+ Autocorrelation plots measure how predictive the last several samples are + of the current sample. Autocorrelation may vary between -1.0 + (deterministically anticorrelated) and 1.0 (deterministically correlated). + We compute autocorrelation approximately, so it may sometimes exceed these + bounds. In an ideal world, the current sample is chosen independently of + the previous samples: an autocorrelation of zero. This is not possible in + practice, due to stochastic noise and the mechanics of how inference + works. +
+ """ + return Div(text=text, disable_math=False, min_width=800) + + +def create_figure_grid(figures: typing.Figures) -> Row: + """Layout the given figures in a grid, and make one toolbar. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + Row + A Bokeh layout object. + """ + toolbar = create_toolbar(figures) + figure_values = list(figures.values()) + figure_rows = [] + while len(figure_values): + figs = figure_values[:N_DISPLAY_COLUMNS] + for i, fig in enumerate(figs): + if i != 0: + fig.yaxis.axis_label = None + figure_rows.append(figs) + for fig in figs: + figure_values.pop(figure_values.index(fig)) + for i, figure_row in enumerate(figure_rows): + if i != len(figure_rows) - 1: + for fig in figure_row: + fig.xaxis.axis_label = None + figure_layout = [] + for i in range(len(figure_rows)): + figure_layout.append(Row(children=figure_rows[i])) + return Row(children=[Column(children=figure_layout), toolbar]) + + +def create_view(widgets: typing.Widgets, figures: typing.Figures) -> Tabs: + """Create the tool view. + + Parameters + ---------- + widgets : typing.Widgets + A dictionary of Bokeh widget objects. + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + Tabs + Bokeh Tabs object. + """ + help_panel = Panel(child=help_page(), title="Help", name="helpPanel") + figure_layout = create_figure_grid(figures) + tool_panel = Panel( + child=Column( + children=[widgets["rv_select"], figure_layout, widgets["range_slider"]], + ), + title="Autocorrelation", + name="toolPanel", + ) + return Tabs(tabs=[tool_panel, help_panel]) + + +def update(data: npt.NDArray, sources: typing.Sources) -> None: + """Update the tool based on user interaction. + + Parameters + ---------- + data : npt.NDArray + A 2D NumPy array where the length of the first dimension is the number of chains + of the model, and the length of the second dimension is the number of draws of + the model. + sources : typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + + Returns + ------- + None + When Bokeh sources are updated with new data, the figures of the tool will be + redrawn. + """ + computed_data = compute_data(data) + for figure_name, figure_data in computed_data.items(): + sources[figure_name]["quad"].data = dict(**figure_data["quad"]) diff --git a/src/beanmachine/ppl/diagnostics/tools/helpers/effective_sample_size.py b/src/beanmachine/ppl/diagnostics/tools/helpers/effective_sample_size.py new file mode 100644 index 0000000000..ddde815253 --- /dev/null +++ b/src/beanmachine/ppl/diagnostics/tools/helpers/effective_sample_size.py @@ -0,0 +1,530 @@ +# Copyright (c) Meta Platforms, Inc. and affiliates. +# +# This source code is licensed under the MIT license found in the +# LICENSE file in the root directory of this source tree. + +"""Methods used to generate the diagnostic tool.""" +from typing import List + +import arviz as az + +import beanmachine.ppl.diagnostics.tools.typing.effective_sample_size as typing +import numpy as np +import numpy.typing as npt +from beanmachine.ppl.diagnostics.tools.helpers.plotting import ( + choose_palette, + create_toolbar, + filter_renderers, + style_figure, +) +from bokeh.models.annotations import Legend, LegendItem +from bokeh.models.glyphs import Circle, Line +from bokeh.models.layouts import Column, Row +from bokeh.models.sources import ColumnDataSource +from bokeh.models.tools import HoverTool +from bokeh.models.widgets import Div +from bokeh.models.widgets.inputs import Select +from bokeh.models.widgets.panels import Panel, Tabs +from bokeh.plotting.figure import figure + + +PLOT_WIDTH = 1000 +PLOT_HEIGHT = 500 +FIGURE_NAMES = ["ess"] + + +def compute_data( + data: npt.NDArray, + first_draw: int = 0, + num_points: int = 20, +) -> typing.Data: + """Compute effective sample size estimates using the given data. + + Parameters + ---------- + data : npt.NDArray + A 2D NumPy array where the length of the first dimension is the number of chains + of the model, and the length of the second dimension is the number of draws of + the model. + first_draw : float, optional default is 0 + The first draw index. + num_points : int, optional default is 20 + The number of divisions in the model samples to compute the effective sample + size for. + + Returns + ------- + typing.Data + A dictionary of data used for the tool. + """ + num_chains, num_draws = data.shape + num_samples = num_chains * num_draws + rule_of_thumb = 100 * num_chains + ess_x = np.linspace( + start=num_samples / num_points, + stop=num_samples, + num=num_points, + ) + draw_divisions = np.linspace( + start=num_draws // num_points, + stop=num_draws, + num=num_points, + dtype=np.integer, + ) + ess_bulk_y = [ + az.stats.diagnostics._ess_bulk(data[:, first_draw:draw_division]) + for draw_division in draw_divisions + ] + ess_tail_y = [ + az.stats.diagnostics._ess_tail(data[:, first_draw:draw_division]) + for draw_division in draw_divisions + ] + rule_of_thumb_x = np.linspace(start=0, stop=num_samples, num=num_points) + rule_of_thumb_y = rule_of_thumb * np.ones(num_points) + rule_of_thumb_label = [rule_of_thumb] * len(ess_x) + return { + "ess": { + "bulk": {"x": ess_x.tolist(), "y": ess_bulk_y}, + "tail": {"x": ess_x.tolist(), "y": ess_tail_y}, + "rule_of_thumb": { + "x": rule_of_thumb_x.tolist(), + "y": rule_of_thumb_y.tolist(), + "label": rule_of_thumb_label, + }, + }, + } + + +def create_sources(data: typing.Data) -> typing.Sources: + """Create Bokeh sources from the given data that will be bound to glyphs. + + Parameters + ---------- + data : typing.Data + A