Word Choice / English Usage: the collection of my selected mistakes

I first wrote. My supervisor then corrected it.
Well, I have missed some of the earlier collection, but these could help me improve in my future writing.
[Note: this is more like my personal memo. Sorry for personal examples.]

* where v.s. that
** Unlike Roll-out simulation '''where''' events are simulated in series, HO uses a special simulation.
* use of ,
* in the context of v.s. under
** The inventory aspect of SCM has been studied '''in the context of''' a multiple-stocking-point problem.
* with v.s. at
** The remaining inventory may be sold as scrap '''at''' a much lower price.
* for v.s. on
** Although information sharing can help reduce supply chain cost, Zhao and Xie showed that it may increase costs '''for''' retailers.
** Demand '''for''' agrochemical products can also tolerate some degree of price change without effect.
* highest v.s. greatest
** its value will be '''greatest'''.
* decrease v.s. decay
** I wrote "... then the value of an eligibility trace will decay backward by each time step."
** My prof corrected it to "... then the value of an eligibility trace will decrease by each earlier time step."
* to v.s. in
** Weights are linear '''in''' the output.
* from v.s. of
** a consequence '''of''' taking action
* of v.s. for
** The prediction difference, called the temporal difference, is the difference between an approximate state cost with recently obtained information and an approximate state cost '''for''' the same state, but without that information.
* whice v.s.
** The first two terms of Equation ref{eq: temporal difference}, or $r_{t+1} + alpha cdot hat{J}_t(s_{t+1})$, represent an approximate state cost with newly obtained information, which are a single-period cost $r_{t+1}$ and a next state $s_{t+1}$.
* to v.s. of
** Due to the ease of integration '''of''' TD, citet{SuttonBarto1998a} recommended using a function belonging to a linear family
* Use of first
** [First Roll-out simulates to obtain an immediate cost.]
** Roll-out '''first''' simulates to obtain an immediate cost.
* which v.s. that
** [HO uses a special simulation, which does not require a base policy.]
** HO uses a special simulation '''that''' does not require a base policy.
** [The GARCH(1,1) model introduces two latent state variables, which inadvertently will be left out if GARCH(1,1) is not accounted for.]
** The GARCH(1,1) model introduces two latent state variables that inadvertently will be left out if GARCH(1,1) is not accounted for.
* which, v.s. which
** [The Residual Gradient method is based on the temporal difference learning technique''', which''' uses information obtained at different times to update the state value approximation.]
** The Residual Gradient method is based on the temporal difference learning technique''' which''' uses information obtained at different times to update the state value approximation.
* indicate v.s. produce
** [Learning rates of 0.1 and 1 indicate lower aggregate costs than learning rates of 0.01 and 10.]
** Learning rates of 0.1 and 1 '''produce''' lower aggregate costs than learning rates of 0.01 and 10.
* beyond the scope of this study v.s. not attempted in this study
** ... an investigation of longer leadtime inventory problems or other pure delayed-reward problems, such as Backgammon, is '''not attempted in this study.'''
* as v.s. to
** [The Rollout method using 100 simulations shows similar results as the four-period and five-period Look-ahead methods.]
** The Rollout method using 100 simulations shows similar results '''to''' the four-period and five-period Look-ahead methods.
* explaining direct then indirect consequences
** The problem investigated in this study includes the setup cost, making the cost function highly non-linear, which in turn, makes an analytical solution difficult to achieve.
* Different meaning: choose action more conservatively v.s. choose more conservative actions
** This supports the explanation that using higher $T$ make Rollout choose action more conservatively.
** This supports the explanation that using higher $T$ make Rollout choose more conservative actions.
* instead of v.s. in place of
** [When it is suspected that the normality assumption does not hold, a Wilcoxson rank sum test is used instead of the t test.]
** When it is suspected that the normality assumption does not hold, a Wilcoxson rank sum test is used '''in place of''' the t test.
* on v.s. to
** [The problem in this Chapter is selected to investigate the effect of the GARCH(1,1) model to the perfermance of the ADP.]
** The problem in this Chapter is selected to investigate the effect of the GARCH(1,1) model '''on''' the perfermance of the ADP.

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