[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

README.md

@@ -8,7 +8,7 @@ From this, it infers $\mathcal{R}(t)$, the time-varying reproduction number, whi
 The core renewal equation is:
 
 $$
-  I(t) = \mathcal{R}(t) \sum_{s} I(t-s) \, w(s)
+  I(t) = \mathcal{R}(t) \sum_{s} I(t - s) \, w(s)
 $$
 
 where $w(s)$ is the generation interval distribution: the probability that $s$ time units separate infection in an index case and a secondary case.
@@ -17,7 +17,7 @@ However inference is complicated by the fact that observational data require the
 The observation equation links infections to expected observations:
 
 $$
-  \mu(t) = \alpha \sum_{s} I(t-s) \, \pi(s)
+  \mu(t) = \alpha \sum_{s} I(t - s) \, \pi(s)
 $$
 
 where $\alpha$ is the ascertainment rate and $\pi(s)$ is the delay distribution from infection to observation.

docs/tutorials/ascertainment.qmd

@@ -41,9 +41,7 @@ For emergency department visits, it can be called the infection-to-ED-visit rate
 For a count observation process, the ascertainment rate scales delayed latent infections to obtain the expected number of observed events:
 
 $$
-  \mu_s(t)
-  =
-  \alpha_s \sum_{d=0}^{D_s} I(t-d)\,\pi_{s,d},
+  \mu_s(t) = \alpha_s \sum_{d=0}^{D_s} I(t - d)\,\pi_{s,d},
 $$
 
 where $s$ identifies the signal, $\alpha_s$ is its ascertainment rate, and $\pi_{s,d}$ is its delay distribution.
@@ -132,14 +130,8 @@ Use `RatioLinkedAscertainment` when the relative quantity, such as IHR / IEDR, i
 
 $$
   \boldsymbol{\eta}
-  \sim
-  \operatorname{MultivariateNormal}
-  \left(
-    \operatorname{logit}(\boldsymbol{\alpha}_0),
-    \boldsymbol{\Sigma}
-  \right),
-  \qquad
-  \boldsymbol{\alpha} = \operatorname{logit}^{-1}(\boldsymbol{\eta}).
+  \sim \operatorname{MultivariateNormal} \left( \operatorname{logit}(\boldsymbol{\alpha}_0), \boldsymbol{\Sigma} \right), \qquad \boldsymbol{\alpha}
+                    = \operatorname{logit}^{-1}(\boldsymbol{\eta}).
 $$
 
 The baseline rates $\boldsymbol{\alpha}_0$ set the prior location.
@@ -170,13 +162,8 @@ During model execution, this component creates one vector sample site, `he_ascer
 `RatioLinkedAscertainment` samples a base rate and a ratio of the linked rate to the base rate:
 
 $$
-  \alpha_{\mathrm{linked}}
-  =
-  \alpha_{\mathrm{base}}\rho,
-  \qquad
-  \rho
-  =
-  \frac{\alpha_{\mathrm{linked}}}{\alpha_{\mathrm{base}}}.
+  \alpha_{\mathrm{linked}} = \alpha_{\mathrm{base}}\rho, \qquad \rho
+                           = \frac{\alpha_{\mathrm{linked}}}{\alpha_{\mathrm{base}}}.
 $$
 
 For a hospital and ED model, the IEDR can be the base rate and the ratio can represent IHR / IEDR.
@@ -203,7 +190,7 @@ The priors are assigned to the base rate and the ratio, and together they induce
 
 The ratio may be any positive value.
 Unlike `JointAscertainment`, this component does not automatically constrain the derived linked rate to the unit interval.
-If both rates should be $<1$ (for instance because both are probabilities), make sure to choose priors that make $\alpha_{\mathrm{base}}\rho > 1$ negligibly likely.
+If both rates should be $< 1$ (for instance because both are probabilities), make sure to choose priors that make $\alpha_{\mathrm{base}}\rho > 1$ negligibly likely.
 The component does not clip an invalid linked rate, because clipping would change the specified statistical model.
 