dictionary of data used for the tool. + + Returns + ------- + typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + """ + return { + "ess": { + "bulk": { + "line": ColumnDataSource(data=data["ess"]["bulk"]), + "circle": ColumnDataSource(data=data["ess"]["bulk"]), + }, + "tail": { + "line": ColumnDataSource(data=data["ess"]["tail"]), + "circle": ColumnDataSource(data=data["ess"]["tail"]), + }, + "rule_of_thumb": { + "line": ColumnDataSource(data=data["ess"]["rule_of_thumb"]), + }, + }, + } + + +def create_figures() -> typing.Figures: + """Create the Bokeh figures used for the tool. + + Returns + ------- + typing.Figures + A dictionary of Bokeh Figure objects. + """ + fig = figure( + plot_width=PLOT_WIDTH, + plot_height=PLOT_HEIGHT, + outline_line_color="black", + title="Effective Sample Size", + ) + style_figure(fig) + return {"ess": fig} + + +def create_glyphs() -> typing.Glyphs: + """Create the glyphs used for the figures of the tool. + + Returns + ------- + typing.Glyphs + A dictionary of Bokeh Glyphs objects. + """ + palette = choose_palette(4) + bulk_glyph_color = palette[0] + tail_glyph_color = palette[1] + rule_of_thumb_color = palette[3] + output = {"ess": {}} + for glyph_name in ["bulk", "tail", "rule_of_thumb"]: + glyph_token = "".join([token.title() for token in glyph_name.split("_")]) + if glyph_name in ["bulk", "tail"]: + color = bulk_glyph_color if glyph_name == "bulk" else tail_glyph_color + output["ess"][glyph_name] = { + "line": { + "glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=1.0, + line_width=2.0, + name=f"ess{glyph_token}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=1.0, + line_width=2.0, + name=f"ess{glyph_token}LineHoverGlyph", + ), + }, + "circle": { + "glyph": Circle( + x="x", + y="y", + size=10, + fill_color=color, + line_color="white", + fill_alpha=1.0, + name=f"ess{glyph_token}CircleGlyph", + ), + "hover_glyph": Circle( + x="x", + y="y", + size=10, + fill_color=color, + line_color="black", + fill_alpha=1.0, + name=f"ess{glyph_token}CircleHoverGlyph", + ), + }, + } + elif glyph_name == "rule_of_thumb": + output["ess"][glyph_name] = { + "line": { + "glyph": Line( + x="x", + y="y", + line_color=rule_of_thumb_color, + line_alpha=0.7, + line_width=4.0, + line_dash="dashed", + name=f"ess{glyph_token}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color=rule_of_thumb_color, + line_alpha=0.7, + line_width=4.0, + line_dash="solid", + name=f"ess{glyph_token}LineHoverGlyph", + ), + }, + } + return output + + +def add_glyphs( + figures: typing.Figures, + glyphs: typing.Glyphs, + sources: typing.Sources, +) -> None: + """Bind source data to glyphs and add the glyphs to the given figures. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + glyphs : typing.Glyphs + A dictionary of Bokeh Glyphs objects. + sources : typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + + Returns + ------- + None + Adds data bound glyphs to the given figures directly. + """ + fig = figures["ess"] + figure_glyphs = glyphs["ess"] + figure_sources = sources["ess"] + for glyph_name, glyphs in figure_glyphs.items(): + glyph_sources = figure_sources[glyph_name] + for glyph_type, glyph in glyphs.items(): + glyph_source = glyph_sources[glyph_type] + fig.add_glyph( + source_or_glyph=glyph_source, + glyph=glyph["glyph"], + hover_glyph=glyph["hover_glyph"], + name=glyph["glyph"].name, + ) + + +def create_annotations(figures: typing.Figures) -> typing.Annotations: + """Create any annotations for the figures of the tool. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + typing.Annotations + A dictionary of Bokeh Annotation objects. + """ + legend_items = [] + fig = figures["ess"] + output = {} + for glyph_name in ["bulk", "tail", "rule_of_thumb"]: + glyph_token = "".join([token.title() for token in glyph_name.split("_")]) + search = f"ess{glyph_token}" + if glyph_name in ["bulk", "tail"]: + label = glyph_name.title() + else: + label = "Rule-of-thumb" + filtered_renderers = filter_renderers(fig, search, "GlyphRenderer", True) + legend_items.append( + LegendItem( + label=label, + renderers=filtered_renderers, + name=f"ess{glyph_token}LegendItem", + ), + ) + output["ess"] = { + "legend": Legend( + items=legend_items, + orientation="horizontal", + border_line_color="black", + background_fill_alpha=1.0, + name="essLegend", + ), + } + return output + + +def add_annotations(figures: typing.Figures, annotations: typing.Annotations) -> None: + """Add the given annotations to the given figures of the tool. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + annotations : typing.Annotations + A dictionary of Bokeh Annotation objects. + + Returns + ------- + None + Adds annotations directly to the given figures. + """ + figures["ess"].add_layout(annotations["ess"]["legend"], "below") + + +def create_tooltips(figures: typing.Figures) -> typing.Tooltips: + """Create hover tools for the glyphs used in the figures of the tool. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + typing.Tooltips + A dictionary of Bokeh HoverTools objects. + """ + output = {"ess": {}} + fig = figures["ess"] + tooltips = [] + for glyph_name in ["bulk", "tail", "rule_of_thumb"]: + glyph_token = "".join([token.title() for token in glyph_name.split("_")]) + if glyph_name in ["bulk", "tail"]: + tooltips = [("Total draws", "@x{0,}"), ("ESS", "@y{0,}")] + elif glyph_name == "rule_of_thumb": + tooltips = [("Rule-of-thumb", "@label")] + filtered_renderers = filter_renderers( + fig, + f"ess{glyph_token}", + "GlyphRenderer", + True, + ) + tips_name = "".join( + [c.lower() if i == 0 else c for i, c in enumerate(list(glyph_token))], + ) + tips = HoverTool( + renderers=filtered_renderers, + tooltips=tooltips, + name=f"{tips_name}Tips", + ) + output["ess"][glyph_name] = tips + return output + + +def add_tooltips(figures: typing.Figures, tooltips: typing.Tooltips) -> None: + """Add the given tools to the figures. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + tooltips : typing.Tooltips + A dictionary of Bokeh HoverTools objects. + + Returns + ------- + None + Adds the tooltips directly to the given figures. + """ + fig = figures["ess"] + figure_tooltips = tooltips["ess"] + for _, tips in figure_tooltips.items(): + fig.add_tools(tips) + + +def create_widgets(rv_name: str, rv_names: List[str]) -> typing.Widgets: + """Create the widgets used in the tool. + + Parameters + ---------- + rv_name : str + The string representation of the random variable data. + rv_names : List[str] + A list of all available random variable names. + + Returns + ------- + typing.Widgets + A dictionary of Bokeh widget objects. + """ + return {"rv_select": Select(value=rv_name, options=rv_names, title="Query")} + + +def help_page() -> Div: + """Help tab for the tool. + + Returns + ------- + Div + Bokeh Div widget containing the help tab information. + """ + text = """ ++ MCMC samplers do not draw truly independent samples from the target + distribution, which means that our samples are correlated. In an ideal + situation all samples would be independent, but we do not have that + luxury. We can, however, measure the number of effectively + independent samples we draw, which is called the effective sample + size. You can read more about how this value is calculated in the Vehtari + et al paper. In brief, it is a measure that combines information + from the \\(\\hat{R}\\) value with the autocorrelation estimates within the + chains. +
++ ESS estimates come in two variants, ess_bulk and + ess_tail. The former is the default, but the latter can be useful + if you need good estimates of the tails of your posterior distribution. + The rule of thumb for ess_bulk is for this value to be greater + than 100 per chain on average. The ess_tail is an estimate for + effectively independent samples considering the more extreme values of the + posterior. This is not the number of samples that landed in the tails of + the posterior, but rather a measure of the number of effectively + independent samples if we sampled the tails of the posterior. The rule of + thumb for this value is also to be greater than 100 per chain on average. +
++ When the model is converging properly, both the bulk and tail lines should + be roughly linear. +
++ The highest density interval region is not equal tailed like a typical + equal tailed interval of 2.5%. Thus it will include the mode(s) of the + posterior distribution. +
++ There is nothing particularly specific about having a default HDI of 89%. + If fact, the only remarkable thing about defaulting to 89% is that it is + the highest prime number that does not exceed the unstable 95% threshold. + See the link to McElreath's book below for further discussion. +
++ A joint plot shows univariate marginals along the x and y axes. The + central figure shows the bivariate marginal of both random variables. +
+ """ + return Div( + text=text, + disable_math=False, + min_width=MARGINAL1D_PLOT_WIDTH + MARGINAL2D_PLOT_WIDTH, + ) + + +def create_figure_grid(figures: typing.Figures) -> Row: + """Layout the given figures in a grid, and make one toolbar. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + Row + A Bokeh layout object. + """ + toolbar = create_toolbar(figures) + grid_box = GridBox( + children=[ + [figures["x"], 0, 0], + [figures["xy"], 1, 0], + [figures["y"], 1, 1], + ], + sizing_mode=None, + ) + return Row(children=[grid_box, toolbar]) + + +def create_view(widgets: typing.Widgets, figures: typing.Figures) -> Tabs: + """Create the tool view. + + Parameters + ---------- + widgets : typing.Widgets + A dictionary of Bokeh widget objects. + figures : typing.Figures + A dictionary of Bokeh Figure objects. + + Returns + ------- + Tabs + Bokeh Tabs objects. + """ + help_panel = Panel(child=help_page(), title="Help", name="helpPanel") + figure_grid = create_figure_grid(figures) + tool_panel = Panel( + child=Row( + children=[ + Column( + children=[ + Row( + children=[ + widgets["x_rv_select"], + widgets["y_rv_select"], + ], + ), + figure_grid, + ], + ), + Column( + children=[ + widgets["x_hdi_slider"], + widgets["y_hdi_slider"], + widgets["x_bw_div"], + widgets["y_bw_div"], + ], + ), + ], + ), + title="Marginal 2D", + name="marginalToolPanel", + ) + return Tabs(tabs=[tool_panel, help_panel]) + + +def update( + x_rv_data: npt.NDArray, + y_rv_data: npt.NDArray, + x_rv_name: str, + y_rv_name: str, + sources: typing.Sources, + figures: typing.Figures, + tooltips: typing.Tooltips, + x_hdi_probability: float, + y_hdi_probability: float, + bw_factor: float, +) -> Tuple[float, float]: + """Update the tool based on user interaction. + + Parameters + ---------- + x_rv_data : npt.NDArray + A 2D NumPy array where the length of the first dimension is the number of chains + of the model, and the length of the second dimension is the number of draws of + the model. + y_rv_data : npt.NDArray + A 2D NumPy array where the length of the first dimension is the number of chains + of the model, and the length of the second dimension is the number of draws of + the model. + x_rv_name : str + The name of the random variable along the x-axis. + y_rv_name : str + The name of the random variable along the y-axis. + sources : typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + figures : typing.Figures + A dictionary of Bokeh Figure objects. + tooltips : typing.Tooltips + A dictionary of Bokeh HoverTools objects. + x_hdi_probability : float + The HDI probability to use when calculating the HDI bounds for the x-axis. + y_hdi_probability : float + The HDI probability to use when calculating the HDI bounds for the y-axis. + bw_factor : float + Multiplicative factor used when calculating the kernel density estimate. + + Returns + ------- + Tuple[float, float] + Returns the bandwidth for both the axes. + """ + computed_data = compute_data( + x_rv_data, + y_rv_data, + x_rv_name, + y_rv_name, + x_hdi_probability, + y_hdi_probability, + bw_factor, + ) + x_bw = computed_data["x"]["distribution"].pop("bandwidth") + y_bw = computed_data["y"]["distribution"].pop("bandwidth") + for figure_name, figure_data in