) ) -#> Average acceptance probability is 0.61

+#> Average acceptance probability is 0.64

and use the ess_mean function from the posterior package to compute the effective sample size of the mean of the target_log_density variable

@@ -383,7 +383,7 @@

Sampling using a Langevin proposal ) ) ) -#> Effective sample size of mean(target_log_density) is 2863 +#> Effective sample size of mean(target_log_density) is 1

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    Example sprintf("Adapter scale est.: %s", toString(adapted_shape)), sep = "\n" ) -#> Average acceptance probability is 0.59 +#> Average acceptance probability is 0.58 #> True target scales: 1.50538046096953, 1.37774732725824, 0.277038897322645 -#> Adapter scale est.: 1.43398887990819, 1.22112523246304, 0.240554869853302

    Example target_distribution = target_distribution, proposal = proposal, initial_state = rnorm(dimension), - n_warm_up_iteration = 1000, - n_main_iteration = 1000, - adapters = list(simple_scale_adapter(), variance_shape_adapter()) + n_warm_up_iteration = 10000, + n_main_iteration = 10000, + adapters = list(scale_adapter(), shape_adapter("variance")) ) mean_accept_prob <- mean(results$statistics[, "accept_prob"]) adapted_shape <- proposal$parameters()$shape @@ -96,9 +96,9 @@

+#> Adapter scale est.: 1.5328097767097, 1.42342707172926, 0.280359693392091