 ## Building a model an ascertainment component

docs/tutorials/day_of_week_effects.qmd

@@ -50,7 +50,7 @@ Ignoring this weekly periodicity forces the noise model to absorb systematic var
 PyRenew models day-of-week effects as a **multiplicative adjustment** applied to predicted counts after the delay convolution and ascertainment scaling:
 
 $$
-  \lambda(t) = d_{w(t)} \cdot \alpha \sum_{s} I(t-s)\,\pi(s)
+  \lambda(t) = d_{w(t)} \cdot \alpha \sum_{s} I(t - s)\,\pi(s)
 $$
 
 where $d_{w(t)}$ is the day-of-week multiplier for the weekday of timepoint $t$, $\alpha$ is the ascertainment rate, and $\pi(s)$ is the delay PMF.
@@ -335,7 +335,7 @@ Day-of-week effects and right-truncation are independent adjustments that compos
 Day-of-week is applied first (adjusting the expected counts for reporting patterns), then right-truncation scales down recent counts for incomplete reporting:
 
 $$
-  \lambda(t) = F(k_t) \cdot d_{w(t)} \cdot \alpha \sum_s I(t-s)\,\pi(s)
+  \lambda(t) = F(k_t) \cdot d_{w(t)} \cdot \alpha \sum_s I(t - s)\,\pi(s)
 $$
 
 ```{python}

docs/tutorials/latent_infections.qmd

@@ -156,17 +156,17 @@ Let $\tau = 0, 1, \ldots, n_{\text{init}} - 1$ index positions in the initializa
 Then:
 
 $$
-  I_{\text{init}}(\tau) = I_0 \cdot e^{r \cdot \tau}, \quad \tau = 0, 1,
-  \ldots, n_{\text{init}} - 1
+  I_{\text{init}}(\tau) = I_0 \cdot e^{r \cdot \tau}, \quad \tau
+                        = 0, 1, \ldots, n_{\text{init}} - 1
 $$
 
-where $r$ is the asymptotic growth rate implied by the reproduction number at the start of the observation period, $\mathcal{R}(t=0) = e^{\text{log\_rt\_time\_0}}$, and the generation interval.
-The function `r_approx_from_R` converts $\mathcal{R}(t=0)$ and the generation interval into $r$ using Newton's method.
+where $r$ is the asymptotic growth rate implied by the reproduction number at the start of the observation period, $\mathcal{R}(t = 0) = e^{\text{log\_rt\_time\_0}}$, and the generation interval.
+The function `r_approx_from_R` converts $\mathcal{R}(t = 0)$ and the generation interval into $r$ using Newton's method.
 
 - **The level is set by `I0`**.</br> `I0` is the infection prevalence at the earliest point in the initialization period, $n_{\text{init}} - 1$ time points before $t = 0$.
   It sets the scale of the entire initialization vector: $I_{\text{init}}(0) = I_0$, with subsequent entries growing or declining exponentially toward $t = 0$.
 
-- **The shape is set by `log_rt_time_0`**.<br> `log_rt_time_0` enters the model in two places: it is the starting point of the $\mathcal{R}(t)$ trajectory ($\mathcal{R}(t=0) = e^{\text{log\_rt\_time\_0}}$), and it determines the exponential growth rate $r$ used to construct the initialization vector.
+- **The shape is set by `log_rt_time_0`**.<br> `log_rt_time_0` enters the model in two places: it is the starting point of the $\mathcal{R}(t)$ trajectory ($\mathcal{R}(t = 0) = e^{\text{log\_rt\_time\_0}}$), and it determines the exponential growth rate $r$ used to construct the initialization vector.
   When `log_rt_time_0 = 0`, $r = 0$ and the initialization vector is flat at level `I0`.
   When `log_rt_time_0 > 0`, infections are growing exponentially at $t = 0$; when `log_rt_time_0 < 0`, they are declining.
 
@@ -232,7 +232,7 @@ init_df = pd.DataFrame(init_data)
 )
 ```
 
-The initialization vector matters because the renewal equation is a convolution: infections on day 0 depend on infections from days $-1$ through $-(K-1)$, weighted by the generation interval.
+The initialization vector matters because the renewal equation is a convolution: infections on day 0 depend on infections from days $-1$ through $-(K - 1)$, weighted by the generation interval.
 A flat initialization (stable) means the renewal equation starts with uniform recent history.
 A growing initialization means the most recent days have disproportionately more infections, which amplifies the effect of the generation interval's short-lag weights.
 
@@ -362,7 +362,7 @@ The variance of $x_t$ grows linearly with time: $\text{Var}(x_t) = \sigma^2 t$.
 The further into the future, the less constrained the process is.
 