computed_data.items(): + figure_sources = sources[figure_name] + if figure_name == "x": + dist = figure_sources["distribution"] + dist.data = figure_data["distribution"] + figure_sources["hdi"].data = figure_data["hdi"] + figure_sources["stats"].data = figure_data["stats"] + if figure_name == "y": + dist = figure_sources["distribution"] + hdi_top = figure_sources["hdi"]["top"] + hdi_bottom = figure_sources["hdi"]["bottom"] + dist.data = figure_data["distribution"] + hdi_top.data = figure_data["hdi"]["top"] + hdi_bottom.data = figure_data["hdi"]["bottom"] + figure_sources["stats"].data = figure_data["stats"] + if figure_name == "xy": + dist = figure_sources["distribution"] + hdi_x_lower = figure_sources["hdi"]["x"]["lower"] + hdi_x_upper = figure_sources["hdi"]["x"]["upper"] + hdi_y_lower = figure_sources["hdi"]["y"]["lower"] + hdi_y_upper = figure_sources["hdi"]["y"]["upper"] + dist.data = figure_data["distribution"] + hdi_x_lower.data = figure_data["hdi"]["x"]["lower"] + hdi_x_upper.data = figure_data["hdi"]["x"]["upper"] + hdi_y_lower.data = figure_data["hdi"]["y"]["lower"] + hdi_y_upper.data = figure_data["hdi"]["y"]["upper"] + figure_sources["stats"].data = figure_data["stats"] + figures["xy"].xaxis.axis_label = x_rv_name + figures["xy"].yaxis.axis_label = y_rv_name + tooltips["xy"]["mean"].tooltips = [ + (x_rv_name, "@x"), + (y_rv_name, "@y"), + ] + tooltips["xy"]["hdi"]["x"]["lower"].tooltips = [(x_rv_name, "@x")] + tooltips["xy"]["hdi"]["x"]["upper"].tooltips = [(x_rv_name, "@x")] + tooltips["xy"]["hdi"]["y"]["lower"].tooltips = [(y_rv_name, "@y")] + tooltips["xy"]["hdi"]["y"]["upper"].tooltips = [(y_rv_name, "@y")] + return (x_bw, y_bw) diff --git a/src/beanmachine/ppl/diagnostics/tools/helpers/plotting.py b/src/beanmachine/ppl/diagnostics/tools/helpers/plotting.py new file mode 100644 index 0000000000..5c2644da84 --- /dev/null +++ b/src/beanmachine/ppl/diagnostics/tools/helpers/plotting.py @@ -0,0 +1,127 @@ +# Copyright (c) Meta Platforms, Inc. and affiliates. +# +# This source code is licensed under the MIT license found in the +# LICENSE file in the root directory of this source tree. + +"""Plotting utilities for the diagnostics tools.""" +from typing import Dict, List + +from bokeh.core.property.nullable import Nullable +from bokeh.core.property.primitive import Null +from bokeh.core.property.wrappers import PropertyValueList +from bokeh.models.renderers import GlyphRenderer +from bokeh.models.tools import ProxyToolbar, ResetTool, SaveTool, ToolbarBox +from bokeh.palettes import Colorblind +from bokeh.plotting.figure import Figure + + +def style_figure(figure: Figure) -> None: + """Give the given figure a uniform style. + + Parameters + ---------- + fig : Figure + Bokeh Figure object. + + Returns + ------- + None + Directly applies a uniform styling to the given figure. + """ + figure.grid.grid_line_alpha = 0.3 + figure.grid.grid_line_color = "grey" + figure.grid.grid_line_width = 0.3 + figure.xaxis.minor_tick_line_color = "grey" + figure.yaxis.minor_tick_line_color = "grey" + + +def choose_palette(n: int) -> tuple: + """Choose an appropriate palette from Bokeh's Colorblind palette. + + Parameters + ---------- + n : int + The number of colors to choose from the Colorblind palette. + + Returns + ------- + tuple + A tuple object that contains color information. + """ + palette_indices = [key for key in Colorblind.keys() if n <= key] + if not palette_indices: + palette_index = max(Colorblind.keys()) + else: + palette_index = min(palette_indices) + return Colorblind[palette_index] + + +def create_toolbar(figures: Dict[str, Figure]) -> ToolbarBox: + """Create a single toolbar for multiple figures. + + This will also remove any ``HoverTool`` tools on the figures. These are removed from + figure groupings as there are sometimes many different hover tools for a single + figure. Aggregating all the hover tools into a single toolbar will make the toolbar + look like it only has hover tools in it, and nothing else. + + Parameters + ---------- + figures : Dict[str, Figure] + A dictionary of Bokeh figures. + + Returns + ------- + ToolbarBox + A single toolbar for the given Bokeh figures. + """ + toolbars = [] + for _, figure in figures.items(): + toolbars.append(figure.toolbar) + figure.toolbar_location = Nullable(Null)._default + tools = [] + for toolbar in toolbars: + tools.extend(toolbar.tools) + tools = [tool for tool in tools if type(tool).__name__ != "HoverTool"] + if len(tools) == 0: + tools = [SaveTool(), ResetTool()] + return ToolbarBox( + toolbar=ProxyToolbar(toolbars=toolbars, tools=tools), + toolbar_location="right", + ) + + +def filter_renderers( + figure: Figure, + search: str, + glyph_type: str = "GlyphRenderer", + substring: bool = False, +) -> List[GlyphRenderer]: + """Filter Bokeh figure renderers given the search string. + + Parameters + ---------- + figure : Figure + A Bokeh figure to filter renderers from. + search : str + The search string to filter for. + glyph_type : str, optional default is "GlyphRenderer" + The glyph type. + substring : bool, optional default is ``False`` + Flag to indicate if we should use the search term as a substring search. + - ``False`` indicates the name of the glyph == search. + - ``True`` indicates the search is a substring of the glyph name. + + Returns + ------- + List[GlyphRenderer] + A list of Bokeh glyph renderer objects. + """ + output = [] + renderers = PropertyValueList(figure.renderers) + for renderer in renderers: + if renderer.name is not None and type(renderer).