 **Hyperparameter:** `innovation_sd` ($\sigma$) is the standard deviation of each daily step on the log scale.
-With `innovation_sd = 0.05`, each day's $\log \mathcal{R}$ changes by roughly $\pm 0.05$, which corresponds to roughly $\pm 5\%$ multiplicative change in $\mathcal{R}$.
+With `innovation_sd = 0.05`, each day's $\log \mathcal{R}$ changes by roughly $\pm0.05$, which corresponds to roughly $\pm5\%$ multiplicative change in $\mathcal{R}$.
 
 ```{python}
 #| label: rw-sample
@@ -408,7 +408,7 @@ If $\mathcal{R}(t)$ drifts above 1, the $\phi$ coefficient pulls it back; if it
 - `innovation_sd` ($\sigma$): standard deviation of daily noise.
 
 The two hyperparameters jointly determine the **stationary standard deviation** $\sigma_{\text{stat}} = \sigma / \sqrt{1 - \phi^2}$, which is the long-run spread of $\log \mathcal{R}(t)$.
-For example, `autoreg = 0.9` and `innovation_sd = 0.05` give $\sigma_{\text{stat}} \approx 0.115$, meaning 95% of long-run $\log \mathcal{R}$ values fall within $\pm 0.23$ of zero, or equivalently $\mathcal{R} \in [0.79, 1.26]$.
+For example, `autoreg = 0.9` and `innovation_sd = 0.05` give $\sigma_{\text{stat}} \approx 0.115$, meaning 95% of long-run $\log \mathcal{R}$ values fall within $\pm0.23$ of zero, or equivalently $\mathcal{R} \in [0.79, 1.26]$.
 
 ```{python}
 #| label: ar1-sample
@@ -441,7 +441,8 @@ DifferencedAR1 models *changes* in $\mathcal{R}(t)$ as an autoregressive process
 In terms of increments,
 
 $$
-  \Delta x_t = \texttt{autoreg} \cdot \Delta x_{t-1} + \varepsilon_t, \quad x_t = x_{t-1} + \Delta x_t,
+  \Delta x_t = \texttt{autoreg} \cdot \Delta x_{t-1} + \varepsilon_t, \quad x_t
+             = x_{t-1} + \Delta x_t,
 $$
 
 so the autoregressive structure applies to the *rate of change* rather than the level.

docs/tutorials/latent_subpopulation_infections.qmd

@@ -146,10 +146,9 @@ Two temporal processes define the evolution of $\log \mathcal{R}_k(t)$:
 Together, these define the full set of reproduction numbers:
 
 $$
-  \log \mathcal{R}_k(t)
-  = \log \mathcal{R}_{\text{baseline}}(t) + \delta_k(t),
-  \qquad
-  \mathcal{R}_k(t) = \exp\big(\log \mathcal{R}_k(t)\big).
+  \log \mathcal{R}_k(t) = \log \mathcal{R}_{\text{baseline}}(t)
+                          + \delta_k(t), \qquad \mathcal{R}_k(t)
+                        = \exp\big(\log \mathcal{R}_k(t)\big).
 $$
 
 ### Population structure

docs/tutorials/observation_processes_counts.qmd

@@ -59,12 +59,12 @@ Observed data can be aggregated or available as subpopulation-level counts, whic
 The deterministic transformation is given by the observation equation:
 
 $$
-  \mu(t) = \alpha \sum_{d=0}^{D} I(t-d)\, \pi_d
+  \mu(t) = \alpha \sum_{d=0}^{D} I(t - d)\, \pi_d
 $$
 
 where:
 
-- $I(t-d)$ is the number of incident (new) infections on day $t-d$
+- $I(t - d)$ is the number of incident (new) infections on day $t - d$
 - $\alpha$ is the **ascertainment rate**, the probability that an infection results in an observed event (e.g., hospitalization)
 - $\pi_d$ is the delay distribution from infection to observation, conditional on an infection leading to an observed event
 
@@ -103,7 +103,7 @@ In this tutorial, we simulate the observation process by specifying infections d
 
 For hospital admissions data, we construct a `PopulationCounts` observation process.
 
-The delay is the key mechanism: infections from $d$ days ago ($I(t-d)$) contribute to today's predicted hospital admissions ($\mu(t)$), weighted by the probability $\pi_d$ that an infection leads to hospitalization after exactly $d$ days.
+The delay is the key mechanism: infections from $d$ days ago ($I(t - d)$) contribute to today's predicted hospital admissions ($\mu(t)$), weighted by the probability $\pi_d$ that an infection leads to hospitalization after exactly $d$ days.
 The convolution sums these contributions across all past days.
 
 Observed hospital admissions are then generated by sampling from a negative binomial distribution:
@@ -223,8 +223,8 @@ hosp_process = PopulationCounts(
 The observation process convolves infections with a delay distribution, maintaining alignment between input and output: day $t$ in the output corresponds to day $t$ in the input.
 
 Hospital admissions depend on infections from prior days.
-A delay PMF of length $L$ covers delays 0 to $L-1$, requiring $L-1$ days of prior infection history.
-The method `lookback_days()` returns $L-1$; the first valid observation day is at index `lookback_days()`.
+A delay PMF of length $L$ covers delays 0 to $L - 1$, requiring $L - 1$ days of prior infection history.
+The method `lookback_days()` returns $L - 1$; the first valid observation day is at index `lookback_days()`.
 Earlier days are marked invalid.
 
 ```{python}

docs/tutorials/observation_processes_measurements.qmd

@@ -198,12 +198,12 @@ The concentration is determined by:
 The predicted concentration at time $t$ is given by
 
 $$
-  \mu(t) = \frac{G}{V} \sum_{d=0}^{D} I(t-d)\, \pi_d,
+  \mu(t) = \frac{G}{V} \sum_{d=0}^{D} I(t - d)\, \pi_d,
 $$
 
 where:
 
-- $I(t-d)$ is the number of infections on day $t-d$
+- $I(t - d)$ is the number of infections on day $t - d$
 - $\pi_d$ is the shedding kinetics PMF, giving the fraction of total shedding occurring $d$ days after infection, analogous to the delay distribution in count observation models
 - $G$ is the number of genome copies shed per infection
 - $V$ is the wastewater volume per person per day
@@ -213,7 +213,8 @@ This has the same convolution structure as the observation equation for count da
 We model the observed **log-concentration** as
 
 $$
-  Y(t) \sim \text{Normal}\big(\log(\mu(t)) + \text{sensor\_mode}, \ \text{sensor\_sd}\big),
+  Y(t)
+  \sim \text{Normal}\big(\log(\mu(t)) + \text{sensor\_mode}, \ \text{sensor\_sd}\big),
 $$
 
 where:
@@ -437,8 +438,8 @@ print(f"Required lookback: {ww_process.lookback_days()} days")
 ### Timeline alignment
 
 The observation process maintains alignment: day $t$ in output corresponds to day $t$ in input.
-A temporal PMF of length $L$ covers lags 0 to $L-1$, requiring $L-1$ days of prior history.
-The method `lookback_days()` returns $L-1$; the first valid observation day is at index `lookback_days()`.
+A temporal PMF of length $L$ covers lags 0 to $L - 1$, requiring $L - 1$ days of prior history.
+The method `lookback_days()` returns $L - 1$; the first valid observation day is at index `lookback_days()`.
 
 ```{python}
 #| label: helper-function

docs/tutorials/right_truncation.qmd

@@ -47,7 +47,7 @@ Ignoring this produces a spurious decline in recent counts.
 PyRenew's observation equation defines the expected observation count as:
 
 $$
-  \mu(t) = \alpha \sum_{s} I(t-s) \, \pi(s)
+  \mu(t) = \alpha \sum_{s} I(t - s) \, \pi(s)
 $$
 
 where $\alpha$ is the ascertainment rate and $\pi(s)$ is the infection-to-observation delay distribution.
@@ -65,7 +65,8 @@ Concretely, let $T$ denote the last observation day and let $\text{offset} = \te
 Then:
 
 $$
-  k_t = (T - t) + \text{offset} = (T - t) + (\text{data pull date} - T) = \text{data pull date} - t
+  k_t = (T - t) + \text{offset} = (T - t) + (\text{data pull date} - T)
+      = \text{data pull date} - t
 $$
 
 Because $k_t$ depends only on the data pull date and the timepoint $t$, its behavior is straightforward: timepoints far in the past (small $t$) have large $k_t$, so $F(k_t) \approx 1$ and counts are fully reported.