__name__ == glyph_type: + if substring and search in renderer.name: + output.append(renderer) + if not substring and renderer.name == search: + output.append(renderer) + return output diff --git a/src/beanmachine/ppl/diagnostics/tools/helpers/trace.py b/src/beanmachine/ppl/diagnostics/tools/helpers/trace.py new file mode 100644 index 0000000000..31c45d956a --- /dev/null +++ b/src/beanmachine/ppl/diagnostics/tools/helpers/trace.py @@ -0,0 +1,821 @@ +# Copyright (c) Meta Platforms, Inc. and affiliates. +# +# This source code is licensed under the MIT license found in the +# LICENSE file in the root directory of this source tree. + +"""Methods used to generate the diagnostic tool.""" +from typing import List + +import arviz as az +import beanmachine.ppl.diagnostics.tools.typing.trace as typing +import numpy as np +import numpy.typing as npt + +from beanmachine.ppl.diagnostics.tools.helpers import marginal1d as m1d +from beanmachine.ppl.diagnostics.tools.helpers.plotting import ( + choose_palette, + create_toolbar, + filter_renderers, + style_figure, +) +from bokeh.core.property.wrappers import PropertyValueList +from bokeh.models.annotations import Legend, LegendItem +from bokeh.models.glyphs import Circle, Line, Quad +from bokeh.models.layouts import Column, Row + +from bokeh.models.ranges import Range1d +from bokeh.models.sources import ColumnDataSource +from bokeh.models.tools import HoverTool +from bokeh.models.widgets import Div +from bokeh.models.widgets.inputs import Select +from bokeh.models.widgets.panels import Panel, Tabs +from bokeh.models.widgets.sliders import Slider +from bokeh.plotting.figure import figure + + +PLOT_WIDTH = 400 +PLOT_HEIGHT = 500 +TRACE_PLOT_WIDTH = 600 +FIGURE_NAMES = ["marginals", "forests", "traces", "ranks"] + + +def compute_data( + data: npt.NDArray, + bw_factor: float, + hdi_probability: float, +) -> typing.Data: + """Compute effective sample size estimates using the given data. + + Parameters + ---------- + data : npt.NDArray + A 2D NumPy array where the length of the first dimension is the number of chains + of the model, and the length of the second dimension is the number of draws of + the model. + bw_factor : float + Multiplicative factor used when calculating the kernel density estimate. + hdi_probability : float + The HDI probability to use when calculating the HDI bounds. + + Returns + ------- + typing.Data + A dictionary of data used for the tool. + """ + num_chains, num_draws = data.shape + num_samples = num_chains * num_draws + rank_data = az.plots.plot_utils.compute_ranks(data) + n_bins = int(np.ceil(2 * np.log2(rank_data.shape[1])) + 1) + bins = np.histogram_bin_edges(rank_data, bins=n_bins, range=(0, rank_data.size)) + hist_bins = len(bins) + output = {} + for figure_name in FIGURE_NAMES: + output[figure_name] = {} + for chain in range(num_chains): + chain_index = chain + 1 + chain_name = f"chain{chain_index}" + output[figure_name][chain_name] = {} + chain_data = data[chain] + marginal = m1d.compute_data(chain_data, bw_factor, hdi_probability) + marginal = marginal["marginal"]["distribution"] + mean = float(np.array(marginal["x"]).mean()) + if figure_name == "marginals": + output[figure_name][chain_name] = { + "line": {"x": marginal["x"], "y": marginal["y"]}, + "chain": chain_index, + "mean": mean, + "bandwidth": marginal["bandwidth"], + } + if figure_name == "forests": + hdi = az.stats.hdi(chain_data, hdi_probability) + output[figure_name][chain_name] = { + "line": {"x": hdi, "y": [chain_index] * 2}, + "circle": {"x": [mean], "y": [chain_index]}, + "chain": chain_index, + "mean": mean, + } + if figure_name == "traces": + output[figure_name][chain_name] = { + "line": {"x": np.arange(0, num_draws, 1), "y": chain_data}, + "chain": chain_index, + "mean": mean, + "bandwidth": marginal["bandwidth"], + } + if figure_name == "ranks": + _, histogram, _ = az.stats.density_utils.histogram( + rank_data[chain, :], + bins=n_bins, + ) + normed_hist = histogram / histogram.max() + chain_rank_mean = normed_hist.mean() + left = bins[:-1] + top = normed_hist + chain + right = bins[1:] + bottom = np.zeros(hist_bins - 1) + chain + draws = [f"{int(b[0]):0,}-{int(b[1]):0,}" for b in zip(left, right)] + quad = { + "left": left.tolist(), + "right": right.tolist(), + "top": top.tolist(), + "bottom": bottom.tolist(), + "draws": draws, + "rank": normed_hist.tolist(), + } + x = np.arange(0, num_samples, 1) + line = {"x": x.tolist(), "y": [chain_rank_mean + chain] * len(x)} + output[figure_name][chain_name] = { + "quad": quad, + "line": line, + "chain": chain_index, + "rank_mean": chain_index - chain_rank_mean, + "mean": histogram.mean(), + } + return output + + +def create_sources(data: typing.Data) -> typing.Sources: + """Create Bokeh sources from the given data that will be bound to glyphs. + + Parameters + ---------- + data : typing.Data + A dictionary of data used for the tool. + + Returns + ------- + typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + """ + output = {} + for figure_name, figure_data in data.items(): + output[figure_name] = {} + for i, (chain_name, chain_data) in enumerate(figure_data.items()): + output[figure_name][chain_name] = {} + n = len(chain_data["line"]["x"]) + chain_index_list = [chain_data["chain"]] * n + chain_mean_list = [chain_data["mean"]] * n + if figure_name == "marginals": + output[figure_name][chain_name]["line"] = ColumnDataSource( + { + "x": chain_data["line"]["x"], + "y": chain_data["line"]["y"], + "chain": chain_index_list, + "mean": chain_mean_list, + }, + ) + if figure_name == "forests": + output[figure_name][chain_name]["line"] = ColumnDataSource( + { + "x": chain_data["line"]["x"], + "y": chain_data["line"]["y"], + "chain": chain_index_list, + }, + ) + output[figure_name][chain_name]["circle"] = ColumnDataSource( + { + "x": chain_data["circle"]["x"], + "y": chain_data["circle"]["y"], + "chain": [chain_data["chain"]], + }, + ) + if figure_name == "traces": + output[figure_name][chain_name]["line"] = ColumnDataSource( + { + "x": chain_data["line"]["x"], + "y": chain_data["line"]["y"], + "chain": chain_index_list, + "mean": ([chain_data["mean"]] * len(chain_data["line"]["x"])), + }, + ) + if figure_name == "ranks": + output[figure_name][chain_name]["line"] = ColumnDataSource( + { + "x": chain_data["line"]["x"], + "y": chain_data["line"]["y"], + "chain": chain_index_list, + "rank_mean": ( + [chain_data["rank_mean"]] * len(chain_data["line"]["x"]) + ), + }, + ) + output[figure_name][chain_name]["quad"] = ColumnDataSource( + { + "left": chain_data["quad"]["left"], + "top": chain_data["quad"]["top"], + "right": chain_data["quad"]["right"], + "bottom": chain_data["quad"]["bottom"], + "chain": [i + 1] * len(chain_data["quad"]["left"]), + "draws": chain_data["quad"]["draws"], + "rank": chain_data["quad"]["rank"], + }, + ) + return output + + +def create_figures(rv_name: str, num_chains: int) -> typing.Figures: + """Create the Bokeh figures used for the tool. + + Parameters + ---------- + rv_name : str + The string representation of the random variable data. + num_chains : int + The number of chains of the model. + + Returns + ------- + typing.Figures + A dictionary of Bokeh Figure objects. + """ + output = {} + for figure_name in FIGURE_NAMES: + fig = figure() + if figure_name == "marginals": + fig = figure( + plot_width=PLOT_WIDTH, + plot_height=PLOT_HEIGHT, + outline_line_color="black", + title="Marginal", + x_axis_label=rv_name, + x_range=Range1d(), + ) + style_figure(fig) + if figure_name == "forests": + fig = figure( + plot_width=PLOT_WIDTH, + plot_height=PLOT_HEIGHT, + outline_line_color="black", + title="Forest", + x_axis_label=rv_name, + y_axis_label="Chain", + x_range=Range1d(), + ) + style_figure(fig) + fig.yaxis.minor_tick_line_color = None + fig.yaxis.ticker = list(range(1, num_chains + 1)) + if figure_name == "traces": + fig = figure( + plot_width=TRACE_PLOT_WIDTH, + plot_height=PLOT_HEIGHT, + outline_line_color="black", + title="Trace", + x_axis_label="Draw from single chain", + y_axis_label=rv_name, + y_range=Range1d(), + ) + style_figure(fig) + fig.yaxis.minor_tick_line_color = "grey" + if figure_name == "ranks": + fig = figure( + plot_width=TRACE_PLOT_WIDTH, + plot_height=PLOT_HEIGHT, + outline_line_color="black", + title="Rank", + x_axis_label="Rank from all chains", + y_axis_label="Chain", + ) + style_figure(fig) + fig.yaxis.minor_tick_line_color = None + fig.yaxis.ticker = list(range(1, num_chains + 1)) + output[figure_name] = fig + return output + + +def create_glyphs(data: typing.Data, num_chains: int) -> typing.Glyphs: + """Create the glyphs used for the figures of the tool. + + Parameters + ---------- + data : typing.Data + A dictionary of data used for the tool. + num_chains : int + The number of chains of the model. + + Returns + ------- + typing.Glyphs + A dictionary of Bokeh Glyphs objects. + """ + palette = choose_palette(num_chains) + output = {} + for figure_name, figure_data in data.items(): + output[figure_name] = {} + for i, (chain_name, _) in enumerate(figure_data.items()): + output[figure_name][chain_name] = {} + color = palette[i] + if figure_name == "marginals": + output[figure_name][chain_name]["line"] = { + "glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=0.7, + line_width=2.0, + name=f"{figure_name}{chain_name.title()}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=1.0, + line_width=2.0, + name=f"{figure_name}{chain_name.title()}LineHoverGlyph", + ), + } + if figure_name == "forests": + output[figure_name][chain_name] = { + "line": { + "glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=0.7, + line_width=2.0, + name=f"{figure_name}{chain_name.title()}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=1.0, + line_width=2.0, + name=f"{figure_name}{chain_name.title()}LineHoverGlyph", + ), + }, + "circle": { + "glyph": Circle( + x="x", + y="y", + size=10, + fill_color=color, + fill_alpha=0.7, + line_color="white", + name=f"{figure_name}{chain_name.title()}CircleGlyph", + ), + "hover_glyph": Circle( + x="x", + y="y", + size=10, + fill_color=color, + fill_alpha=1.0, + line_color="black", + name=f"{figure_name}{chain_name.title()}CircleHoverGlyph", + ), + }, + } + if figure_name == "traces": + output[figure_name][chain_name]["line"] = { + "glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=0.6, + line_width=0.6, + name=f"{figure_name}{chain_name.title()}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color=color, + line_alpha=0.6, + line_width=1.0, + name=f"{figure_name}{chain_name.title()}LineHoverGlyph", + ), + } + if figure_name == "ranks": + output[figure_name][chain_name] = { + "quad": { + "glyph": Quad( + left="left", + top="top", + right="right", + bottom="bottom", + fill_color=color, + fill_alpha=0.7, + line_color="white", + name=f"{figure_name}{chain_name.title()}QuadGlyph", + ), + "hover_glyph": Quad( + left="left", + top="top", + right="right", + bottom="bottom", + fill_color=color, + fill_alpha=1.0, + line_color="black", + name=f"{figure_name}{chain_name.title()}QuadHoverGlyph", + ), + }, + "line": { + "glyph": Line( + x="x", + y="y", + line_color="grey", + line_alpha=0.7, + line_width=3.0, + line_dash="dashed", + name=f"{figure_name}{chain_name.title()}LineGlyph", + ), + "hover_glyph": Line( + x="x", + y="y", + line_color="grey", + line_alpha=1.0, + line_width=3.0, + line_dash="solid", + name=f"{figure_name}{chain_name.title()}LineGlyph", + ), + }, + } + return output + + +def add_glyphs( + figures: typing.Figures, + glyphs: typing.Glyphs, + sources: typing.Sources, + num_chains: int, +) -> None: + """Bind source data to glyphs and add the glyphs to the given figures. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + glyphs : typing.Glyphs + A dictionary of Bokeh Glyphs objects. + sources : typing.Sources + A dictionary of Bokeh ColumnDataSource objects. + num_chains : int + The number of chains of the model. + + Returns + ------- + None + Adds data bound glyphs to the given figures directly. + """ + range_min = [] + range_max = [] + for figure_name, figure_sources in sources.items(): + fig = figures[figure_name] + for chain_name, source in figure_sources.items(): + chain_glyphs = glyphs[figure_name][chain_name] + fig.add_glyph( + source_or_glyph=source["line"], + glyph=chain_glyphs["line"]["glyph"], + hover_glyph=chain_glyphs["line"]["hover_glyph"], + name=chain_glyphs["line"]["glyph"].name, + ) + if figure_name == "marginals": + range_min.append(min(source["line"].data["x"])) + range_max.append(max(source["line"].data["x"])) + if figure_name == "forests": + fig.add_glyph( + source_or_glyph=source["circle"], + glyph=chain_glyphs["circle"]["glyph"], + hover_glyph=chain_glyphs["circle"]["hover_glyph"], + name=chain_glyphs["circle"]["glyph"].name, + ) + if figure_name == "ranks": + fig.add_glyph( + source_or_glyph=source["quad"], + glyph=chain_glyphs["quad"]["glyph"], + hover_glyph=chain_glyphs["quad"]["hover_glyph"], + name=chain_glyphs["quad"]["glyph"].name, + ) + range_ = Range1d(start=min(range_min), end=max(range_max)) + figures["marginals"].x_range = range_ + figures["forests"].x_range = range_ + figures["traces"].y_range = range_ + + +def create_annotations(figures: typing.Figures, num_chains: int) -> typing.Annotations: + """Create any annotations for the figures of the tool. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + num_chains : int + The number of chains of the model. + + Returns + ------- + typing.Annotations + A dictionary of Bokeh Annotation objects. + """ + renderers = [] + for _, fig in figures.items(): + renderers.extend(PropertyValueList(fig.renderers)) + legend_items = [] + for chain in range(num_chains): + chain_index = chain + 1 + chain_name = f"chain{chain_index}" + legend_items.append( + LegendItem( + renderers=[ + renderer + for renderer in renderers + if chain_name in renderer.name.lower() + ], + label=chain_name, + ), + ) + legend = Legend( + items=legend_items, + orientation="horizontal", + border_line_color="black", + click_policy="hide", + ) + return {"traces": {"legend": legend}, "ranks": {"legend": legend}} + + +def add_annotations(figures: typing.Figures, annotations: typing.Annotations) -> None: + """Add the given annotations to the given figures of the tool. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + annotations : typing.Annotations + A dictionary of Bokeh Annotation objects. + + Returns + ------- + None + Adds annotations directly to the given figures. + """ + for figure_name, figure_annotations in annotations.items(): + fig = figures[figure_name] + for _, annotation in figure_annotations.items(): + fig.add_layout(annotation, "below") + + +def create_tooltips( + rv_name: str, + figures: typing.Figures, + num_chains: int, +) -> typing.Tooltips: + """Create hover tools for the glyphs used in the figures of the tool. + + Parameters + ---------- + rv_name : str + The string representation of the random variable data. + figures : typing.Figures + A dictionary of Bokeh Figure objects. + num_chains : int + The number of chains of the model. + + Returns + ------- + typing.Tooltips + A dictionary of Bokeh HoverTools objects. + """ + output = {} + for figure_name, fig in figures.items(): + output[figure_name] = [] + for chain in range(num_chains): + chain_index = chain + 1 + chain_name = f"chain{chain_index}" + if figure_name == "marginals": + glyph_name = f"{figure_name}{chain_name.title()}LineGlyph" + output[figure_name].append( + HoverTool( + renderers=filter_renderers(fig, glyph_name), + tooltips=[ + ("Chain", "@chain"), + ("Mean", "@mean"), + (rv_name, "@x"), + ], + ), + ) + if figure_name == "forests": + glyph_name = f"{figure_name}{chain_name.title()}CircleGlyph" + output[figure_name].append( + HoverTool( + renderers=filter_renderers(fig, glyph_name), + tooltips=[("Chain", "@chain"), ("Mean", "@x")], + ), + ) + if figure_name == "traces": + glyph_name = f"{figure_name}{chain_name.title()}LineGlyph" + output[figure_name].append( + HoverTool( + renderers=filter_renderers(fig, glyph_name), + tooltips=[ + ("Chain", "@chain"), + ("Mean", "@mean"), + (rv_name, "@y"), + ], + ), + ) + if figure_name == "ranks": + glyph_name = f"{figure_name}{chain_name.title()}LineGlyph" + output[figure_name].append( + HoverTool( + renderers=filter_renderers(fig, glyph_name), + tooltips=[("Chain", "@chain"), ("Rank mean", "@rank_mean")], + ), + ) + glyph_name = f"{figure_name}{chain_name.title()}QuadGlyph" + output[figure_name].append( + HoverTool( + renderers=filter_renderers(fig, glyph_name), + tooltips=[ + ("Chain", "@chain"), + ("Draws", "@draws"), + ("Rank", "@rank"), + ], + ), + ) + return output + + +def add_tooltips(figures: typing.Figures, tooltips: typing.Tooltips) -> None: + """Add the given tools to the figures. + + Parameters + ---------- + figures : typing.Figures + A dictionary of Bokeh Figure objects. + tooltips : typing.Tooltips + A dictionary of Bokeh HoverTools objects. + + Returns + ------- + None + Adds the tooltips directly to the given figures. + """ + for figure_name, fig in figures.items(): + for tips in tooltips[figure_name]: + fig.add_tools(tips) + + +def create_widgets(rv_name: str, rv_names: List[str]) -> typing.Widgets: + """Create the widgets used in the tool. + + Parameters + ---------- + rv_name : str + The string representation of the random variable data. + rv_names : List[str] + A list of all available random variable names. + + Returns + ------- + typing.Widgets + A dictionary of Bokeh widget objects. + """ + return { + "rv_select": Select(value=rv_name, options=rv_names, title="Query"), + "bw_factor_slider": Slider( + start=0.01, + end=2.00, + step=0.01, + value=1.0, + title="Bandwidth factor", + ), + "hdi_slider": Slider(start=1, end=99, step=1, value=89, title="HDI"), + } + + +def help_page() -> Div: + """Help tab for the tool. + + Returns + ------- + Div + Bokeh Div widget containing the help tab information. + """ + text = """ ++ Rank plots are a histogram of the samples over time. All samples across + all chains are ranked and then we plot the average rank for each chain on + regular intervals. If the chains are mixing well this histogram should + look roughly uniform. If it looks highly irregular that suggests chains + might be getting stuck and not adequately exploring the sample space. + See the paper by Vehtari et al for more information. +
++ The more familiar trace plots are also included in this widget. You can + click on the legend to show/hide different chains and compare them to the + rank plots. +
+\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"\\n\"+\n", + " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", + " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", + " \"
\\n\"+\n", + " \"\\n\"+\n",
+ " \"from bokeh.resources import INLINE\\n\"+\n",
+ " \"output_notebook(resources=INLINE)\\n\"+\n",
+ " \"\\n\"+\n",
+ " \"\"}};\n",
+ "\n",
+ " function display_loaded() {\n",
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+ " if (el != null) {\n",
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+ " if (el != null) {\n",
+ " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
+ " }\n",
+ " } else if (Date.now() < root._bokeh_timeout) {\n",
+ " setTimeout(display_loaded, 100)\n",
+ " }\n",
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+ "\n",
+ " function run_callbacks() {\n",
+ " try {\n",
+ " root._bokeh_onload_callbacks.forEach(function(callback) {\n",
+ " if (callback != null)\n",
+ " callback();\n",
+ " });\n",
+ " } finally {\n",
+ " delete root._bokeh_onload_callbacks\n",
+ " }\n",
+ " console.debug(\"Bokeh: all callbacks have finished\");\n",
+ " }\n",
+ "\n",
+ " function load_libs(css_urls, js_urls, callback) {\n",
+ " if (css_urls == null) css_urls = [];\n",
+ " if (js_urls == null) js_urls = [];\n",
+ "\n",
+ " root._bokeh_onload_callbacks.push(callback);\n",
+ " if (root._bokeh_is_loading > 0) {\n",
+ " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
+ " return null;\n",
+ " }\n",
+ " if (js_urls == null || js_urls.length === 0) {\n",
+ " run_callbacks();\n",
+ " return null;\n",
+ " }\n",
+ " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
+ " root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
+ "\n",
+ " function on_load() {\n",
+ " root._bokeh_is_loading--;\n",
+ " if (root._bokeh_is_loading === 0) {\n",
+ " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
+ " run_callbacks()\n",
+ " }\n",
+ " }\n",
+ "\n",
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+ " element.rel = \"stylesheet\";\n",
+ " element.type = \"text/css\";\n",
+ " element.href = url;\n",
+ " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
+ " document.body.appendChild(element);\n",
+ " }\n",
+ "\n",
+ " for (let i = 0; i < js_urls.length; i++) {\n",
+ " const url = js_urls[i];\n",
+ " const element = document.createElement('script');\n",
+ " element.onload = on_load;\n",
+ " element.onerror = on_error.bind(null, url);\n",
+ " element.async = false;\n",
+ " element.src = url;\n",
+ " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
+ " document.head.appendChild(element);\n",
+ " }\n",
+ " };\n",
+ "\n",
+ " function inject_raw_css(css) {\n",
+ " const element = document.createElement(\"style\");\n",
+ " element.appendChild(document.createTextNode(css));\n",
+ " document.body.appendChild(element);\n",
+ " }\n",
+ "\n",
+ " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.3.min.js\"];\n",
+ " const css_urls = [];\n",
+ "\n",
+ " const inline_js = [ function(Bokeh) {\n",
+ " Bokeh.set_log_level(\"info\");\n",
+ " },\n",
+ "function(Bokeh) {\n",
+ " }\n",
+ " ];\n",
+ "\n",
+ " function run_inline_js() {\n",
+ " if (root.Bokeh !== undefined || force === true) {\n",
+ " for (let i = 0; i < inline_js.length; i++) {\n",
+ " inline_js[i].call(root, root.Bokeh);\n",
+ " }\n",
+ "} else if (Date.now() < root._bokeh_timeout) {\n",
+ " setTimeout(run_inline_js, 100);\n",
+ " } else if (!root._bokeh_failed_load) {\n",
+ " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
+ " root._bokeh_failed_load = true;\n",
+ " } else if (force !== true) {\n",
+ " const cell = $(document.getElementById(null)).parents('.cell').data().cell;\n",
+ " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
+ " }\n",
+ " }\n",
+ "\n",
+ " if (root._bokeh_is_loading === 0) {\n",
+ " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
+ " run_inline_js();\n",
+ " } else {\n",
+ " load_libs(css_urls, js_urls, function() {\n",
+ " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
+ " run_inline_js();\n",
+ " });\n",
+ " }\n",
+ "}(window));"
+ ],
+ "application/vnd.bokehjs_load.v0+json": "(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n\n if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"\\n\"+\n", + " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", + " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", + " \"
\\n\"+\n", + " \"\\n\"+\n",
+ " \"from bokeh.resources import INLINE\\n\"+\n",
+ " \"output_notebook(resources=INLINE)\\n\"+\n",
+ " \"\\n\"+\n",
+ " \"\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"<xarray.Dataset>\n", + "Dimensions: (chain: 4, draw: 1000)\n", + "Coordinates:\n", + " * chain (chain) int64 0 1 2 3\n", + " * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 992 993 994 995 996 997 998 999\n", + "Data variables:\n", + " theta() (chain, draw) float32 0.771 0.771 0.771 ... 0.7648 0.7648 0.7648\n", + "Attributes:\n", + " created_at: 2022-08-29T17:14:03.748882\n", + " arviz_version: 0.12.1
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<xarray.Dataset>\n", + "Dimensions: (y(0,)_dim_0: 1, y(1,)_dim_0: 1, y(2,)_dim_0: 1,\n", + " y(3,)_dim_0: 1, y(4,)_dim_0: 1, y(5,)_dim_0: 1,\n", + " y(6,)_dim_0: 1, y(7,)_dim_0: 1, y(8,)_dim_0: 1, y(9,)_dim_0: 1)\n", + "Coordinates:\n", + " * y(0,)_dim_0 (y(0,)_dim_0) int64 0\n", + " * y(1,)_dim_0 (y(1,)_dim_0) int64 0\n", + " * y(2,)_dim_0 (y(2,)_dim_0) int64 0\n", + " * y(3,)_dim_0 (y(3,)_dim_0) int64 0\n", + " * y(4,)_dim_0 (y(4,)_dim_0) int64 0\n", + " * y(5,)_dim_0 (y(5,)_dim_0) int64 0\n", + " * y(6,)_dim_0 (y(6,)_dim_0) int64 0\n", + " * y(7,)_dim_0 (y(7,)_dim_0) int64 0\n", + " * y(8,)_dim_0 (y(8,)_dim_0) int64 0\n", + " * y(9,)_dim_0 (y(9,)_dim_0) int64 0\n", + "Data variables:\n", + " y(0,) (y(0,)_dim_0) float32 1.0\n", + " y(1,) (y(1,)_dim_0) float32 1.0\n", + " y(2,) (y(2,)_dim_0) float32 0.0\n", + " y(3,) (y(3,)_dim_0) float32 1.0\n", + " y(4,) (y(4,)_dim_0) float32 1.0\n", + " y(5,) (y(5,)_dim_0) float32 1.0\n", + " y(6,) (y(6,)_dim_0) float32 1.0\n", + " y(7,) (y(7,)_dim_0) float32 1.0\n", + " y(8,) (y(8,)_dim_0) float32 1.0\n", + " y(9,) (y(9,)_dim_0) float32 0.0\n", + "Attributes:\n", + " created_at: 2022-08-29T17:14:03.754606\n", + " arviz_version: 0.12.1